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

6.2.2 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 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. 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

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.

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By Tim Short

I am a former investment banking and securitisation specialist, having spent nearly a decade on the trading floor of several international investment banks. Throughout my career, I worked closely with syndicate/traders in order to establish the types of paper which would trade well and gained significant and broad experience in financial markets.
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