Categories

## Introduction

We have just far spent £337bn on the COVID response in the UK. This is reported by the FT at: https://www.ft.com/content/f0c7ab6d-33ba-4777-8dd8-0960a78a556a The virus itself generated much of this spend, but much of it was generated merely by the lockdown.  The results of the Imperial model were a primary motivation for lockdown. That model was a Monte Carlo Simulation.  I explain here briefly what a Monte Carlo simulation is and bring out one objection (among many) to the Imperial approach.

## What is Monte Carlo Simulation?

Monte Carlo simulations exist to address a class of problems which do not have an analytical answer.  Imagine I am in the pub and my home is 40 paces away.  If I walk at two paces a second, I will arrive home in 20s.  That’s an analytical question which has an exact answer.  Here is a non-analytical question.  I have drunk a bottle of tequila in the pub.  The probability that I take a pace forward is only 50%; there is an equal probability that I take a pace backward.  This does not appear to be analytical.  You can’t say immediately what the probability is that I get home.

This is where Monte Carlo Simulation comes in.  What you can do is simulate my journey home from the pub and see if I get home.  (It’s called Monte Carlo because the method is based on random numbers, as we will see next.)

## Sample Python Code

Here’s a really simple Python script called Randwalk that simulates the walk home.  It’s called that because this is a random walk simulation.  This sort of thing might be familiar to you from Brownian motion.

You can see that all it does is roll a dice 100 times and check to see if the dice shows three or less.   That’s the 50/50 part.  If the dice does show three or less, I take a step back.  If the dice shows more than three, I take a step forward.  This is repeated 1000 times, meaning I take 1000 steps in this version.

This entire code consists of a conditional statement in a loop.  It’s extremely simple.

## Output from Simple Python

We can then plot the output and we will see something like the below.

As you can see, a jagged pattern is generated.  On this occasion, plenty of my steps were unfortunately in the wrong direction, and I never got home.  But that won’t happen every time.  I was luckier in the run below, or maybe I drank less tequila.

As you can see, here I was more than 40 paces north in this simulation.  So I got home.  (I haven’t bothered to clean up the code to stop running when I “arrive home” in order to keep it simple, but that could easily be done.)

## Using Monte Carlo on the Random Walk Problem

So now we see how we can use Monte Carlo Simulation to answer the original question.  What we need to do is run scenarios like the above a large number of times and see how often I get home.

Here is some only slightly more complicated Python called SimpMC which does that.

This just puts the whole of the previous code in another loop.  So we do the simulation multiple times — that variable is itot = 10 in the code above.  We then calculate the fraction of scenarios in which I get home.

## Monte Carlo Results

This generates an answer of 0.2. But it is different every time I run it.  Sometimes I get 0.3 and sometimes 0.4.  That is happening because I have inadequate statistics.  So let’s set the run number to 100.

Now I get: 0.14, 0.17, 0.21, 0.19, 0.15.  Better but still not stable.  Let’s set the run number to 1000.

Now I get: 0.195, 0.191, 0.208, 0.192, 0.205.  That’s starting to get there.  I am clearly converging on a probability estimate here.  If I ran overnight, I would get a good answer.

## Why is this an Objection to the Imperial Model

Finally to the objection to the Imperial model.  Their code was unstable on multiple cores.  Their response to this was “it’s a stochastic model so it will give different answers each time.”  That response does not fly, as I will now explain.

Saying it is a stochastic model just means it uses this random number Monte Carlo approach.  However — that does not mean it should produce different outcomes when run on multiple cores.  It should not be unstable at all.  The reported instability in the Imperial model is 80,000 deaths. This means that merely the error bar in the Imperial result is larger than the current total number of COVID deaths! — and that should not happen.  To claim otherwise is to mix up the randomnesses.  (I just made that word up but that seems fine.)

For sure, we saw randomness in the randwalk code — but that was just one run.  When we did lots of runs in the SimpMC code, we started t0 converge.  We got the same result every time in other words when we did enough runs.  The Imperial model produces different results each time you run a large number of scenarios through it with the same parameters.  That is equivalent to me getting different answers on the 1000 run version of SimpMC.  If that happens, it doesn’t mean I wrote a stochastic model.  It means I wrote a buggy model.  Imperial have potentially cost us a lot of money here.

Categories

## Conclusions

The performance of the ZEUS FLT has been investigated for a range of physics of interest, with special regard to the use of data from the tracking detectors. The motivation throughout this work has been to investigate the means by which signal events may be efficiently be selected by the trigger while at the same time holding leakage of beam-gas events through the trigger to a minimum. It has been shown that the RBOX will be able to successfully combine data from the FTD and the CTD in such a way as to further this aim despite the differing geometries of these two detectors.

The most important area of physics at HERA is the study of the proton structure function via the analysis of DIS NC and CC processes. An efficient trigger performance for these events is therefore essential. For this reason, the performance of the RBOX has been optimized with respect to them. The performance of the CTD alone for these events has been shown to be good which meant that it was difficult to further improve the situation. Nevertheless, it has been shown that the RBOX will be able to reduce the loss of CC events by a factor of two within the same beam-gas leakage constraints as placed on the CTD. This should greatly enhance the quality of measurements made.

While the performance of the RBOX has been shown to be good for DIS events, it is important not to lose sight of other areas of physics interest. With this in mind, other processes have been simulated with a view to examining performance in more broad terms. In particular, an investigation of heavy flavor pairs both with and without the influence of initial state gluon bremsstrahlung has been made. This has shown that transverse energy and charged multiplicity are the deciding factors which control the efficiency with which a type of event will be accepted. Also it has been shown that the effects of gluon bremmstrahlung may lead to significant changes in event characteristics for charmed pair events. Most importantly, it is now known that the RBOX will provide a good efficiency for heavy flavor events without the necessity to re-optimize the trigger parameters as designed for DIS.

Further, the efficiency of the RBOX for J/ψ events has been shown to be good. As was mentioned in the introductory chapter, these events will have a scattered electron at a very low angle. These two facts raise the prospect of using the electron calorimeter of the luminosity monitor to make precise measurements of the scattered electron which in turn will permit ZEUS to probe the gluon distribution in a kinematic domain which is completely inaccessible to other machines.

Accurate knowledge of a trigger efficiency is as important as boosting that efficiency. It has been shown here that the full kinematics of a CC event need not be considered when measuring the kinematic dependence of CTDFLT efficiency. This has allowed a picture to be constructed of the likely variation of efficiency which is comprehensive in terms of range. Also, much greater precision has been obtained than would be possible within available computer resources using another method.

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Categories

## Investigation of J/Psi Event Acceptance in the FLT

Chapter 9

9.1 Introduction

Events containing a J/ψ can be used at HERA to probe the low-x gluon distribution of the proton[87]. In order to do this, it is necessary to know the efficiency of the FLT for these events. In this chapter, trigger efficiencies are measured for the CTDFLT, the FTDFLT and the standard parametrization of the GFLT which was described in section 8.3.

Further, a comparison was made of measured parameters for the J/ψ sample and a beam-gas sample. This enabled a first approximation to a dedicated sub-trigger to be suggested.

J/ψ event tagging methods previously suggested[88] have utilized the luminosity monitor. Here, the response of the entire detector is simulated in an effort to identify differences between signal and background.

9.2 Event Generation

The ASCII interface for the HERWIG generator described in section 8.1 was used again here in conjunction with program versions 5.2/5.3. 26,000 J/ψ events were generated.

HERWIG allows a choice of five structure functions. These were all investigated and found to produce no discernible differences in the properties of events seen in the detector. For the sake of consistency, option five was used throughout[89].

9.3 Results

Investigation then centered on the task of separating the J/ψ events from the beam-gas background. The beam-gas sample produced to allow background studies was generated using the UA5 generator. Forty thousand events were produced with a homogeneous distribution along the beam-line from z = -19 m to z = +1 m.

9.3.1 Trigger Efficiencies

Table 9.1 shows the proportions of events accepted by the full simulations of the CTDFLT, the FTDFLT and by the parametrization of the GFLT. The results for the RBOX are also shown. [At the time of this work the design of the RBOX was complete. It was felt that using the most modern version of the simulation was important. This was no longer compatible with the RBOX code so only a small event sample was passed through the RBOX code. This is why the statistical errors are larger in this case.]

Table 9.1: Event classifications from ZGANA.

The event classes have the meaning used previously in section 5.2.3 so the CTD class two and three must be summed to provide a total acceptance. This means that the CTDFLT accepts 93.1% with beam-gas leakage of 7.6%. For a leakage rate of 1 kHz m-1 this gives a background of 1528 Hz from the 20 meter source length.

The beam-gas leakage in the FTDFLT corresponds to a rate of 2100 Hz. At the time of the simulation from which results are described here, no FTD class zero was defined in ZGANA: events without diamonds were rejected. In the final system, these events will be described as unclassified. The beam-gas leakage in the parametrizations of the GFLT corresponds to a leakage rate of 1138 Hz.

9.3.2 Comparison of Signal and Background

The statistics on the plots relate to the beam-gas sample. Where relevant, the mean of the J/ψ distribution is given on the plot. The figures that are shown relating to calorimeter data (figure 9.1 to figure 9.3) show sizable differences between signal and background and therefore are useful in a dedicated sub-trigger.

Figure 9.1: Sum of visible transverse energy in the electromagnetic calorimeter.

Figure 9.2: Sum of total transverse momentum (x-direction only).

Figure 9.3: Sum of total transverse visible energy.

In particular, figure 9.3 explains why the parametrization of the GFLTB rejects some events: there are many signal events with low transverse energy deposition. These will fail the CALFLT cuts.

Figure 9.4 shows that approximately 25% of the beam-gas sample has hits in the veto-wall. Very few signal events register in the veto-wall: in a sample of 500 CC events, no hits were observed.

Figure 9.4: Veto-wall hits.

The C5 collimator is located three meters upstream (for the protons) of the interaction region and is designed to reduce the halo of off-beam particles in the beam. It is possible for good events to produce C5 hits by virtue of having tracks in the backward direction but in general, hits in the collimator are strongly indicative of a background event. It would clearly be advisable for the trigger to take advantage of this to veto events with C5 hits. Figure 9.5 shows that only a negligible fraction of signal events have C5 collimator hits whereas figure 9.6 shows that substantial discrimination against background is a prospect.

Figure 9.5: Number of hits in C5 collimator for J/ψ events.

Figure 9.6: Number of hits in C5 collimator for beam-gas events.

9.4 Discussion

Table 9.1 shows that excellent acceptance is obtained by the tracking trigger. In addition, as previously described in section 5.1, the RBOX will combine data from the FTD and the CTD and so these figures may be expected to improve. However, the table also shows that further optimization is advisable in the GFLT: some ways to produce a dedicated sub-trigger were seen to be plausible from considering the figures, many of which show substantial discrimination between signal and background. To investigate the utility of this as a first approximation to a dedicated sub-trigger was devised. It is important to emphasize that no optimization has been done on the trigger parameters: the cut values could be tuned and other sub-detectors included.

Table 9.1: Event classifications from ZGANA.

The sub-trigger was developed from a simple philosophy. Calorimeter triggers were set so that they were ‘free’: i.e. plots of measured values were studied to find cut values that would produce no beam-gas leakage but still provide some benefit in terms of J/ψ acceptance. Then if there were clear grounds to reject the event this course was taken. Finally the tracking detector triggers were applied to those events still unclassified.

The full details of this trigger are shown in figure 9.7 and the results obtained in table 9.2. It can be seen that the efficiency is comparable to that of the CTDFLT but with improved beam-gas leakage figures. The leakage rate implied here is 954 Hz. It should be noted that it is not trivial to improve on the CTDFLT because its performance is already good.

Figure 9.7: Sub-trigger decision flowchart.

Table 9.2: Event classifications for the dedicated sub-trigger.

Previous work[90] on J/ψ events in the FLT achieved an efficiency of 66% with beam-gas rates below the acceptable limit. That particular trigger is a complex entity utilizing many sub-detector components; moreover, it has been optimized. Operating here would permit cross checking of efficiencies and result in complementary data-sets for J/ψ physics.

A characteristic of J/ψ events is the presence of leptons with high transverse momentum in the opposite direction to the quark jet, as described in section 1.2.3.2. It should in general be possible to find these tracks in the CTD or the RTD and a more complex trigger, perhaps at higher levels, could search for these by correlating with the CAL or muon detectors.

9.5 Conclusions

The tracking detector FLT will provide excellent efficiency for J/ψ events since good performance has been obtained with the CTD and RBOX. Reasonable performance may be expected from the GFLT. An optimized sub-trigger along the lines suggested here would provide very good efficiency for J/ψ events.

Categories

## Heavy-Flavour Events in the Regional First Level Trigger

Chapter 8

8.1 Introduction

Prior to machine turn-on, uncertainties about the details of many types of events exist. The trigger must be able to achieve high acceptances combined with good beam-gas rejection independent of the details of the final event shape. To this end, it is useful to use different generators to examine the effects of theoretical uncertainties on the trigger efficiency. An important question also concerns the effect that gluon bremsstrahlung will have on measurements in the detector.

Although DIS events are a major aspect of HERA physics, it is necessary to ensure that other important reactions are not removed at the FLT: such a reaction is the generation of bbbar and ccbar pairs by boson-gluon fusion (BGF) at low Q2 and low x (see section 1.2.3.1).

The standard ZEUS Monte Carlo for boson-gluon fusion is HFLGEN 1.3 based on the AROMA generator,[82]. Parton showers, string fragmentation and decays are carried out by JETSET[83]. A second generator HARHEA, working within the framework of the HERWIG 5.0 Monte Carlo, also produces BGF events[84–86]. HARHEA differs from HFLGEN in using a cluster hadronization model and including gluon radiation from the initial state quarks.

A HERWIG ASCII interface was written for ZEUSGeant such that the data could be read by ZGANA. This enabled direct comparison of measured parameters in the CTDFLT and the FTDFLT.

8.2 Simulation

One thousand NC ccbar and bbbar events were generated from each of the two heavy flavor generators. Also four thousand beam-gas events distributed homogeneously along the beam-line from z = -19m to z = +1m were produced using the FRITIOF generator (version 1.5).

An initial comparison of the two generators was achieved by using a parametrization of the CTD and calorimeter FLTs. This aims to provide a simple understanding of the likely response of the whole FLT to a set of events. Its philosophy is based on energy deposition and charged tracks. If tracks are found from the vertex, then only loose energy constraints are applied. On the other hand, if no tracks are found then substantial energy deposition (at high angles) is required.

In fact, if no track pointing to the vertex was found in the CTD, an event was accepted if the calorimeter registered more than 5 GeV/c in transverse momentum; if a vertex track was detected, an event was accepted if the transverse momentum was greater than 12 GeV/c. Section 4.3.1.1 explains how these quantities are measured by the CALFLT. Finally, the events were passed through the standalone CTDFLT and FTDFLT simulations and the RBOX simulation to examine the combined tracking response.

8.3 Results

Table 8.1 shows the percentage of events passing the parametrization of the FLT for the four types of events. There is a small difference in the two BGF generators for ccbar events but a major difference is seen for bbbar events. In both cases, it is much easier to trigger on the bottom pair events.

Table 8.1: Percentage of events accepted by the simple parametrization of the tracking and calorimeter first level trigger.

Table 8.2 shows the percentage of ccbar events falling into each of the tracking trigger classes and table 8.3 shows the same figures for bbbar events. These figures may be compared with those for beam-gas leakage, shown in table 6.7. As before, for the CTD standalone mode class 3 events will probably be accepted along with class 2 events so these figures must be summed to produce a final figure.

Table 8.2: FLT classifications for the full FLT simulations for ccbar events.

Table 8.3: FLT classifications for the full FLT simulations for bbbar events.

8.4 Discussion

The parametrization of the GFLT is dependent on track multiplicity and transverse energy deposition. The results obtained for GFLT efficiency are thus entirely explained by figure 8.2 and figure 8.3 which show that high acceptance is related to both high mean track multiplicity and high mean transverse energy. This may be clearly illustrated by plotting the means of the figures against the efficiencies.

This is done in figure 8.1. For comparison, figure 8.4 and figure 8.5 show the distribution of transverse energy and charged multiplicity for beam-gas events.

Figure 8.1: Effect of multiplicity and transverse energy on acceptance.

Figure 8.2: Multiplicity of charged tracks per event with a pt > 0.5 GeV/c for heavy flavor events.

Figure 8.3: Total transverse energy (GeV) per event as measured by the calorimeter for heavy flavor events.

Figure 8.4: Total transverse energy (GeV) per event as measured by the calorimeter for beam-gas events.

Figure 8.5: Multiplicity of charged tracks per event with a pt > 0.5 GeV/c for beam-gas events.

In the tracking detectors, a vertex decision is made in the triggers using essentially tracks with a transverse momentum > 0.5GeV/c. The tracking chamber triggers use the ratio of tracks from the vertex to all tracks. This ratio is therefore affected by changes in track multiplicity and transverse momentum.

The distributions in polar angle explain the event classes found. Figure 8.6 shows the polar angle of Geant tracks (tracks with energy of less than 1 GeV were omitted).

Figure 8.6: Polar angle of Geant tracks for both types of heavy flavor events in full and FTD-only angular ranges. The solid lines are HFLGEN events and the dashed lines are HERWIG events.

It can be seen that across the broad angular range, both generators are in good agreement with both giving higher multiplicities for bbbar events than for ccbar events. This explains the CTDFLT classes found, which showed both generators giving similar acceptances which were higher in the case of bbbar events. But in the FTDFLT, it can be seen that there is a significant deterioration in efficiency in HERWIG ccbar events which is not seen in bbbar events. In order to examine this more closely, figure 8.6 also shows the same plots magnified to show only the angular region covered by the FTD, 0.195 rad to 0.495 rad. It can clearly be seen that the event classes found are reflective of the observed multiplicities.

8.5 Conclusions

It has been shown that the effects of gluon bremsstrahlung may be neglected for bbbar events but become more significant in the case of ccbar. The combined FTD and CTD FLT acceptance is excellent for both bbbar and ccbar events with either generator. Higher multiplicities and higher transverse energy for bbbar events mean that they are more likely to pass the tracking trigger. The performance of the tracking triggers would not need to be optimized further in a dedicated sub-trigger. The simple parametrization of the combined calorimeter and tracking trigger indicates that a simple transverse energy cut by the calorimeter reduces bbbar acceptance by at least 10% but eliminates almost 60% of all ccbar events accepted by the tracking trigger alone. A dedicated sub-trigger would need to relax the transverse energy cut and restore beam-gas efficiency to reasonable levels by using information from other components such as collimators, the veto-wall and also timing data.

Categories

## Kinematic Dependence of ZEUS CTDFLT Efficiency

Chapter 7

7.1 Introduction

The motivation behind the work described in this chapter was the desire to know to high precision the CTDFLT efficiency across the whole of the accessible phase space. This is important for measurement of cross-sections as mentioned in the previous chapter. The naıve approach of simply generating large numbers of events in kinematic bins is not a suitable one since the constraints of available computer resources mean that the requisite precision cannot be obtained over all phase-space. For this reason, a method of simplifying the problem was searched for. For CC events, it is inherently plausible that the efficiency of the CTDFLT depends only on the polar angle of the current jet theta-jet. This hypothesis was shown to be consistent with the data by generating a large sample of events in small regions of phase space with fixed theta- jet.

The results for each angle were combined to produce high-precision efficiency data. These were then used to plot a map in x – Q2 space by assuming the same efficiency for all points in the phase space with the same jet angle. The method was also investigated with respect to NC events. As would be expected however, it was found to be unsatisfactory due to the scattered electron which plays an important part in triggering these events.

7.1.1 Special Jacquet-Blondel Kinematics

It is possible to manipulate the usual kinematic equations (see equation 1.26 in section 1.2.2.3) so that the theta-jet dependency becomes more explicit; in particular using half angle formulae and setting E_e = 30GeV gives equation 7.1:

So for a fixed jet angle, various different combinations of values of x and Q^2 are available for a given y. Contours of fixed y are shown in the x=theta-jet plane in figure 7.1 and for the Q^2 – theta-jet plane in figure 7.2.

Figure 7.1: Contours of fixed y in the x – theta-jet plane.

Figure 7.2: Contours of fixed y in the Q^2 – theta-jet plane.

We may define a SL polar angle such that a track from the nominal interaction point at this angle will leave the sensitive volume of the CTD at a position on the end-plate midway between where the two central wires are attached. The minimum angles for the instrumental SLs are 11. degrees, 18.9 degrees, 25.4 degrees for SL1, SL3 and SL5 respectively.

It is obvious that there will be no information from the CTDFLT concerning tracks with angles smaller than 11.6 degrees (or greater than 168.4 degrees). In fact, there will be some spread of tracks around the nominal jet angle so that some proportion of events have no tracks within the sensitive volume of the CTD. Clearly one expects this proportion to increase as the nominal jet angle is changed such that the tracks are expected to be closer to the beam-pipe.

7.2 Event Generation

A low-statistics pass across the whole of the angular range was made. Fifty events were generated in angular bins of two degrees. The information needed to produce bins in x and Q^2 corresponding to the required angular range is shown graphically in figure 7.1 and figure 7.2.

The events were generated with 10 degrees < theta-jet < 90 degrees. It was not necessary to generate any events with jet angles of larger than 90 degrees because symmetry means that eta(theta – 90 degrees) = eta(theta). Below 10 degrees there is not expected to be any activity in the detector. A similar sample was generated for NC events.

A selected set of five angles were chosen for high statistics runs. These angles were 13 degrees, 23degrees, 33degrees, 43degrees and 63 degrees. These were chosen with reference to the super-layer polar angles mentioned above. They correspond to the cases in which one expects the jet to pass through the one or two instrumental SLs for the two lowest angles and all three instrumented SLs for the remaining three angles.

Angular bins with a a range of one degree either side of the nominal value were defined for the low-statistics run. To measure the variation with respect to y from 0.1 to 0.9 were defined. Approximately one thousand events were generated in each bin so that in total 36250 events were used in this study. The CTDFLT simulation was run to find the efficiency.

7.3 Results

The results for theta-jet = 63 degrees are shown in table 7.1, for theta-jet = 43 degrees in table 7.2, for theta-jet = 33 degrees in table 7.3, for theta-jet = 23 degrees in table 7.4 and for theta-jet = 13 degrees in table 7.5.

Table 7.1: CTDFLT efficiencies in the kinematic bins for theta-jet = 63 degrees +/- 1 degree.

Table 7.2: CTDFLT efficiencies in the kinematic bins for theta-jet = 43 degrees +/- 1 degree.

Table 7.3: CTDFLT efficiencies in the kinematic bins for theta-jet = 33 degrees +/- 1 degree.

Table 7.4: CTDFLT efficiencies in the kinematic bins for theta-jet = 23 degrees +/- 1 degree

Table 7.5: CTDFLT efficiencies in the kinematic bins for theta-jet = 13 degrees +/- 1 degree

7.4 Discussion

Figure 7.3 shows that the results are consistent with the hypothesis that there is a smooth dependence of efficiency on jet angle. From the numbers in the tables it can be seen that efficiency is constant for a given angle independent of all other kinematic variables. Also the expected deterioration in efficiency is seen as the jet angle becomes closer to the beam-line.

Figure 7.3: Low statistics full angle pass for CC events.

For NC events however, figure 7.4 shows that the pattern does not show the same simple dependency on jet angle only. This is due to the presence of the scattered electron. It is unsafe therefore to attempt to proceed further with the method for this type of event.

Figure 7.4: Low statistics full angle pass for NC events.

Returning to the CC sample, it is now plausible to combine the various tables of results at the same jet angles to produce high-precision results. Since the results represent statistically independent measurements of the same quantity, they may be combined by taking the mean and dividing the error by root n where n is the number of entries in the relevant table. This yields the figures in table 7.6.

Table 7.6: Final combined figures for CTDFLT efficiency.

These figures may be used to generate contours of constant trigger efficiency in the x – Q^2 plane, remembering that symmetry allows the same efficiencies to be plotted for 180 degrees – theta also. This is shown in figure 7.5.

Figure 7.5: Efficiency for CC events.

7.5 Conclusions

It has been shown that CTDFLT CC efficiency is dependent on theta-jet only. Precise knowledge of the expected efficiency may now be obtained over a large part of the accessible phase space by deducing the jet angle from the kinematics of a given event if that event lies on or near one of the angles studied with high statistics. Otherwise, an interpolation may be made.

Categories

## ZEUS Regional First Level Trigger Box

Chapter 6

6.1 Introduction

In this chapter the operation of the RBOX is described. Its development has proceeded by using a simulation of the entire detector. First an overview of the purpose of the RBOX is given in this section. After describing the simulation the principles of the algorithm under which it will function are considered. Results are presented supporting the conclusion that combining tracking detector information leads to definite benefits. An outline of the hardware design is given.

6.1.1 Requirements

The RBOX must provide track angular information suitable for matching to the calorimeters. If a track points in a certain direction, it will be desirable to extrapolate to the relevant calorimeter component and look for energy deposition. Also it is necessary to produce an event classification for the GFLTB. This classification must describe whether the integrated tracking FLT has accepted an event. This indicates the confidence with which the detectors have identified the event as containing a high proportion of tracks coming from the interaction region.

6.1.2 Information Available to the RBOX

The RBOX receives information from hardware in the CTD and the FTD, as described in section 5.2. In both cases the hardware is divided into units relating to the subdivision in φ of the two detectors. In the CTD, there are thirty-two sector processors: the CTD is divided in φ into 11.25 degree sectors. In the FTD the sextant processors each handle a 60° section.

The RBOX will receive the multiplicities of matched and unmatched super-diamonds from the sextant processors. This means a measure of the amount of activity in the detector is possible. Further, the sextant processors will output the coordinates of matched super-diamonds to the RBOX in a from suitable for matching with the CTD.

In order to do this, it was necessary to know the coordinate ranges of super-diamonds which might be matched with a given segment. These ranges are termed coincidence domains. Once the domains have been defined, each matched super-diamond could be assigned to a ‘pseudobin’ and a ‘pseudosector’. These are simply the sector or z/r bin in which it would be expected to find CTD segments given various diamond positions. This is illustrated in figure 6.1.

Figure 6.1: Mapping of the FTD onto CTD to define coincidence domains.

In the simulation for which results are presented later in this chapter the coincidence domains were deduced empirically. Large numbers of single straight tracks from the origin were simulated. It was arranged that these tracks would have polar angles such that all possible co-ordinates for matched sets of super-diamonds and segments could be found. This produced very simple results in the trigger simulation: pairs of matched super-diamonds and three matched segments were nearly always found. The coordinates of the super-diamonds, together with the corresponding coordinates of the matched segments, were noted. The RBOX will use the domains defined to perform matching between the FTD and the CTD.

6.1.3 Processing

The RBOX will use the sub-triggers which had been developed for the individual detectors as previously described. However each does not now represent a final decision but rather makes up a part of the information used by the RBOX to form a decision. The FTDFLT version used in the simulation which will be described in this chapter is identical to that which had been used standalone. However the version of the CTDFLT used in the RBOX simulation was modified in the light of the new situation of combining data with the FTD. This RBOX ‘quasi-CTD’ ratio is similar to the standalone CTDFLT in that it considers a ratio formed from matched segments over total segments. However the RBOX uses only SL5 segments whereas the standalone CTDFLT uses more SLs as described diagrammatically in figure 5.1. It remains useful however to compare these RBOX results with the code that was developed for the CTD alone as described in the previous chapter. This is what is meant in this chapter when when results described as CTD standalone are given for comparison.

The main extension possible in the RBOX is to produce a combined trigger which uses both sub-triggers as appropriate and also forms completely new ratios using information from both detectors. In this way maximal coverage in θ can be achieved together with performance improvements.

6.2 Simulation

The simulation was carried out using the ZEUS trigger version[67] of the Geant program, in conjunction with the ZEUS trigger analysis program ZGANA[68]. Both programs have been undergoing continuing evolution so a continued effort has been necessary to keep work up to date as new versions are released.

6.2.1 Geant and ZEUSGeant

Geant[69] [70] is a program written at CERN which is designed to be a universal physics simulation which may be applied by collaborations of particle physicists to the particular geometry peculiar to their detector. Since its inception in 1974 it has greatly extended its functionality and is in wide use on many different types of machine. Like a great many scientific programs today in existence, it is written in the FORTRAN language. It is fully integrated with graphics packages also from CERN[71] [72]. The combined package has found wide application in the HEP community and all the work presented in this thesis utilizes it.

The code is distributed via PATCHY[73] machine-independent format. This is designed to allow any of a set of common computers/operating systems (e.g. DEC VAX/VMS, IBM, SUN workstations) to generate FORTRAN code suitable for running on that machine. Large files are initially issued which are then operated on by smaller ‘correction sets’ as bug reports are filed and additions to the code are made which are not so substantial as to warrant a new version. This mechanism also allows the substitution and addition of special user programs for the purpose of code development.

The Program relies on the concept of ‘volumes’ which are defined in terms of their size, shape and composition. The facility exists to create detector elements using a set of standard three-dimensional templates. Clearly, structures of arbitrary complexity may be constructed by use of many such volumes. Sixteen standard materials are defined in terms of their densities, radiation lengths and nuclear absorption lengths.

Other materials may be added to the standard list. In this way, a very precise simulation of how any detector will interact with a particle can be produced.

Geant makes use of the ZEBRA[74] management system which aims to utilize computer memory efficiently by allowing definition of data structures at run-time. This is advantageous because FORTRAN does not allow variable length arrays.

This package is also useful in terms of reducing disk space requirements. This is crucial because very large data volumes result from the necessity to have large numbers of events in studies so as to provide adequately small statistical errors. To give a flavor of this problem, a standard data sample of one thousand CC events required in excess of 124 Mb of storage space at the time of writing.

Geant accurately simulates the dominant physics processes over an energy range from 10 keV to 10 TeV. To do this it contains interfaces to may previously standalone programs and can consider a large number of processes, as shown in table 6.1. Geant contains information about 48 particles: again, the user may define others if this is required.

Table 6.1: Geant physics processes.

The ZEUS version of Geant mainly consists of a set of command procedures which make the physics routines accessible together with a description of the ZEUS detector in terms of the volumes and materials mentioned earlier. This description is obviously an entity of great complexity, mirroring the nature of the detector. It requires at present around 50,000 lines of FORTRAN.

Some additional physics processes which are of special interest at HERA are also added at this stage. For example. background processes which are expected to be important have internal generators. In particular, beam-gas interactions may be studied using either the UA5[75] or FRITIOF[76] packages. The differences between these two are discussed in section 6.4.3.1.

6.2.2 ZGANA

Once the ZEUS Geant program has been run, a data-file is created representing the response of the detector to the physics events generated. The presence of the detector of course affects the numbers and trajectories of particles produced and this too has been simulated. It now remains to simulate the function of the trigger electronics.

This is the purpose of the ZGANA package, which contains an extremely detailed specification which is actually larger than the detector simulation itself. A data model based on ZEBRA is used here: the Adamo[77] system. This allows the implementation in code of the way data will flow and the relationships between different hardware groupings.

The VAX specific Module Management System[78] was used to control the substitution of user-written code for supplied ZGANA modules and the grafting on of additional code to represent the working of the RBOX. This meant that a realistic simulation of the information available could be obtained and used to develop the RBOX.

6.2.3 Event Generation

A beam-gas sample was produced using the FRITIOF generator. These were homogeneously distributed along the beam-line from z = -1900 cm to +100 cm. The sample was not filtered to remove events which cause no activity in the detector. The proportion of FRITIOF events resulting in hits in the CTD, FTD, RTD, CAL, HES, FMUON, BAC, LUMI or VETO was found to be 52%.

A sample of 1000 CC events and 1000 NC events was generated to test the response of the sub-triggers to physics. A cut of Q2 > 100 GeV/c2 was imposed as is normal to remove the effect of the beam-pipe on acceptance. The effective ranges of the kinematic variables are shown in table 6.2.

Table 6.2: Kinematic variables of CC sample.

The variables x, y were generated according to the behavior of the cross-section in the allowed ranges. Typical resulting distributions are shown in figure 6.2 for x and figure 6.3 for Q2.

Figure 6.2: Typical values of x for physics sample.

Figure 6.3: Typical values of Q2 for physics sample.

6.3 Details of the Algorithm

6.3.1 Introduction

In analogy with the two separate FLTs, event classification in the RBOX proceeds from the construction of cuts in four ratios. Each of these constitutes a separate sub-trigger. Two of these are more-or-less directly related to standalone sub-triggers. One is similar to the CTDFLT ratio and one is identical to the FTDFLT simulation developed standalone. There are in addition two combined sub-triggers which use information from both detectors. Sub-trigger three is known as the ‘barrel combined’ sub-trigger.

This is because of the spatial region of tracks to which it will be suited. The combined part of this ratio is clearly forward since matching between the CTD and the FTD cannot take place in the barrel region. But the ‘CTD only’ part of the sub-trigger extends the coverage into the barrel region. Sub-trigger four only considers matches between the CTD and the FTD and hence provides no useful data in the barrel region. For this reason, it is known as the forward combined sub-trigger.

6.3.2 Standalone FTD Sub-trigger

The first ratio comes from the FTD diamond matching procedure in exactly the same way as described for the standalone case in section 5.3.1.

6.3.3 Standalone CTD Sub-trigger

There is a ‘quasi-standalone’ CTD sub-trigger which is slightly different to the standalone version which was described in section 5.2. It might be described as a CTDFLT which is biased towards events going into the barrel region since it uses only data from SL5. This means that tracking information is available for polar angles between 25.4° and 154.6° for this sub-trigger. A ratio is formed of the number of segments found in SL5 which are consistent with having come from the interaction region divided by the total number of segments found. Again, a cut is made on this value since it will be close to unity for good physics events and close to zero for background events.

6.3.4 Barrel Combined Sub-trigger

Sub-trigger three proceeds by using the flags set by the CTD to check all sectors in SL1 for segments which have not been successfully extrapolated. Extrapolation is said to be successful if a pair of segments is found in SL1 and SL5 giving an intersection with the z-axis which coincides with the vertex to within a cut, together with a SL3 segment which is within one z/r bin of the line joining them.

Once those SL1 segments which were unmatched in the CTD have been identified, an attempt is made to match them with the FTD. Having received from the FTD the information in a preprocessed from, it is a simple matter to try to find pairs of super-diamonds which have the same pseudo-sector and pseudo-bin as previously unmatched SL1 segments. Thus the total number of segments matched either in the CTD alone or in the CTD and FTD combined may be obtained and a new ratio cut produced.

6.3.5 Forward Combined Sub-trigger

Sub-trigger four operates in a manner quite similar to the barrel combined sub-trigger: however it uses a different subset of the total information available. As mentioned in the previous section, the RBOX must provide angular data on tracks suitable for matching with the calorimeter. This data will take the form of an 8 x 8 bitmap as described in detail in section 6.5. However there is no reason why this information cannot be used by the RBOX in its internal processing: this is the data used by sub-trigger four.

Since the purpose here is to match CTD segments with the FTD, the bits set by the RBOX which are intended to facilitate matching with the FCAL are of especial interest. These are termed ‘forward bits’ or FBINs: in each of eight φ sectors they indicate if a good track has been found in each of the three θ regions which would correspond to the FCAL. So the RBOX uses the CTD information to produce the FBINs and do the matching: it is convenient to use the same theta regions for both purposes.

The forward combined sub-trigger tries to match all FBINS which have been set in the RBOX to pairs of FTD1 and FTD3 matched super-diamonds. This is different to sub-trigger three which only considers segments which had not been matched already by the CTD.

At this point, every event is characterized by four ratios between zero and one. Each is constructed from the number of matched segments and/or diamonds divided by the relevant total. Good events should produce numbers which will be near to one. Beam-gas events will not produce a great deal of correlation within and between detectors and will thus have numbers close to zero.

6.4 Results

6.4.1 Sub-trigger Ratios

The ratios obtained for beamgas events are shown in figure 6.4.

Figure 6.4: Sub-trigger ratios for beam-gas sample (zero bin removed).

In all of these plots, the zero bin has been omitted and the number of entries so removed is indicated.

The majority of beam-gas events actually fall into this bin but these are not of interest because they will in general cause no activity in the detector and no trigger decision will be made. On the other hand, it is possible for events to fall into the zero bin but still to have a non-zero denominator. If this is the case, it means that the event can be positively rejected for it has segments or super-diamonds or both but none of them have been matched. This is a good indication that the event comes from upstream.

Table 6.3 shows the proportions of beam-gas events which may positively be rejected in this way for each sub-trigger.

Table 6.3: Proportion of beam-gas events in zero bin with non-zero denominator for the four sub-triggers.

Figure 6.5 shows the sub-trigger ratios obtained for the charged current (CC) sample. This effectively removes the unclassifiable events and so interest clearly lies in this remainder which are likely to reflect the true nature of the background signal passing the trigger. Again, the zero bin has been removed. On subsequent pages, the same plots are shown again (figure 6.6 and figure 6.7) with the zero bins included. It is apparent from the plots that the forward combined sub-trigger achieves much lower matching ratios than the other sub-triggers. This is due to the artificial inflation of the denominator: a single segment often sets more than one FBIN. This is because of the need to allow for the smearing of the nominal interaction point with Δz of 20 cm.

Figure 6.5: Sub-trigger ratios for CC sample (zero bin removed).

Figure 6.6: Sub-trigger ratios for beam-gas sample.

Figure 6.7: Sub-trigger ratios for CC sample.

The electronics will allow SL3 segments in the z/r bin which would be expected from the SL1 segment to set an FBIN, or either of the adjacent bins. This means that a single SL3 segment will set 2 or 3 FBINs. However, it is only in general possible to match one of these with FTD super-diamonds, making the forward combined sub-trigger ratio lower than would otherwise be the case.

A sample of single straight tracks was considered from this point of view. It was necessary to filter this sample so that only events setting a single SL1 segment remained. This was done because real particles sometimes interacted before they reached the detector resulting in confusing output. It was found for single tracks generated with 20° < theta < 30°, 72% of single SL1 segments set more than one FBIN.

The important fact to remember is that this is not per se inimical to to good trigger efficiency. The beam-gas plot shows that background events are almost never able to satisfy this stringent criterion and so the use of this sub-trigger (with a lax cut) remains highly advantageous.

Two methods of combining the ratios obtained as described above to produce a final decision were investigated. Both had the starting point that any event without either SL1 segments or FTD1 diamonds was unclassifiable by the RBOX and placed into a separate ‘no decision’ class. The possibility of rejecting events which fail any cut is clearly unsatisfactory: even setting loose cuts resulted in a large proportion of all events being rejected by each individual sub-trigger. This would permit good beam-gas rejection but only at the expense of poor CC efficiency. In preference, the idea of accepting all events which passed any of the sub-triggers was adopted.

Simulation progressed in the expectation that a set of cuts could be defined in such a way as to enable the selection of a high proportion of good events from each plot. It was also hoped that the degree of correlation between the plots would not be high for signal events so that events in a low bin on one plot might frequently be found in a high bin in another. This would mean that overall a good efficiency might be obtained by combining all the ratios.

6.4.2 Tracking Triggers

Cut values were chosen for each of the sub- triggers and optimized iteratively. It was decided to find the highest CC efficiency available in the CTD, the FTD and the RBOX while maintaining beam-gas leakage at similar levels in each case to aid comparison.

The effect of making a particular cut more stringent is to reduce acceptance of both physics and background events. This effect is illustrated in figure 6.8 for CC events and in figure 6.9 for neutral current (NC) events. A perfect trigger would accept all physics and reject all beam-gas and would thus reside in the top left corner of the plots.

Figure 6.8: Profile of efficiency vs. leakage for CC events.

Figure 6.9: Profile of efficiency vs. leakage for NC events.

It can clearly be seen that the RBOX more closely approaches this ideal for CC events than either of the other triggers. In the case of the NC sample, the performances of the CTDFLT and the RBOX FLT are less strikingly different. The RBOX is still better at rejecting beam-gas over most of the range, but the CTDFLT performs well here because it is successful in triggering on the electron.

It is interesting to note the effect of the effect of the number of tunable parameters on the shape of the distributions in the figures. The FTDFLT contains only one parameter and the figure shows therefore a smooth curve. The CTDFLT however contains two such parameters as was mentioned previously. This results in the two curves seen. At the low efficiency end of the CTDFLT, the curves become close to vertical. This is because in this region of the plot, which would clearly never be used in a real situation, the cuts are very tight. This means that they are being applied in a region which contains very few beam-gas events. The effect of making small adjustments to these cuts is to alter the signal efficiency without changing the leakage.

This results in the shapes seen. In the four-parameter RBOX FLT, the situation is rather complex but the shape is consistent with the usual form of efficiency vs. leakage plots.

It should be recalled that in the RBOX FLT, all events passing any cut are accepted. The values of the cuts on ratios which were chosen as representing optimal performance for the RBOX are tabulated in table 6.4. The particular cut values are justified by cross-correlation plots showing one ratio plotted against another. These are shown in figure 6.10 for signal events and in figure 6.11 for background events. In both cases lines are drawn showing the cuts.

Table 6.4: RBOX FLT cut values for the four subtriggers.

Figure 6.10: Cross-correlation plots for CC events.

Figure 6.11: Cross-correlation plots

It is important to realize that the cut values shown above for CTD and FTD sub-triggers in the RBOX are distinct from the cut values used for the standalone triggers in the CTD and FTD which were run to allow comparison with the RBOX. The standalone cuts were adjusted to produce similar levels of leakage so that efficiencies might more easily be compared. This meant that in the case of the FTDFLT, the requirement was that more than 27% of diamonds found were matched. In the CTDFLT, an event was accepted as class 2 if more than 10% of SL1 segments were matched out to SL5. Otherwise, an event was placed in the weak accept class 3 if more than 25% of sectors in SL1 which have segments also have their vertex segment bits set.

The results obtained using these various cut values are tabulated below. [The error σ in the efficiency x is calculated from σ = (√(x(1-x))/n) where n is the number of events in the class[79].]

It can be seen from table 6.5 that good CC acceptance was obtained using the RBOX. For the CTDFLT standalone results, it should be recalled that initially class 3 events will be accepted and so count as class 2 (the meaning of the classes was given in section 5.2). So in assessing the relative performances of the CTD, FTD and RBOX FLTs, the sum of CTD class 3 and class 2 events should be compared with FTD class 2 and with RBOX class 2.

Table 6.5: Results for 1000 CC events generated with a Q2 cut of 100 GeV2/c2.

Table 6.6 shows the results for NC events. They are similar to those obtained with the CC sample except the presence of the electron improves efficiency in the cases of the RBOX and the CTD.

Table 6.6: Results for 1000 NC events generated with a Q2 cut of 100 GeV^2/c^2.

There is some upper limit on the efficiencies which may be achieved. An idea of this can be gained by considering the proportion of signal events in which the trigger can be gained by considering the proportion of signal events in which the trigger identifies tracks. If no entities are found from which to construct tracks, the event cannot be triggered on. The fraction of events with either segments or super-diamonds found is 97.4% for CC events and 99.5% for NC events. In this context the performance of the RBOX trigger can be seen to be good.

Excellent results were obtained for beam-gas rejection. These are shown in table 6.7. The aim of the trigger is to obtain good physics efficiency together with good beam-gas rejection. The standalone results for the same sample are shown here also for purposes of comparison. It can be seen that the RBOX is on this basis able to outperform either of the standalone sub-triggers, because the leakage is less than in either of the standalone cases and the previous tables showed that this is achievable in conjunction with superior physics acceptances.

Table 6.7: Results for 2000 FRITIOF beamgas events generated from z = -1900 cm to z = +100 cm.

In particular, the FTD standalone sub-trigger cannot achieve very high CC acceptance within a tight beam-gas leakage constraint. In fact, an efficiency of 82% is obtainable with leakage of 14%. Similarly, the standard CTDFLT cuts result in an efficiency of 88% with leakage of 16%. The RBOX, however, is able to achieve 93% CC acceptance with less beam-gas leakage than in either of the standalone cases.

The origin distribution along the beam-line for accepted events can be seen in figure 6.12.

Figure 6.12: Beam-gas leakage vertex profile along the beam-line. CC efficiencies are also noted here, using the symbol ηcc.

6.4.3 Beamgas Background

6.4.3.1 Comparison of Different Generators

To gain an appreciation of the amount of variation that may be produced in the detector by the use of different background generators, samples of 2000 events from FRITIOF and UA5 were passed through identical versions of ZEUSGeant and ZGANA. In order not to duplicate the results presented in the previous section and to focus attention on the differences produced only by the generators, a non-standard distribution along the beam-line was used for these two samples. In fact, they were generated homogeneously along the section with -19 m < z < + 9 m. The results obtained are shown in table 6.8 below.

Table 6.8: Event classifications for the full FLT simulations for events from two different beam-gas generators.

It can be seen that leakage rates are compatible for both generators while significant differences emerged in the balance of the remainder between rejected and unclassified events. In particular, this study indicates that results obtained with different generators should be comparable to within the 5% level. It has been shown[80] that FRITIOF has both a harder transverse energy spectrum and a higher multiplicity than the UA5 generator. These are the reasons for the differences found here because both factors mean that tracking detectors have a higher probability of correctly identifying the upstream vertex.

6.4.3.2 Reasons for Beam-gas Leakage

it is important to know the causes of beam-gas leakage in the tracking FLT. Only UA5 events were considered here for the sake of consistency. It was a plausible hypothesis that leakage was due to the events having primary or secondary vertices near the interaction region. [Vertex information was simply taken from Geant and denotes the coordinate origin of Geant tracks, not all of which will necessarily be observed in the detector.] To investigate this, plots were prepared showing the numbers of vertices within a certain distance in z of the interaction point for both accepted and rejected events from a total sample of 6000. These ranges were chosen to be -250 cm < z < +250 cm. The first corresponds roughly to the size of the CTD and the second is the same as the Δz of the interaction region.

The results for numbers of vertices are shown in four plots, one for each range in z for both accepted and rejected events. On the plots, the abbreviation ‘ir’ is used to denote ‘interaction region’ for the wide range in z and ‘ip’ to denote ‘interaction point’ for the narrower range. It can be seen from figure 6.13 that no accepted event is without a vertex in the CTD region. In contrast, for the rejected events the zero bin is by far the largest while there is a tail out to higher numbers of vertices. The means of the two distributions show that a rejected event is more likely to have few vertices in the CTD region.

The figure also shows that a substantial proportion (63%) of accepted events actually have vertices very close to the nominal interaction point, whereas this is true for only around 12% of rejected events. The remaining accepted events are highly active ones causing many hits in the detector and resulting in false correlations. This can be seen in the plots in figure 6.14 which show distributions of hit multiplicity for all beam-gas events and those which were accepted and rejected by the CTDFLT. For comparison, the distribution for all CC events is shown. It can be seen that the mean hit multiplicity for rejected beam-gas events is 0.65 of the mean for all events while this average ratio is 5.43 for accepted events.

The properties of the track momenta may also shed some light on the reasons for beam-gas leakage. The plots in figure 6.15 show the transverse and z-momenta for Monte Carlo tracks in all events and those which were accepted and rejected. It can be seen from considering the means of the distributions that rejected events tend to have lower values of both while accepted events tend to have higher than average
momenta.

In summary, it can be seen that the properties of an accepted beam-gas event as opposed to an ‘average’ beam-gas event are: very high hit multiplicities, large numbers of tracks originating from near the interaction region, and comparatively higher track transverse and longitudinal momentum. The striking difference in hit multiplicities means that the mechanism for acceptance of beam-gas is primarily false correlation: there are simply so many track segments found that many of them must match up. Of secondary importance is the presence of tracks originating from the interaction region which should clearly be perceived as good tracks by the trigger. Since the sample
was generated with -19m < z < +1m this must be due to secondary interactions: particles from upstream beam-gas events travel to the interaction region and interact again with a machine element.

Figure 6.13: Number of track vertices per event for narrow and wide ranges around the interaction point by event classification.

Figure 6.14: Hit multiplicity distributions by event class.

Figure 6.15: Transverse and longitudinal momenta of tracks by event class for beam-gas.

6.4.4 Calorimetry

It was decided to extend this study by looking at the effect of calorimeter information. This is clearly not something that is possible in the RBOX but should give an indication of what might be achieved in the GFLTB which receives data from most components including the RBOX and the calorimeters.

The effect of transverse energy cuts was investigated. The values of the cuts used were different for each class of event processed by the tracking trigger. These were fixed empirically by studying the energy distributions of events in the different classes and adjusting the cuts accordingly. Clearly, there are many more sophisticated methods of using information from the calorimeters but the concern here is only to provide a simple test to ensure that improvements made in the RBOX are not lost or irrelevant after input from the calorimeters.

The values chosen for the transverse energy cuts are shown in table 6.9 for the CTD and table 6.10 for the RBOX.

Table 6.9: Transverse energy cuts chosen for the CTD.

Table 6.10: Transverse energy cuts chosen for the RBOX.

These figures are quite acceptable intuitively as far as their variation with event classes is concerned. For events accepted by the tracking trigger only modest transverse energy deposition is required. This does not harm physics acceptance but provides great discrimination against beam-gas. However, as the tracking triggers become more certain that the event did not come from the vertex, higher depositions are required for the calorimeters to override the tracking triggers.

It was found that using calorimeter data, the RBOX achieved a CC efficiency of 98.5%, while the CTD achieved an efficiency of 99.2%. This means that the leakage figures for both may be compared since the efficiencies are the same within the statistics. Figure 6.16 shows that the RBOX has consistently better beam-gas rejection than the CTDFLT after the inclusion of calorimeter data. Integrating over the range of the plot, a total of 99 events (of 2000) were accepted by the CTD in combination with the CAL as opposed to only 47 by the RBOX and CAL. For a leakage rate of 1kHzm-1 this corresponds to 470Hz and 990Hz respectively at the FLT. The importance of the RBOX may readily be seen bearing in mind the 1kHz maximum rate in the GFLTB.

Figure 6.16: Beam-gas leakage vertex profile along the beam-line after calorimeter transverse energy cuts. CC efficiencies are also noted here, using the symbol eta_cc

The fact that the cuts are in each case slightly higher for the RBOX than for the CTD standalone may be explained in the light of these results. Since efficiency is so high in both cases that it cannot practicably be improved upon, attention focuses on improving rejection of background. Since the quality of information available to the RBOX is of higher quality, it is possible to impose stricter transverse energy cuts in the RBOX, thus rejecting more background, without affecting CC efficiency.

6.5 Hardware Design of the RBOX

The RBOX processing is divided up into modules both functionally and geometrically, as shown in figure 6.17. The RBOX will have two crates. Crate one contains eight hit counting modules (HCM) and one final decision module (FDM). Crate two contains eight overlap track modules (OTM) and a module to count the FTD super-diamonds.

Figure 6.17: Regional box functional subdivision.

The HCMs receive hit information (flag bits) from up to five φ sectors. This data comes from the CTD sector processors and the OTMs which deal with the CTD/FTD overlap. There is a one-to-one correspondence in φ between the OTMs and HCMs. The modules and their interconnections are shown in figure 6.18.

Figure 6.18: Regional box hardware scheme.

The FDM will use internal bitmaps which will have granularity in θ, φ of 4 x 32. This corresponds in φ to the sector processors subdivision. In θ, two regions cover the forward direction, and the remaining two cover the barrel and rear directions.

Input to the FDM consists of the total number of sectors with tracks found in each of four θ regions; these regions may be the same as the four listed above or may be combinations of them[81].

The diamond counting module will deliver to the FDM the value of the ratio of matched to unmatched diamonds. The FDM is responsible for determining the values of the ratios for the other three sub-triggers described in this chapter. It will then produce a final decision from all of the ratios. The processing to do this will be based on Xilinx chips.

The output from the FDM to the GFLTB is carried by 16-bit cables. One will be sufficient to indicate the event class and the sector hit multiplicity. This corresponds to the processes “Count hit sectors” and ”Classify event” of the functional subdivision. Further cables will carry the bitmap of tracks found.

The OTMs use a different angular granularity reflecting the requirement to output track angular distributions for calorimeter matching. The process ”Find overlap tracks” is divided into eight wedges, one wedge per OTM. These modules provide the 8 x 8 bitmap output to the GFLTB as well as the information to the HCMs. The theta division corresponds to the calorimeter division and is shown in figure 6.19.

Figure 6.19: Subdivision in θ of RBOX bitmap to GFLTB.

Categories

## ZEUS Tracking Detector First Level Trigger

Chapter 5

Tracking Detector FLT

5.1 Introduction

The processing of data from the CTD and the FTD will be integrated at the output stage of the tracking FLT. The RBOX is responsible for this. Chapter Eight describes how performance benefits may be obtained by extending track-finding methods to use data from both of the tracking detectors. It is likely for financial reasons that there will be some staging of detector readout and trigger electronics. For this reason, the RBOX is able to run separately the two tracking detector standalone triggers which are described here.

5.2 CTDFLT

There are four types of readout module in the CTDFLT: cell processors for SL1, SL3 and SL5 (CP1, CP3, CP5) and sector processors (SP).

Measurement of the z-coordinate is central to the CTDFLT, the principle of which is shown in figure 5.1.

Figure 5.1: Principle of the CTDFLT.

5.2.1 Cell Processors

The z-by-timing value (see section 3.2.3.2) from the FADC is converted to a z/r bin number before input to the CPs. This is a fairly simple operation (because the radius is constant for a given SL) which is carried out by PROMs[60] on the z-by-timing cards.

The CPs work with these values because straight tracks at constant polar angle will produce several hits in the same z/r bin. This means it is relatively straightforward to perform pattern recognition in this space to find such tracks.

Pairs of cells are read out by each CP[61] because the tilt of the cells means that straight tracks from the origin will pass through two cells. The CPs search for patterns of hits at the same z/r. This pattern recognition logic is implemented in two stages consisting of RAM look-up tables and Xilinx[62] field programmable gate array (FPGA) chips which are also used in the GFLTB. Xilinx chips allow logical networks of great complexity to be defined. Their most important property is that the networks may be reconfigured in the light of new requirements.

The input stages of the CP1 boards consider hits arriving within a short time-span of each other in an 8 x 32 bit table. The eight bits represent the layer number within SL1 and 32 bits is the division into z/r for this SL. Due to hardware constraints, the entire table cannot be processed simultaneously but instead is considered in a 4 x 8 bit window. This window is stepped along the 32 bit length of the table. Each window is further subdivided into an upper and lower half of 4 x 4 bits. For each half, a 64k x 4 RAM produces four bits from the input z/r pattern:

• Vertex cut bit
• Centre cut bit
• pattern weight (two bits)

The first bit is set if hits are found consistent with a track from the vertex and the center bit is set if the hits were mostly in the middle two bins of the 4-bin half-window (this reduces the frequency with which the same track sets bits in two CPs). If wires are missing in a sequence of hits they may still be formed into a straight line from the interaction point but it is desirable to accord such a pattern less significance than one which has all wires hit. The pattern weight is a measure of this significance.

Analogous processes take place in CP3 and CP5 boards but here only four wires in a cell are instrumented for z-by-timing.

A hit pattern in a cell consistent with the hits being part of a good track is called a track segment. The CPs form a 31-bit word which is a z/r bitmap. This indicates whether or not candidate segments have been found in that particular z/r bin and is sent to the relevant SP.

5.2.2 Sector Processors

There are thirty-two SPs corresponding to the number of cells in SL1. Because tracks curve in the magnetic field, more than one CP in the larger radius SLs sends data to a SP. In fact, four CP3s and six CP5s are ‘OR’ed together to constitute a single trigger sector, as shown in figure 5.2.

Figure 5.2: One of the 32 trigger sectors of the CTDFLT.

Tracks from the interaction region which have a polar angle of greater than approximately 26° will cross all three instrumented SLs.

Assuming that there are no inefficiencies, this would mean that three segments would be found by the CPs. Each SP proceeds by trying to match segments. If the line joining segments in SL5 and SL1 points to the vertex to within some cut, and also passes through SL3 within +/-1 bin of a segment there, then a good track has been found.

Six bits allow for communication from each SP to the RBOX, which must combine information from all sectors to produce a decision for the CTDFLT as a whole. These six bits consist of three track bits and three vertex bits. The vertex bits come from processing in rz and the track bits come from r-φ processing.

If in a particular sector a good track has been found as described above, then the SL5 vertex bit is set. This indicates that successful extrapolation of at least one SL1 segment out to SL5, including a SL3 segment, to find a combined track which points to the vertex has taken place.

However, it is possible that the SL5 segment is not found, if for instance the track has a polar angle such that it leaves the CTD before reaching SL5. In this case it is still possible to do track-finding by combining segments in SL1 and SL3 only. The SL3 vertex bit is set if extrapolation is successful to this extent. If the rz processing in SL1 finds a segment, the SL1 vertex bit is set.

The three track bits, on the other hand, are measures of activity which has been formed into a track by the relevant CP but which may or may not have come from the vertex. The SL1 track bit indicates that there were sufficient hits in the CP1 in a sector for it to be able to form a track segment. If in addition this was true in one of the CP3s assigned to this sector, then the SL3 track bit is set. Finally, if all three instrumented SLs contain track segments then the SL5 track bit is set.

It is thus to be expected that a single good track within the θ region covered by all instrumented SLs will set all three vertex bits. A real event will of course usually contain more than one track and it is likely that some of these will be due to secondary interactions which will have origins distinct from the interaction region. A decision must be made in the RBOX as to what extent the event looks as if it consists of a minimum number of tracks coming from the interaction region – clearly a description satisfied by a good physics event.

The CTDFLT decision is made by the formation of a ratio; this is the central idea of all the tracking detector triggers. Ratios are formed representing how closely the event conforms to the hypothesis that it emanates from the interaction region and a cut is made on this ratio in order to reject background. The value of the cut is a tunable parameter and has very great influence in the optimization of the particular trigger.

It is the purpose of the three track bits from each SP to permit such a ratio to be formed. The numerator will be a function of the vertex bits, of which large numbers will be set by a good event. The denominator is a function of the track bits which are a measure of activity in the detector. If the ratio is high this means that a large proportion of activity in the detector is associated with good found tracks and the event may be triggered on with some confidence.

There is much overlap of information relating to the same tracks between different CPs and SPs which therefore need to have a high degree of connectivity. The 16 crates in the whole system, each of which contains the track-finding and z-by-timing boards for two trigger sections, are linked together in a circle so that data from adjacent trigger sectors is available to the processors.

All crates use a customized back-plane which concentrates readout bus lines, system control, timing and power supply in the bottom third allowing up to 300 interconnections to be made between cards.

5.2.3 Processing

The RBOX forms several ratios in its processing to produce a final CTDFLT decision which is based on two cuts. Firstly it finds the number of sectors which have their SL5 vertex bits set. It divides by the number of sectors which have their SL5 track bit set.

If the ratio so formed is greater than a cut then the event is accepted. In the simulation this cut is presently set to be 10%. An accepted event is labeled class two in the case of the CTD. If the ratio is less than the cut value but there are nevertheless more than two segments in SL5 then the event is rejected (class one).

For events which fall into neither of the above two classes, the SL1 data is utilized. If the ratio of sectors with their SL1 track bits set divided by the number with vertex bits set is greater than a cut, then the event is placed in class three. This cut is now set at 25%. These are quite possibly good events but one will have less confidence in accepting them. At present these events are simply added to the class twos in order to boost physics acceptance but it is important to remember that scope exists to treat them differently. For example the class threes might be required to fulfill more stringent conditions at later stages of processing.

The possibility exists to introduce a similar procedure for SL3 segments but studies so far have not looked at this question in sufficient detail to prove the necessity to do this. An additional class of accepted events could thus be provided for.

If the event has failed to be classified so far, then an assessment is made of its information content: if it has any segments in SL1 then it is rejected. If this is not the case, there is insufficient information for the processors to work with and the event is classified zero or ‘no decision’. Table 5.1 shows the classes and figure 5.3 shows diagrammatically how they are arrived at.

Table 5.1: Summary of CTDFLT event classifications.

Figure 5.3: CTDFLT event classification flowchart.

5.2.4 Timing

Other elements of the system are related to timing considerations. Since the drift times are longer than the beam crossing interval, the CTD will contain ionization from more than one crossing at any given moment. It is necessary to consider the arrival times of pulses in order to assign them to a beam crossing. Each crate contains a Local Timing Controller (LTC), each of which is connected to a separate Master Timing Controller (MTC) which receives clock signals from the GFLTB. In this way, the LTCs make a time signal in 48 ns bins available on each crate.

The CPs have logic designed to recognize patterns and sequences of hits so as to identify the crossing which produced the trigger. A mis-identification would result in a 96 ns difference between measured and real drift times for hits which would produce easily recognizable effects on segments as shown in figure 5.4.

Figure 5.4: Effect of crossing mis-identification on segments and maximum difference in drift times on adjacent sense wires.

An arrival time circuit (ATC) works in parallel with the pattern recognition. This generates two flags – ‘new’ and ‘valid’. The ATC works in 48 ns time-bins (i.e. two per beam crossing) and the new flag is set if a hit arrives which was preceded by three empty bins. This can be regarded as the first hit of a new event, as shown in the same figure. The maximum difference in arrival time of hits from the same track on adjacent sense wires occurs if the track passes through a wire and is given by Δt = d/vd where d is the separation between sense wires, equal to 8 mm x cos φ, φ is the angle of the track with respect to the sense wires and vd is the drift velocity. Using the nominal drift velocity of 50 microns per ns this means that Δt = 160 ns with φ = 90°. This is more than the three bin (48 ns x 3 = 144 ns) gap requirement. However, φ will not approach 90° but will be closer to 45° for tracks from the interaction point. It follows from this that the maximum gap permitted in a sequence of hits is two bins if they are to all be considered a part of the same event.

The maximum drift time covers ten bins and so the valid flag is set ten bins after the new flag was raised and remains up for one time-bin or until the last hit in the sequence arrives. The flag is sent directly to the output stage of the CPs.

5.3 FTDFLT

5.3.1 Introduction

The Forward Tracking Detector First Level Trigger (FTDFLT) is based on the same principle as the CTDFLT: straight tracks from the interaction region are again searched for. However the different geometry of the two detectors means that different logic is necessary to achieve this.

As described in section 3.3.1, the FTD has three sub-chambers each containing planes of wires with 60° relative offsets. These planes are known as u, v or w-layers depending on their orientation. The planes contain a large number of wires which cannot be used individually in the trigger because of hardware constraints. For example, the number of connections which may be made to a single electronic readout board is a limiting factor. It is necessary to OR wire signals together in such a way as to retain sufficient resolution to leave the FLT efficiency unimpaired.

5.3.2 Diamonds

The concept of diamonds[63],[64] was developed to represent an optimal method of combining cells. Two of the three planes in an FTD sub-chamber are used to define a hit location, simply by ‘AND’ing the hits together. These must then be confirmed by a further hit cell in the third plane. This third cell is not required to be exactly in coincidence with the first two: the precision of the match is a parameter which may be adjusted in order to optimize performance. At the moment, it is envisaged that either the central cell in the third layer or either of the two adjacent cells may confirm a diamond. Figure 5.5 shows the method of forming diamonds.

Figure 5.5: Method of diamond forming to confirm three-dimensional hits.

A cell numbering convention has been defined whereby for good three-dimensional combinations, the sum of hit cells will be zero. There is a further combination of diamonds into super-diamonds in the outer regions. Near the beam-pipe where high resolution is required, the processing to find hit diamonds proceeds exactly as described. However, further out, they are combined into larger entities composed of 2 x 2 standard diamonds. At the largest radii, a super-diamond contains nine standard diamonds.

For financial reasons, only FTD sub-chambers one and three will be instrumented with diamond logic. It can be seen by similar triangles (figure 5.6) that if a pair of super-diamonds found in the two detectors lie on the same straight track from the interaction region, then their coordinates are related by equation 5.1.

Figure 5.6: Principle of the FTDFLT.

Conversely, tracks emanating from upstream of the interaction region will fail to satisfy this relationship by an amount which increases proportionally to their distance from the nominal interaction point.

The wire planes are orthogonal to the z-axis, and the u, v and w-layers are separated by 5 cm in z. In principle it would be necessary to examine how layers have been used to form a super-diamond. However it has been shown[65] that in fact this small correction is not significant. It is therefore assumed that the same z-coordinate is obtained everywhere in a sub-chamber and so this reduces to a simple factor which can be applied to the radius of a hit super-diamond in FTD1 to predict the radius of a matching super-diamond. For infinite momentum tracks, the coordinate should be the same for both super-diamonds.

These principles form the basis on which the FTDFLT works. It attempts to match super-diamonds from FTD1 with those from FTD3. In the ideal case, all super-diamonds in a good event will be matched. In practice, some super-diamonds will fail to be matched because of inefficiencies and interactions etc. The FTDFLT finds the ratio of super-diamonds in FTD1 which have been matched with FTD3 super-diamonds divided by the total number of FTD1 super-diamonds and makes a cut on this quantity.

This is a valid approach since beam-gas events have fewer tracks coming from the interaction region, and hence will have less correlation of super-diamonds between the two sub-detectors.

5.3.3 Hardware

Figure 5.7 shows the hardware design for the FTDFLT. The chamber will be readout by FADCs as described in section 3.3.1. These are interfaced via a discriminated post-amp signal to cell-hit boards (CHBs)[66] which produce hit wire numbers. Each CHB should be able to contain logic units able to read out 32 cells. This means that a total of 16 CHBs, fitting into a single crate, will suffice for the FLT readout of FTD1 and FTD3. As shown in the diagram, this CHB crate has three fan-outs linked to two fan-ins on the second crate. The second crate contains six Sextant Boards (SBs) and six Segment Builder Modules (SBMs). This subdivision is a consequence of the FTD geometry.

The SBM and CHB electronics will rely on Xilinx FDGAs for logic implemented by look-up tables. These chips will be reprogrammable by the ROC. The CHBs will define hit cells by requiring a minimum number of hit wires out of the six in a cell.

Figure 5.7: Outline of two-crate FTDFLT hardware design.

The SB logic will form super-diamonds from hit cells and then apply coincidence logic to search for tracks from the interaction region in the manner previously described.

Finally the SBMs use hit and coincident diamonds to from the ratio for the FTDFLT decision and also to prepare for matching with CTD data.

Timing considerations are as important in the FTD as in the CTD since the FTD also contains ionization from more than one crossing at any given moment. A five bit shift register is connected to each wire-hit with each bit corresponding to a beam-crossing interval. An OR of the last four bits is fed into the CHB so that each hit remains valid over sufficient time such that all hits pertaining to a particular event will at some point be considered together.

Finally, the Readout-Controllers (ROCs) are responsible for sending information concerning the status of the FTDFLT to RC and the EVB, for handling of test data, and for reading out the contents of registers etc. for diagnosing trigger performance.

Categories

## The ZEUS Trigger Environment

Chapter 4

The ZEUS Trigger Environment

## 4.1 Introduction

Triggering is the selection of physics events of interest in conjunction with the rejection of background processes which it is not desired to investigate. The success of any HEP experiment is critically dependent on its ability to achieve a high trigger efficiency.

Identification of interesting physics must be as close to perfect as possible in order to avoid the introduction of unacceptable systematic errors and to maximize the amount of recorded data relating to physics events. A trigger is a complex entity comprising, at HERA, readout electronics, hardwired algorithms and much sophisticated software running on powerful dedicated processors well matched to particular tasks.

At HERA, triggering has assumed even greater importance than in the past partly due to the high rates of background and partly due to the short beam-crossing interval of only 96 ns. At other machines, a longer interval simplifies trigger design so that no pipe-lining of data is required. For example, the Large Electron-Positron collider at CERN has a crossing every 10 μs. Experience gained at HERA will prove invaluable in the design of the yet more complex triggers which will be required at the next generation of colliders, notably the Superconducting Supercollider in Texas which will have a beam crossing interval of 16 ns.

### 4.1.1 Overview of Dataflow

An overview of the system is shown in figure 4.1.

Figure 4.1: Flow of data through the DAQ system.

Each component feeds data to local pipelines and the global first level trigger (GFLT). If this decides to accept the event, the pipelines are read out to the second level trigger (SLT): raw data from each component remains separate at this stage though the global second level trigger (GSLT) can clearly consider the results from processing in all components. If the GSLT issues an accept, the event builder (EVB) assembles the whole of the information acquired for the event and sends it to the third level trigger (TLT). This, mediated by the Central Data Acquisition (CDAQ) VAX and run control (RC), writes events passing the final stage to tape. There is also some facility for local disk storage.

## 4.2 Rates and Background

The trigger philosophy has been developed with the characteristics of physics events in mind. These in general have many tracks coming from the origin which will be observed in the tracking detectors. Large depositions of energy, especially at high angles to the beam-line, often result from physics processes. If there is a neutrino in the final state, this will not be seen by any part of ZEUS and so and asymmetry in transverse energy may be found.

It is envisaged that there will be three main sources of background in ZEUS; cosmic rays passing through the detector, losses from the proton beam, and interactions of the beam with residual gas inside the beam-pipe. The latter are known as beam-gas interactions and much effort has been expended to try and devise triggering strategies to prevent them from causing triggers.

Cosmic ray events will on the whole be rejected by the use of timing information from the calorimeters.

Protons not following the nominal beam trajectory hit machine elements thus producing hadronic showers including pions. These can subsequently decay into muons which are very penetrating. There are approximately 2 x1013 protons in the beam. The circumference of the ring is 6,336 m. If it is assumed that the beam will have a lifetime of about ten hours, these interactions may occur at a rate of up to 100 kHz per meter of beam-line. However, structural elements such as collimators, beam scrapers and the veto-wall will substantially reduce the rate of these events causing activity in the detector.

It is estimated that the rate of beam-gas interactions will be up to 2 kHz per meter.[23] Near the interaction region they will fake good events in the tracking trigger. Upstream of it, their modest energy deposition may be misinterpreted by the calorimeter as a high transverse energy deposition representing a large Q2 interaction. This is because upstream tracks which are in fact only leaving the beam-pipe by a shallow angle can arrive a long way away from it once they are intercepted at the interaction region.

Also, upstream beam-gas can have secondary interactions producing tracks which come from the interaction region. This background is potentially the most serious. All of these backgrounds can be reduced by combining together triggers from different detector components. These have different discrimination powers against the various types of background and by combining them in a flexible way the sensitivity to physics can be maintained while minimizing the background. This is discussed in the next section.

## 4.3 The Trigger

Assuming the design luminosity of 1.5 x 1031 cm2 s-1 leads to the rates shown in table 4.1 for events observed in the acceptance of the ZEUS detector.

Table 4.1: Rates of physics and background.

As mentioned above, the ZEUS trigger will have three levels. In order to allow more sophisticated processing on a more complete subset of component data at successive levels, each level will have a longer period of time with which to make a decision. This is shown in table 4.2.

Table 4.2: Processing time allowed per event by level of trigger.

### 4.3.1 The First Level Trigger

It is impossible to decide whether or not to accept an event within the 96 ns between beam crossings. In the first level trigger (FLT),[24], [25], [26] this forces the storage of data in pipelines which must be able to hold data relating to 5 μs.

Processing takes place both at the level of individual components and in the Global First Level Trigger Box or GFLTB.[27], [28], [29], [30], [31], [32] Because of these constraints the sophistication of processing that may be done by components at this level is restricted.

The output rate from the FLT will be 1 kHz, after the fast clear (section 4.3.1.2). The components must write the data relating to the event to their internal pipeline.

Each of the components have 26 beam crossings to perform calculations on their data. They must then send the results of these calculations to the GFLTB. If the GFLTB decides to accept the event, it will send an accept bit to each component exactly 20 beam crossings later. The GFLTB must therefore complete its calculations within this 20 beam crossing period. The components then read out the relevant data to the component second level trigger.

The tracking detector FLT is is central to the work presented in this thesis. Its discussion is therefore postponed to the following chapter.

#### 4.3.1.1 Calorimeter FLT

The calorimeter first level trigger (CALFLT)[32], [33], [34] is designed to detect isolated electrons and muons and to measure momenta and energy deposition. It is essential to use angular information in this trigger. The distinction between transverse energy and momentum in the CALFLT is an important one. Momentum is a vector quantity whereas energy is a scalar. The difference between energy and momentum is expressed in the statement that momentum is signed so that tracks in a opposite hemispheres might sum to give zero transverse momentum whereas energy would always add.

Transverse energy is a calculated value in which depositions at high angles are accorded more weight. This quantity is a good measure of activity in the detector characteristic of desired physics events. Look-up tables (LUTs) are used to consider transverse energy deposition in order to recognize patterns associated with good events.

The original intention to measure longitudinal momentum will not now be fulfilled due to financial reasons. The calorimeter is mostly non-projective: only the electromagnetic section of the barrel has cells aligned parallel to lines radiating from the interaction point. For this reason, the subdivision of the calorimeter into regions for trigger purposes is different to its physical division. Entities known as ‘trigger towers’ are formed from calorimeter cells such that a straight line from the interaction point will be fully contained within them.

Most towers contain two electromagnetic calorimeter (EMC) cells representing approximately 25 radiation lengths as was shown in table 2.1. Beyond that are the two pairs of HACs (hadronic cells) which map most closely on to the EMCs. In a small number of towers at the edges of the FCAL and of the RCAL, the BCAL is between the first cell in the tower and the interactions region. In this case, the tower contains only HACs (see section 2.2.1). The makeup and number of towers in the calorimeter is shown in table 4.3.

Table 4.3: Calorimeter tower numbers and makeup by location.

It can be seen from the table that there are a total of 1,360 towers: these all provide a HAC sum. Of this total, 974 also provide an EMC sum. The non-projective cells must be grouped into projective towers. This is done by using the EMC sections to define tower geometry and then assigning HACs behind them to form a tower with the best possible match. It transpires that 896 projective towers with a sensible geometric division emerge from this process. The calorimeter is now divided into sixteen trigger regions: four for each of the RCAL and FCAL and eight for the barrel. This is shown in figure 4.2. Each region contains 7 x 8 towers.

Figure 4.2: Trigger regions in the calorimeter.

Each calorimeter cell is read out by two photomultiplier tubes. EMC and HAC energy depositions are summed within a tower by on-board cards known as trigger sum cards (TSCs). These sums are sent to trigger encoder cards (TECs) in the rucksack: each TEC covers four towers. So there are 14 TECs in a crate to cover the 56 towers in each of the sixteen trigger regions.

For each tower, EMC and HAC energy deposition is measured on two digitization scales by flash analogue-to-digital converters (FADC): high gain (12.5 GeV on an 8 bit scale) and low gain (400 GeV over 8 bits in the FCAL and 100 GeV over 8 bits in the RCAL and BCAL). If the deposition exceeds a scale an overflow bit is set. If neither the HAC nor the EMC in a tower set off the high-gain channel, the TEC ceases to perform energy sum calculations and begins testing for electrons and minimum ionizing particles as described later.

The geometric position of each tower in terms of θ and φ is known to the TEC. It uses these and the finest resolution energy scale available (depending on whether the high or low gain channel has been used) to find transverse energy depositions. Total and transverse energy sums for the four towers covered by each TEC are sent to a trigger adder card (TAC). There are two of these in a crate.

The TEC’s run test procedures may result in three bits being set for each tower. An E-bit is set if the depositions found are characteristic of an isolated electron: these will predominantly deposit their energy in the EMC part of a tower. The design aims to find all electrons with energy greater than 5 GeV.

The EMC threshold is set at 2.5 GeV however since an electron may deposit its energy in adjacent cells. Since there is a small likelihood that an electron with energy between 2.5 GeV and 5.0 GeV will ‘punch through’ the EMCs to reach the HAC layer, only 0.1 GeV is allowed in the HAC layer. If the EMC deposition is greater than 5.0 GeV, then the ratio EEMC to EHAC must be greater than 10. A slightly different requirement is implemented in the more active FCAL but clearly the requirement for this bit to be set is also based on substantial symmetry between the two types of cell.

The rate at which charged particles passing through matter lose energy by ionization depends on their energy. In fact, the rate decreases to a minimum and then increases to a plateau at high energy. Particles above the minimum are called minimum ionizing particles or MIPs. The energy deposited by a particle at the minimum in a tower is shown in table 4.4.

Table 4.4: Total HAC and EMC energy deposited by a MIP by location of tower.

If a situation not unlike the reverse of what is necessary to set the E-bit occurs, then an M-bit (M is for minimum ionization particle) is set. It is required that the deposition E fulfills the condition 0.2 EMIP ≤ E ≤ 2 EMIP. It is generally likely that a muon is the cause. Muons are comparatively penetrating and so do not deposit most of their energy in the EMCs. Genuine hadrons will usually have energies which are much too large to set the M-bit.

Towers in the active region around the beam-pipe are not permitted to set E or M bits. If insufficient energy is deposited to set either of these bits, LUTs are used to find if the tower is ‘low-activity’ for the Q-bit. ‘Q’ stands for ‘quiet’. In fact, the requirement to set the Q-bit is that the pulse height be less than 20% of the pulse height required to set the M-bit.

In the TACs, pattern logic searches for groups of up to four E or M-bits set and surrounded by Q-bits in each of the sixteen regions. NC events have a high-energy isolated electron and this pattern logic forms an excellent trigger on these events. On the other hand, isolated muons are characteristic of many interesting physics processes including heavy quark production.

The exact thresholds for these bits vary depending on the location of the tower being processed. The thresholds for the E, Q and M-bits must be matched to each other because otherwise a legitimate electron may fail its isolation requirement. Therefore a quiet tower is defined by having less than the minimum EMC energy for an E-bit and the minimum HAC energy for an M-bit. For example, in the FCAL a quiet tower must have EEMC < 2.5 GeV and EHAC < 2.268 GeV. These bits are sent to the CALFLT processor.

The CALFLT processor receives the energy sums for the sixteen regions and also on a finer sub-region scale. This finer scale is designed to have better resolution around the beam-pipe and to prevent loss of the flexibility to examine data relating to areas covered by more than one trigger crate. The CALFLT processor will be able to examine in this way deposition in the FCAL and the RCAL in annular regions at different radii from the beam-pipe. This is useful because beam-gas events are more likely to have high deposition around the beam-pipe region than physics events for Q2 values of interest to ZEUS.

Sums are made of the number of towers in each region which have energy sufficient to set the bits. This enables the processor to search for jets which will appear as clusters of towers with bits set.

The processor sends data to the GFLTB relating to the whole calorimeter and to the 16 sub-regions. The global data is: EEMC, EEMC + EHAC, Ex, EMC + Exm HAC , Ey, EMC + Ey, HAC, Ex, EMC, Ey, EMC , missing energy, cluster data and the total number of E and M-bits set.

Further, the result of a beam-gas likelihood algorithm is sent. [This uses the regional energy sums and also the sum of energy in the beam-pipe region (because beam-gas events cause much activity here). Also the presence of towers showing kinematically disallowed energies is a useful sign. Because they have upstream vertices, beam-gas events can fake larger transverse energy than would be possible for any real event.] On the sub-region scale, the M and Q-bitmaps are sent to the GFLTB along with Etot , Etrans, Eemc , Ex and Ey.

#### 4.3.1.2 Fast Clear

To ensure that the accept rate to the second level trigger is no greater than 1 kHz an element of parallel processing of calorimeter data has been introduced[35]. The fast clear (FC) will consider data simultaneously from the FCAL, RCAL and BCAL relating to events which have had an FLT issued. Each accept is accompanied by an indication of whether the GFLTB will permit the FC to abort the event, based on the strength of its acceptance by components other than the calorimeter.

The FC works by searching for clusters[36] and finding their angle and energy. Cuts are made to discriminate against beam-gas which can be quite stringent compared to those in the FLT because the FC will be permitted to abort a trigger only if the other components show a weak accept decision.

An important quantity in the FC is shown in equation 4.1.

In CC events, hadron jet do not often have trajectories which take them through the RCAL. On the other hand, about 80% of particles in beam-gas interactions are hadronic. So physics events have high-angle clusters with large Ef. It has been shown that a cut based on this ratio for the highest energy cluster in the RCAL yields a rejection factor of 400[37]. This clearly indicates that efficient recognition of electron or hadron jets is possible.

If an abort does occur, the GFLTB stops component readout to the second level. The FC operates in around 10 to 30 μs. This is longer than the 5 μs available to the GFLTB because the FC does not have to consider every event. In this way, more detailed considerations of clusters are possible thus enhancing efficiency while the design goal of 1 kHz input to the GSLT is not compromised. In fact, the exact amount of time available depends on the FLT rate but flexibility has been inbuilt here by simply declaring that the FC will cease incomplete operations on an event and allow it to proceed through the readout chain as soon as the next FLT decision is issued.

#### 4.3.1.3 Other FLT Components

Forward muon detectors

A muon trigger[38] will be formed taking account of direction and momentum by requiring a strip-to-strip coincidence between first and last planes of streamer tubes (LT1 and LT5, see section 2.3.1). The susceptibility of this method to background is reduced by additionally requiring signals in corresponding φ-sectors of all five planes LT1 to LT5, as shown in figure 4.3.

Figure 4.3: Forward muon detector first level trigger.
Figure 4.4: Barrel muon detector first level trigger.

The time-of-flight plane will assist the association of a triggered muon with its correct beam-crossing. The FMUFLT will have three subdivisions in terms of polar angle as shown in table 4.5.

Table 4.5: FMUFLT polar angle subdivision.

Correlation matrices select tracks consistent with having originated in the interaction region. This is done by logically dividing the readout channels into θ and φ windows as shown in figure 4.4 for the BMUO. The RMUO is covered by four sections.

Veto-wall signals indicating the passage of a muon from the beam halo inhibit triggers in the RMUO while CTD timing data reduce the cosmic background in the barrel to a manageable level. Coarse scale muon multiplicities are sent to the GFLTB: these give the number of muons found in left or right barrel and rear regions.

Veto-wall By virtue of its presence, this device (section 2.4.1) will reduce rates from beam-gas and beam-halo[39]. Apart from the veto signal to the RMUO described above, it is instrumented to set three flags. These will indicate to the GFLTB the presence of signal in the inner and outer scintillator planes and sum up such activity to produce a multiplicity.

Luminosity monitor The LUMI[40] continuously scans the energies of photons registered in its photon detector and of electrons in its other sub-component. The energies measured are sent to the GFLTB. The LUMIFLT raises a flag if the arrival times and the sum of the two energies are consistent with a bremsstrahlung event in the interaction region: Ee + Eγ = Ebeam. A photo-production flag indicates Ee in a proper window and photon energy below a threshold (in practice no deposit).

Leading proton spectrometer Horizontal and vertical position measurements will be made for the FLT in the last three stations (section 2.4.3). Coordinates in the three planes are linearly related for straight tracks from the interaction region (figure 4.5). Selection logic searches for valid spatial coincidences. Beam halo events however are expected to produce a rate of 3 kHz so this will not be a standalone trigger. By combination with an independent trigger the GFLTB will use the hit pattern from the LPS to obtain an additional background rejection factor.

Figure 4.5: LPS input to FLT: proton search.

#### 4.3.1.4 Global First Level Trigger Box

The GFLTB collates data from all participating components and performs calculations to make the final decision at this level on whether or not to accept an event. It also has test and calibration functions. It will send data to RC enabling online investigation of dead-time, luminosity etc.

To make an event decision, it performs logical operations of great complexity. These have been designed to a high level of sophistication in advance of data taking at ZEUS, but flexibility exists to make adjustments because it is certain that reality will differ to some extent from simulation.

The information from the components comes on 16-bit cables. Fifty-one 16-bit words of data arrive for every beam-crossing. This information is fed into a set of sub-triggers. The hardware allows for 64 such sub-triggers to be defined, all of which must eventually be combined into a single decision. The sub-triggers are grouped into several functional classes dealing with similar data as shown in figure 4.6.

Figure 4.6: Schematic of logic in the GFLTB.

An example of the kind of cross-matching possible in the global box may be seen from the diagram: isolated muons found in the calorimeter are correlated with tracks from the tracking detectors which may plausibly have been produced there by the same muon. Further, transverse energy from the calorimeter is multiplied by the track count from the tracking detectors: this quantity should be large for good events.

### 4.3.2 The Second Level Trigger

The SLT has access to a more complete and precise set of data than the FLT by virtue of the longer timescale on which it operates. It is currently envisaged[41] that the Global Second Level Trigger (GSLT) box[42], [43] will make an event decision available to components around 7 ms after the beam crossing. Unlike the FLT, the SLT is asynchronous: different parts of the system are at any given moment analyzing data which was not all acquired at the same time.

#### 4.3.2.1 Tracking Detector SLT

The algorithm for the CTDSLT[44], [45], [46], [47], [48] proceeds in two stages: segment finding[49] and track finding[50]. Segment finding is the grouping of hits in an eight wire cell to produce small portions of tracks: these are then combined to form a complete track. The pulse heights from the DSPs (section 3.2.3.1) will enable electron tracks to be identified when the events are fully reconstructed because their characteristic dE/dx differs from that of other charged particles.

Drift times are the input to the CTDSLT which resides on a network of transputers. These are microprocessors with four bidirectional communication channels which mean that a wide range of topologies are available. They have their own language (Occam[51]) which is designed to fully exploit the inherent parallelism of the networks.

For applications in the CTDSLT, factors of four improvements in time requirements have been measured using Occam[52] as compared to more conventional languages.

In axial SLs only, hits in each cell are examined to find track segments. Each cell is considered in turn, and the ‘single cell mask’ is stepped around the whole chamber.

‘Roads’ are defined so that the drift time at the nest wire is predicted from the previous hit on a segment. The gradient, intercept, variance and the mean z and r coordinates are passed on to the track finding stage.

The track finding sorts segments in overlapping octants making use of their angular values to consider groups likely to be on the same track. Three-dimensional tracks are formed from z-by-timing data associated with r segments via a straight line fit in rz. The CTDSLT will send two tables of results to the GSLT. Exit point and direction and pt will be available with error estimates for each track that has been found.

Also the charge and origin will be known. The vertex for the event as a whole is calculated, as is the total number of tracks found together with an estimate of how many tracks were missed (from the number of unused segments).

The present design of the FTDSLT envisages a tree search method which will be implemented in online memory. It will identify coordinate outputs from the chamber corresponding to straight tracks from the interaction region. It will require one cell hit in each layer: this corresponds to a polar angle requirement of 7° < theta < 30°. The FTDSLT should find all such tracks with momentum over 1 GeV/c coming from within 20 cm of the vertex.

#### 4.3.2.2 Calorimeter SLT

As is common in the SLT as a whole, transputer networks are used for readout and triggering[53].

Timing of energy deposition in the calorimeter is very precisely measured at the second level. Because the distance from the interaction region is not the same for the FCAL and the RCAL there will be a 2 ns difference in arrival times for good physics events. More importantly, most beam-gas events originate from upstream of the interaction point at negative z-coordinates. These are expected to produce a difference in arrival times of 12 ns[54]. This permits discrimination between physics and background. Prior to this enhancement of capability, the design called for those calorimeter towers around the active beam-pipe region to be disbarred from setting isolated electron bits because of the intolerable leakage rate that would result. With this timing information however it appears that this restriction may be relaxed thus improving efficiency. In addition, events with unphysical longitudinal momentum will be vetoed.

#### 4.3.2.3 Other SLT Components

Other components are in communication with the GSLTB. It is clearly to be expected that the quality and quantity of information available at the second level will in general be superior to that at the FLT.

GFLTB The GFLTB sends the results of its calculations to the GSLTB along with component data and the FC information.

BAC Eight-bit 10 MHz FADCs sum charges over two successive beam crossings. Two networks of transputers will be used: one will be in communication with the GSLT and the other with the EVB[55]. If an energy threshold is met, cluster data will be sent to the GSLT. Also, a muon trigger is formed from coincidence logic in the bottom yoke where there are no muon chambers. The data should in general be more precise than that from the BACFLT.

BMUON Coordinates of found muons should be available.

FMUON The FMUSLT will make an estimation of momentum from the sagitta of the particle found at the first level using the LT planes.

LPS A bit will be sent to the GSTLB to confirm or negate the LPSFLT. Further, a measurement of the proton momentum is made and is expressed as a fraction of the beam momentum. Horizontal and vertical projections of the transverse momentum of the proton are supplied.

LUMI The measurements made at the first level remain available. Further, the location of electromagnetic shower centers is measured and also photon shower centers if the bremsstrahlung flag is up.

VETO The number of hits and their positions should be available.

### 4.3.3 The Third Level Trigger

The composition of the code to be run at this level[56] has proved to be quite volatile. This is due to two factors. Firstly, there is great uncertainty as to the form of events, both background and physics, which will survive the first two levels of trigger. Because of the high efficiency with which these reject beam-gas, the entire Monte Carlo production which has taken place so far has resulted in only around 350 events (from a generated sample of 750,000). This is clearly not a large enough sample to base definitive conclusions on.

Secondly, the compute power available within resources at this level has fluctuated. The system is now based on Silicon Graphics (SGI) processors, the specification of which have quite considerably improved over time. Initially, it was thought that code would need to be written specially for this application: later it seemed that it would be possible to run the full offline reconstruction code online! At present, there has been some retreat from this bold position so that now it is envisaged that there will be some form of vertex rejection to eliminate remaining beam-gas before running the ‘offline’ code. Possibilities for this include pattern recognition or a helix fit to find tracks and look for upstream vertices. Use of CTD stereo layers will permit a better z-resolution so as to improve on the SLT. Also, the VXD data becomes available here for the first time. It is likely that most of the remaining beam-gas will have a vertex very close to the interaction region so improvement of the resolution here is the critical factor.

The TLT[57], [58], [59] is intimately linked to the Event builder (EVB). The EVB resides on transputer-based standard ‘VME’ boards similar to those of the GSLT and CALSLT.

The EVB assembles the events and makes them available in a Triple Port Memory. The TLT then reads events into SGI workstation memory. It is hoped that the SGI workstations will provide an online event display. These will also read out the EVB to IBM and VAX computers. The IBM will write events to tape with a rate of 0.5 Mb s-1. The speed with which this is possible is the final constraint on the whole of the trigger. Over 100 Gb will be accumulated during a year of operation.

The amount of processing time is a function of the input rate and the number of TLT nodes. It is currently envisaged that there will be 32 4D/35 processor nodes and 6 4D/25 machines handling communications. The time allowed per event is given by dividing the number of nodes by the number of events which must be handled every second: 32/100 = 0.32 s per event.

The VAX is the main Central Data Acquisition computer (CDAQ) and represents the interface between the experiment and operators in the control room. Many interlinked processes will run on the CDAQ VAX. Run control will start TLT processes and setup runs without human intervention. For monitoring purposes, RC will be connected to components down optical transputer links running from the rucksack to the control room. These will carry ‘analyse’, ‘reset’ and ‘error’ signals. Slow control will monitor parameters not varying on the timescales of beam crossings, such as temperatures in the racks housing readout electronics, cooling fan status and gas flow rates.

Categories

## ZEUS Detector Tracking Elements

Chapter 3

Tracking Elements of the ZEUS Detector

3.1 Introduction

Both of the experiments planned for HERA, ZEUS and H1, have specialized tracking detectors in the forward direction because of the beam asymmetry mentioned previously. At ZEUS, there are four separate tracking chambers. The system as a whole can take measurements of varying degrees of accuracy for tracks with polar angles between 7.5° and 170°.

All of the tracking detectors are wire drift chambers in which the passage of a charged particle leaves a trail of ionization. Anode wires in each chamber are equipped with electronics to readout pulses due to the arrival of charge produced by this ionization.

All of the chambers are designed to operate in a high magnetic field. This causes particle trajectories to bend thus enabling momentum measurement. The tracking detectors differ in their geometry and in gas mixture, field shape and strength depending on their location. In particular, the magnetic field is highly non-uniform in some regions and this has had to be taken into account.

Of the four detectors, the CTD and the Vertex Detector (VXD) are cylindrical while the Forward Detector (FDET) and Rear Tracking Detector (RTD) are planar. The VXD is smaller than the CTD and occupies the space between it and the beam-pipe. The FDET is a composite of two detectors, the Forward Tracking Detector (FTD) and the Transition Radiation Tracker (TRD).

3.2 The Central Tracking Detector (CTD)

3.2.1 Introduction

The CTD has an overall length of 240 cm with inner radius of 16.2 cm and outer radius of 85 cm. However some space must be left inside the chamber to house readout electronics, and allow for cabling and cooling requirements. The sense wires are strung along the 205 cm active length of the chamber between two 20 mm thick aluminum end-plates.

The requirements which the CTD was designed to satisfy are:

• Event triggering by vertex measurement (i.e. rejection of upstream gas), see section 5.2.
• High resolution momentum measurement of tracks.
• Identification of electrons by measurement of energy loss.

3.2.2 Mechanical Construction

The CTD[17] is radially subdivided into super-layers (SLs) which are numbered from one at the smallest radius to nine at the largest. Each SL thus forms an annular cylinder eight wires thick. There are two types of SL. In the axial SLs, the sense wires run parallel to the z-axis (see figure 3.1). In the stereo layers however a twist of 5° has been introduced corresponding to a two-cell displacement at the end-plates, in order to allow reconstruction of the z-coordinate of the tracks.

Within a SL, groups of eight sense wires are termed cells. The line of eight wires is at an angle of 45° to a radial line from the center of the chamber. This angle matches the Lorentz angle so as to maximize use of drift space. This geometry is shown in figure 3.2. There are 32 cells in SL1 with more in the outer SLs so that the cell size is roughly constant.

Cells consist of the eight sense wires plus a variety of other wires which are all designed to supply and shape the electric field within a cell such that electron drift trajectories are uniform. The maximum drift distance is 25.6 mm.

The uniform electrical field within each cell means that the drift velocity is independent of trajectory within the cell, simplifying reconstruction. It would be helpful if the drift velocity could be fixed such that the maximum drift time was small compared to the beam-crossing interval. This would minimize difficulties in identifying which crossing a particular track is associated with. This would indicate a small cell size, but this would then require a larger number of wires to be readout. So the cell size has been fixed at ca. 2.5 cm which maintains a small probability that two events will overlap in the same cell, satisfies the requirement that a not unreasonably large number of wires must be readout, and produces a maximum drift time of 500 ns.

There are a total of 4,608 sense wires in the CTD. It is necessary to terminate the wires in the 390 Ω characteristic impedance of the chamber in order to prevent pulses being reflected back into it. At the FTD end, this is done by a resistor network (for those wires not equipped with z-by-timing readout). At the RTD end, it is done by pre-amp. cards[18] which are designed to increase the signal strength.

The pre-amps are connected to 42 m long high quality coaxial cables which run through the drag-chain. This connects the chamber to the rucksack (section 2.4.4) which houses the majority of the electronics. Post-amp boards amplify the signals. At this point the readout chain splits into two with both parts simultaneously being fed data. Both parts are concerned with coordinate identification in different planes.

3.2.3.1 R-φ Coordinates

The pulses from the post-amps are sampled by 8 bit 104 MHz flash analogue-to-digital converters (FADCs). The results are continuously written to 512-location deep pipelines. On-board Digital Signal Processors (DSPs)[19] produce drift times and do pulse height/area analysis. [DSPs are microcomputers providing several MIPS of computing power and suited to high data through-puts.]

The radius of a hit is defined by the wire number. The coordinate may then be found from this and the drift time. There is, however, a left-right ambiguity. The drift time may be used to find the distance from the sense wire plane of the ionization causing it but not on which side of the wire it was produced. This has the effect that two sets of hits are found in each cell. Because of the 45° angle of the sense wire planes, one of these sets does not point to the interaction region and can be easily discarded. The design resolution is 100 μm.

3.2.3.2 Z-coordinate

There are two methods of measuring the remaining z-coordinate, with differing degrees of precision. All of the sense wires in SL1 and half of those in SL3 and SL5 are instrumented for z-by-timing.[20] Those wires which are instrumented have pre-amps at both ends of the chamber and corresponding post-amps in the rucksack. On a given wire, pulses arrive at different times at the two ends of the chamber depending on where along the wire the ionization was produced. Pre-amplifiers mounted on the chamber drive the signal along coaxial cable to the rucksack where post-amplifiers feed into constant fraction discriminator units. One end of the chamber has an extra 10 ns delay so that the pulses will always arrive in the same order. This enables time-to-amplitude conversion to take place based on charging a capacitor starting from the arrival of the start pulse and ending with the arrival of the stop pulse. The time difference is then proportional to the charge on the capacitor which is sampled by a FADC which has seven bits available to measure the z-coordinate. The design resolution is 3 cm.[21] The FADC data is sent to the pipeline (section 4.3.1), which is read out in the event of a trigger.

Secondly, the wires in the stereo layers enable a three-dimensional track fitting. The drift times for hits in the axial layers for a given track are clearly independent of its location in z. However, moving in the z-direction, the cells in the corresponding stereo layers appear to rotate. Correlating the shift in r coordinates allows a measurement of the z-coordinate. At present it is likely that this data will only be used in the full event reconstruction, where it should provide a resolution in z of 1.2 mm.

3.3 Forward Detector (FDET)

The FDET consists of three FTD sub-chambers with two TRD modules in the gaps between them.

3.3.1 The Forward Tracking Detector (FTD)

A drawing of a sub-chamber is shown in figure 3.3.

Figure 3.3: Sketch of an FTD sub-chamber.

The FTD is intended to complement the angular coverage of the CTD and is crucial in providing data relating to tracks close to the beam-pipe. Each of the FTD sub-chambers contains three readout planes, each containing more than a thousand wires. The sense wires are parallel to each other within a plane but there is a 60° offset between the planes to permit three dimensional hit location.

The Siegen group is designing 100 MHz FADC cards similar to those that have been produced for the CTD which will be used to readout the FTD. However, the design here will be simpler.

3.3.2 The Transition Radiation Detector (TRD)

Charged particles crossing an interface between materials having different dielectric properties will lose energy by emission of photons. These photons will in turn transfer energies to atomic electrons via excitation and ionization processes. In this way, if the original particle was sufficiently energetic, an electromagnetic shower may be built up.

The TRD relies on this phenomenon. It has two parts. Firstly there is a radiator stack which consists of a nitrogen filled polypropylene fiber mass. Photons are produced here. A second stage is a drift chamber. The photons leave the radiator stack and enter a drift/amplification region. This part of the chamber is filled with xenon and the photons will excite atomic electrons which will cause an avalanche by further interactions. The shower results in an anode pulse which is read out by FADCs as in the CTD. The primary purpose of the TRD is to permit electron tagging. Transition radiation is not produced by π’s with momentum below 40 GeV/c[22] so while π’s and electrons have similar dE/dx characteristics the pulse shapes produced will differ. This should allow the TRD to distinguish between the two with a discrimination factor of 100 (for electrons with energies between 1 GeV and 30 GeV).

3.4 The Rear Tracking Detector (RTD)

The RTD is basically identical to one FTD sub-chamber but of slightly smaller size. Its sensitive volume extends down to 10° in the rear direction.

3.5 The Vertex Detector (VXD)

In order to obtain improved resolution, the design of the VXD progressed assuming the use of a ‘slow’ gas; dimethyl ether was chosen. This then meant that the cell size would be smaller than in the CTD in order to restrict drift times to a reasonable length. Constraining the number of readout channels led to a maximum drift time of 500 ns over a distance of no more than 3.6 mm. There are twelve sense wires at 3 mm intervals in a VXD cell.

Taken in conjunction with the CTD, the VXD will improve the resolution with which tracks coming from the interaction region may be measured. The design goal is to improve the resolution on the impact parameter to 50 μm or better. This enhances the prospects of identifying particles with short lifetimes which decay before they leave the interaction region. If this occurs, the VXD may be able to separate tracks coming from the interaction in which the short-lived particle was created, and those coming from the point at which it decayed. There will be no z information from the VXD.

Categories

## ZEUS Detector: Non-Tracking Elements

Chapter 2

Non-Tracking Elements of the ZEUS Detector

2.1 Introduction

The ZEUS detector consists of three main types of detector: those which are sensitive to charged tracks, those that measure energy deposition and those which identify muons. The UK’s major responsibility on ZEUS is the Central tracking Detector (CTD). Because of this and the fact that a large part of the work outlined in this thesis has been connected with tracking components, their description deserves a separate chapter, which follows.

The tracking detectors reside in the inner region close to the interaction point. The remaining major components fall into two functional classes: calorimetry and muon detection. The most significant characteristic common to all groups of components results from the substantial asymmetry in the beam energies at HERA. The forward direction is defined to be the one in which the proton moves. Clearly it is therefore to be expected that the forward hemisphere will be the more active. For this reason components here are more sophisticated than their near region counterparts. An overview of the detector is shown in figure 2.1.

Figure 2.1: Section through the ZEUS detector along the beam-line.

2.2 Calorimetry

2.2.1 Introduction

The purpose of the calorimeter is to investigate jet properties by measuring their energy deposition. The design aims to cover the full solid angle so far as is consistent with the presence of the beam-hole. It allows for the discrimination of jet angles with resolution of better than 10 mrad. Discrimination between hadrons and electrons is foreseen. The resolution on the jet energy should be

The calorimeter at ZEUS has been designed to be ‘compensating’ i.e. it will give the same response per unit energy irrespective of whether the depositing particle is electromagnetic or hadronic. This reduces the systematic error in the energy measurement, as can be seen from the following example. In a given event π0 decay leads predominantly to electromagnetic showers via π0 → 2γ whereas charged π’s will give a hadronic deposition. So in an uncompensated calorimeter the measurement of a set of events with the same energy would depend on the ratio of charged to uncharged π’s in the events.

ZEUS has adopted a compensating calorimeter of depleted uranium/scintillator design. Here the high-Z absorber plates are interleaved with plastic scintillator tiles which are read out by photomultiplier tubes. Achievement of compensation requires careful consideration of the layer thicknesses because of the different cross-sections for the various processes via which hadronic and electromagnetic particles lose energy.

The calorimeter is made up of a large number of cells which are of two types: electromagnetic or hadronic. These are referred to as EMCs or HACs. Figure 2.2 shows the arrangement of cells. Electrons are less penetrating than hadrons and will thus predominantly interact in the EMCs which are the first part of the calorimeter to be encountered by particles emanating from the interaction region. There are two layers of HACs behind these in the FCAL and the BCAL and one layer in the RCAL.

Figure 2.2: Arrangement of cells in the calorimeter.

2.2.2 Forward, Rear, Barrel Calorimeter (F/R/BCAL)

The calorimeter has three major sections. Their coverage in terms of polar angle and depth is shown in table 2.1. Depth is measured in radiation lengths, X0, over which distance the energy of an electron will be reduced by a factor of e. It can be seen that there is some angular overlap between sections.

Each section has one interaction length of EMC at its face closest to the interaction point. Behind that, the layer of HACs varies from ca. 6 λ in the forward direction to ca. 3 λ in the rear. For readout purposes, cells are grouped into ‘towers’. In the FCAL and RCAL these are non-projectives as are the BHAC towers. Tower sizes are shown in table 2.2.

2.2.3 Backing Calorimeter (BAC)

The BAC, together with the iron return yoke, is between the inner and outer muon chambers. It is designed to be complementary to the main calorimeter and the muon chambers. It will allow measurement of late-showering particles and it will provide a muon trigger in the bottom yoke where there will be no muon chambers.

There will be around nine layers of BAC modules depending on the exact location. The layers are made up of either seven or eight tubes which each contain one gold/tungsten wire and use an argon/CO2 gas mixture. Four modules will be grouped on readout into towers of around 50 cm x 50 cm base and summed in depth. The final position resolution should be 1.3 mm and the design energy resolution for hadrons is σ(E)/E approximately = 100%/√E.

Silicon pad detectors will be mounted on ceramic cards which lie a few radiation lengths inside the EMC parts of the calorimeter. The separator is based on diodes with a small (3 cm x 3 cm) active area. This improves segmentation and thus position resolution.

The diodes are operated in depleted mode. The passage of a charged particle creates many charge carriers. The resulting pulse is readout and is of different heights for electrons and hadrons even if they are of the same energy. The ability of the calorimeter as a whole to distinguish electrons is therefore improved. Using only HES data, electron identification efficiency of 90% should be obtainable with only 4% hadronic contamination.

2.3 Muon Detectors

2.3.1 The Forward Muon Detector (FMUON)

This component is based on a toroidal magnet. Its detectors comprise streamer tubes and drift chambers, both of which measure ionization, and a time-of-flight (TOF) plane between the two toroids. It comprises in addition to two ‘wall’ sections (LW1,2) a ‘spectrometer’ section with five detector planes. These five planes are labeled LT1 to LT5. Particles from the interaction region encounter the wall sections first and then the spectrometer. The walls provide overlap of angular coverage with the BMUON. The planar sections are divided into eight sectors in φ. The TOF plane consists of sixteen elements, each are made up of a pair of scintillation counters separated by 10 cm.

This component will provide small angle muon momentum resolution of 20%. This information is essential to complement tracking detector data. The purpose of the TOF plane is to ensure that particles are not associated with an incorrect beam crossing.

2.3.2 Barrel/Rear Muon Detectors (B/RMUO)

There are two sets of eight chambers in the barrel section, which thus has an octagonal cross-section looking down the beam-line in which the inner and outer octagons are separated by the magnetized iron yoke and and the backing calorimeter. The RMUO has two parts, inner and outer, each of which has a depth of one chamber. A chamber consists of two doublets of streamer tubes which are parallel to the beam-line in the barrel and are placed horizontally in the RMUO. These are readout by time-to-digital converters. Analog readout of strips in the orthogonal dimension is available in both cases.

2.4 Other Elements

2.4.1 The Veto-wall (VETO)

This is a large iron wall seven meters in front of the interaction region which has a hole in it through which the proton beam passes. It has hodoscopes on each side consisting of forty-eight individual scintillation counters. There is a ‘halo’ of protons not following the nominal beam trajectory and these may produce highly penetrative muons by collision with machine elements. The main purpose of the veto-wall is to veto these events and thus reduce the rate of spurious triggers in the detector.

2.4.2 The Luminosity Monitor

The measurement of cross-sections is of primary importance at ZEUS. This requires monitoring to arrive at the figure for time integrated luminosity. It is essential also to have the information online so as to be able to optimize the luminosity in the interaction region. In order to do this, the LUMI uses the process of photon emission from the interaction of the two beams ep → epγ. Also, the LUMI will identify photo-production processes by tagging small-angle electrons.

The detector itself has two parts, an electron detector near the electron beam at z = -36 m and a photon (γ) detector around the proton beam at z = – 108 m. The electron detector is a shielded lead/scintillator sandwich. The γ-detector is based on a γ-calorimeter which consists of layers of 1 cm2 silicon pads. A photon causes a shower of electrons through them permitting precise position measurement. A Čerenkov counter to veto electrons is included in the design; a prototype has been built using a 150 cm thickness of polyurethane foam.

It is expected[16] that in 25% of DIS events, the proton will interact diffractively, retaining its identity and losing momentum. If this happens, it may then leave the beam-pipe and be measured by the LPS with efficiency ca. 0.6 at the most favorable momentum.

The LPS will have six detector stations along the proton line between z = +24 m and z = +90 m as shown in figure 2.3. These will be based on turret extensions into which ‘pots’ can be inserted. Pots contain detector elements: their purpose is to allow for precise control of location of the detectors over the last few centimeters close to the beam-pipe.

The first three stations will have a single pot and the last three will be double pot assemblies. The single pots will be horizontal with respect to the beam-line and the double pots will be vertical. The exact location of the detectors is important because it determines the proton phase space acceptance of the LPS.

Each pot will contain a detector element comprising seven planes of silicon micro-strips with differing orientations to provide two-dimensional measurement and will be shaped to fit closely to the beam-pipe. The total area covered by the strips will be 1,560 cm2.

Figure 2.3: The LPS stations along the straight section of the beam-line.

2.4.4 Rucksack

The immediate environment of the detector is hostile to electronics owing to radiation from the uranium in the calorimeter and to proximity to the beam. Also, space is at a premium. Large systems of electronics are required however in order to read out the detector components and implement triggers. These factors have resulted in the inclusion in the design of a ‘rucksack’ which is simply a mobile construction of three floors each of which contains racks and space for the associated requirements in terms of cooling and safety.

The rucksack is connected to the components via a drag-chain which is designed to carry cables for readout. The rucksack must be mobile. This is because the yoke – the large iron clam-shells and the BMUO/BAC – retracts to allow access to the inner detectors. The rucksack moves in the same rails in which the yoke runs.

2.4.5 Solenoid

A magnetic field must be supplied in the region of the tracking detectors so that charged tracks will bend in it and thus their momentum may be measured. A 1.9 m diameter superconducting solenoid is located between the calorimeter and the CTD in order to supply this. It is required to supply a field of 1.8 T within two major design constraints. Firstly, the electron beam trajectory is very sensitive to variation in the B-field and so non-uniformities must be as small as possible. For example, the axis of the field must be centered to within +/- 1 mm.

Secondly, the structure of the solenoid must not present a large amount of material to the passage of electrons and photons as this would introduce an unacceptable systematic error in calorimeter measurements. Therefore the design goal states that at an angle of 90° the solenoid should have a thickness of less than 0.9 radiation lengths.