- Email: [email protected]
The RICH in the LHCb trigger
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 553 (2005) 152–156 www.elsevier.com/locate/nima
The RICH in the LHCb trigger Niko Neufeld, for the LHCb Collaboration CERN, Geneva, Switzerland Available online 30 August 2005
Abstract This paper presents the LHCb trigger system with an emphasis on the use of RICH data in the software triggers. A global and a local algorithm for fast particle ID are discussed and results of performance measurements are given, which show that complex RICH pattern recognition is well within the time budget of the LHCb trigger computer farm. r 2005 Elsevier B.V. All rights reserved. PACS: 29.85.c Keywords: Pattern recognition; Particle identification; Trigger
1. Introduction LHCb is a detector dedicated to the highprecision study of the CP violation in the decay of B hadrons [1]. It will run at the LHC at CERN starting in 2007 at a nominal luminosity of 2:0 1032 cm2 s1 . The cross-section for the signal at the LHC energy is 500 mb, the total cross-section is 100 mb. A powerful trigger system is required to select the interesting signal events from the huge background. To measure the tiny CP-violating effects requires furthermore particle identification, in particular to identify kaons and pions.
In this paper, the trigger is shortly reviewed, emphasizing the flexibility and the resources available for sophisticated processing. The second part describes two strategies using RICH data for fast hadron identification within the trigger-algorithms.
2. The three levels of the LHCb trigger The visible interaction rate1 in LHCb is 10 MHz, compared to the bunch-crossing rate of the LHC of 40 MHz. A fully synchronous and pipe-lined first level trigger (‘‘Level-0’’) is implemented in custom hardware. It uses calorimeter
E-mail address: [email protected]. 0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.08.042
1
Defined by some minimal activity in the spectrometer.
ARTICLE IN PRESS N. Neufeld / Nuclear Instruments and Methods in Physics Research A 553 (2005) 152–156
and muon detector information to reconstruct high-pt objects and uses this information together with a measurement of the charged multiplicity and the number of primary vertices to reduce the accepted event rate to 1 MHz. The second and third level of the LHCb trigger are software-triggers running on a large farm of commodity CPUs. The first level software trigger (‘‘Level-1’’) uses information from the Vertex Locator, part of the silicon tracking detector (for a rough momentum reconstruction) and a summary information from the preceding trigger level. It reconstructs primary vertices and the impact parameters of tracks to these vertices. This is used to reject almost all of the minimum bias background and reduces the rate to 40 kHz. During the running time of this trigger algorithm all data must be stored in the detector front-end.2 When an event is accepted the complete detector data, including the RICH, are read and fed into the second level software trigger (High Level Trigger or ‘‘HLT’’). This trigger uses the—now available—complete tracking information for a more precise measurement of the impact parameters, thus repeating and improving the algorithm used at the preceding level. This reduces the accepted rate of events to 10 kHz at which a more exclusive selection starts. Finally some 2 kHz are recorded to tape. 200 Hz of ‘‘hot’’ specially promising events are promptly fully reconstructed and made available for immediate analysis. The LHCb trigger system is shown in Fig. 1. The custom hardware of the Level-0 is described in [2] and the references therein. The hardware used for running the two levels of software trigger is described in Refs. [2,3]. It consists of a large switching network using the standard Ethernet Local Area Network technology and a large farm of PCs. A custom system is used to distribute the trigger decisions and event destinations to the front-end electronics boards. They use this information to serve the nodes in the CPU farm in a round-robin fashion with event-data for a trigger-
2
The maximum time for the Level-1 algorithm is thus limited by the buffer-size in the front-end electronics, which corresponds to 58 ms.
153
Fig. 1. The LHCb trigger.
algorithm. The same infrastructure is used for ‘‘Level-1’’ and ‘‘HLT’’.
3. Using RICH information in the trigger The high level trigger of LHCb involves the selection of exclusive B decay modes by checking the invariant mass-combinations of 2–6 tracks. An þ þ þ example is Bs ! Dþ s Ds ! K K p K K p . Typically there are 30 tracks to be considered. If the selection is based only on the charge 156 107 combinations need to be tested. Using K=p identification the number of combinations, which must be tested could be reduced to 24 102 103 . Using the methods described in the following sections, the time required for the necessary particle identification can be reduced by a factor 4 compared to the standard ‘‘offline’’ algorithm and takes only 3.7 ms. This compares
ARTICLE IN PRESS 154
N. Neufeld / Nuclear Instruments and Methods in Physics Research A 553 (2005) 152–156
well with the time-budget available in the ‘‘HLT’’ of 60 ms.3 In the following first a description of the pattern recognition is given, the speeding up of which is the key ingredient to what follows in the next sections: a local algorithm PID based on the treatment of individual tracks and a global PID algorithm, which treats all tracks at once. 3.1. Parameterizing the geometry To relate the position of a photon detected on the hybrid photon detector (HPD [4]) to an angle between track and the emitted Cherenkov photon requires the solution of a quartic equation [5] due to the optics of the RICH system. This is computationally quite expensive. Currently, this is estimated to take up to half a second. This can clearly not be done, even at a low rate, in the trigger within the resources available. To overcome this problem a different approach for estimating the effect of the detector geometry on the Cherenkov rings has been chosen. Fig. 2 shows the hit pixels on the HPD planes, where the crosses mark the impact point of the tracks as if they were reflected. Simulated photons are tracked through the detector to the HPD plane. These photons are emitted at a fixed yC ¼ 30 mrad and uniformly distributed in the azimuthal angle f. Afterwards the effect of the optics on each photon can be determined by calculating the radius r of each photon with respect to the impact of the track they were emitted from. Using the mean radius, r¯, one can plot the distortion of the rings as a function of f. This is shown in Fig. 3. All rings show approximately the same distortion which can be fitted to be dr ¼ A cosð2fÞ ðA 2:5 mmÞ To correct for the optics one has
ray-trace a few photons through the radiator to determine the mean radius. apply the correction: yC ¼ 30r=ð¯r A cosð2fÞÞ mrad.
The resulting resolution on yC is good, 0.7 mrad, to be compared with the expected resolutions from
Fig. 2. Rings of Cherenkov photons, emitted at yC ¼ 30 mrad on the HPD plane (dots). The center of the HPD plane is the origin of the coordinate system. The reflected impact points of tracks are indicated with crosses.
Fig. 3. Ring-distortion as a function of the mean radius.
the radiators, between 0.58 and 2.0 mrad. yC is shown in Fig. 4. 3.2. A track-based (local) particle ID algorithm Each track is taken in turn, and only a ‘‘heavy’’/ ‘‘light’’ differentiation is done.4 A peak search is performed within a 2s window for the signal and 4s window for the background by maximizing
3
This corresponds to the time needed for the algorithm on a reference 1 GHz Pentium III CPU. On a 2007 CPU this time should be between 10 and 20 ms.
4 Everything lighter than a kaon is treated as pion, everything heavier as a kaon.
ARTICLE IN PRESS N. Neufeld / Nuclear Instruments and Methods in Physics Research A 553 (2005) 152–156
155
Table 1 Efficiencies () of local PID for 0ppp100 GeV=c
Rejecting pions Selecting kaons
K –K
p –K
90% 44%
44% 8%
K 1
Efficiency
0.8
0.6
0.4
Fig. 4. Resolution of yC for simulated photons. 0.2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S B= ð1 þ BÞ, where S is the signal and B the background peak, respectively. There are two possible strategies. One aims at rejecting pions by cutting on ðrS=Bmax rtruepion Þ. Here rS=Bmax is the Cherenkov ring radius. This approach has a high efficiency but a rather poor purity. The other strategy selects kaons by taking a band around ðrS=Bmax rtruekaon Þ. This has a worse efficiency for kaons but a greater purity. Table 1 summarizes the performance of the local method.
0
π
0
20
40 60 Momentum (GeV/c)
80
100
Fig. 5. Performance of online global algorithm.
The likelihood is computed first assuming all tracks to be pions. Then each in turn is changed to a kaon. The track which gives the largest increase in likelihood is fixed to be kaon. This is repeated until no further increase can be gained.
3.3. A global particle ID algorithm The main difficulty for any ‘‘local’’ algorithm is the treatment of below-threshold tracks: it is impossible to ‘‘compare’’ the w2 of a ring above the threshold to no ring. This is can be overcome by looking at the overall (‘‘global’’) event likelihood, as is done in the ‘‘offline’’ algorithm [5]. The following are the main steps:
Photon hits are assigned to the track with the closest ring image only within a tunable radius depending on the resolution s of the yC . P The event likelihood is calculated from the w2 of all hit pixels relative to the track they are assigned to. Per ring a term P ¼ en nn =n! is added where n is the number of hits on the ring and n the expected number of hits.
Tuning the K-efficiency to 95% keeps the p misidentification rate at 26%. This is shown in Fig. 5. From the figure it is also clear that the difficulty lies in the low momentum region. Restricting the sample to tracks with momenta 45 GeV=c gives a misidentification rate of 9%. For comparison Fig. 6 shows the performance of the offline algorithm, also tuned to 95% kaon efficiency. It shows that the online method performs very well at considerably lower computational costs: the algorithm takes 3.7 ms5 for all 5 This is time for the algorithm alone, not accounting for the necessary decoding of the raw-data. Including the decoding the total time is 18 ms. It should be noted that most of the decoding will have to be done in any case.
ARTICLE IN PRESS N. Neufeld / Nuclear Instruments and Methods in Physics Research A 553 (2005) 152–156
156
CPUs. Using new very fast techniques for patternrecognition allows even taking advantage of RICH pattern-recognition in the real-time environment of the software trigger. Two algorithms have been developed based on this pattern recognition. Both are fast, the global treatment of all tracks and photons simultaneously is superior in pion rejection efficiency. The availability of fast pion/kaon separation in the HLT will allow a relaxation of other selection cuts and opens the possibility to pursue more inclusive selections.
K
1
Efficiency
0.8
0.6
0.4
0.2
π
0 0
20
40 60 Momentum (GeV/c)
80
100
Fig. 6. Performance of offline global algorithm.
tracks compared to almost 250 ms for the offline procedure.
4. Conclusions LHCb has a powerful three-level trigger system to select the rare CP-violating decays of B hadrons at the LHC. Maximum flexibility is achieved by running most of the trigger on general-purpose
References [1] LHCb Collaboration, Reoptimized Detector Design and Performance, No. 2003-030 in CERN/LHCC, CERN, Geneva, Switzerland, 2003. [2] LHCb Collaboration, Trigger System Technical Design Report, No. 2003-031 in CERN/LHCC, CERN, Geneva, Switzerland, 2003. [3] LHCb Collaboration, Online System Technical Design Report, No. 2001-040 in CERN/LHCC, CERN, Geneva, Switzerland, 2001. [4] N. Kanaya, Performance study of the pixel hybrid photon detectors for the LHCb RICH, in: these proceedings, 2004. [5] R. Forty, O. Schneider, RICH Pattern Recognition, Technical Report LHCb-98-040, CERN (1998).
Nuclear Instruments and Methods in Physics Research A 553 (2005) 152–156 www.elsevier.com/locate/nima
The RICH in the LHCb trigger Niko Neufeld, for the LHCb Collaboration CERN, Geneva, Switzerland Available online 30 August 2005
Abstract This paper presents the LHCb trigger system with an emphasis on the use of RICH data in the software triggers. A global and a local algorithm for fast particle ID are discussed and results of performance measurements are given, which show that complex RICH pattern recognition is well within the time budget of the LHCb trigger computer farm. r 2005 Elsevier B.V. All rights reserved. PACS: 29.85.c Keywords: Pattern recognition; Particle identification; Trigger
1. Introduction LHCb is a detector dedicated to the highprecision study of the CP violation in the decay of B hadrons [1]. It will run at the LHC at CERN starting in 2007 at a nominal luminosity of 2:0 1032 cm2 s1 . The cross-section for the signal at the LHC energy is 500 mb, the total cross-section is 100 mb. A powerful trigger system is required to select the interesting signal events from the huge background. To measure the tiny CP-violating effects requires furthermore particle identification, in particular to identify kaons and pions.
In this paper, the trigger is shortly reviewed, emphasizing the flexibility and the resources available for sophisticated processing. The second part describes two strategies using RICH data for fast hadron identification within the trigger-algorithms.
2. The three levels of the LHCb trigger The visible interaction rate1 in LHCb is 10 MHz, compared to the bunch-crossing rate of the LHC of 40 MHz. A fully synchronous and pipe-lined first level trigger (‘‘Level-0’’) is implemented in custom hardware. It uses calorimeter
E-mail address: [email protected]. 0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.08.042
1
Defined by some minimal activity in the spectrometer.
ARTICLE IN PRESS N. Neufeld / Nuclear Instruments and Methods in Physics Research A 553 (2005) 152–156
and muon detector information to reconstruct high-pt objects and uses this information together with a measurement of the charged multiplicity and the number of primary vertices to reduce the accepted event rate to 1 MHz. The second and third level of the LHCb trigger are software-triggers running on a large farm of commodity CPUs. The first level software trigger (‘‘Level-1’’) uses information from the Vertex Locator, part of the silicon tracking detector (for a rough momentum reconstruction) and a summary information from the preceding trigger level. It reconstructs primary vertices and the impact parameters of tracks to these vertices. This is used to reject almost all of the minimum bias background and reduces the rate to 40 kHz. During the running time of this trigger algorithm all data must be stored in the detector front-end.2 When an event is accepted the complete detector data, including the RICH, are read and fed into the second level software trigger (High Level Trigger or ‘‘HLT’’). This trigger uses the—now available—complete tracking information for a more precise measurement of the impact parameters, thus repeating and improving the algorithm used at the preceding level. This reduces the accepted rate of events to 10 kHz at which a more exclusive selection starts. Finally some 2 kHz are recorded to tape. 200 Hz of ‘‘hot’’ specially promising events are promptly fully reconstructed and made available for immediate analysis. The LHCb trigger system is shown in Fig. 1. The custom hardware of the Level-0 is described in [2] and the references therein. The hardware used for running the two levels of software trigger is described in Refs. [2,3]. It consists of a large switching network using the standard Ethernet Local Area Network technology and a large farm of PCs. A custom system is used to distribute the trigger decisions and event destinations to the front-end electronics boards. They use this information to serve the nodes in the CPU farm in a round-robin fashion with event-data for a trigger-
2
The maximum time for the Level-1 algorithm is thus limited by the buffer-size in the front-end electronics, which corresponds to 58 ms.
153
Fig. 1. The LHCb trigger.
algorithm. The same infrastructure is used for ‘‘Level-1’’ and ‘‘HLT’’.
3. Using RICH information in the trigger The high level trigger of LHCb involves the selection of exclusive B decay modes by checking the invariant mass-combinations of 2–6 tracks. An þ þ þ example is Bs ! Dþ s Ds ! K K p K K p . Typically there are 30 tracks to be considered. If the selection is based only on the charge 156 107 combinations need to be tested. Using K=p identification the number of combinations, which must be tested could be reduced to 24 102 103 . Using the methods described in the following sections, the time required for the necessary particle identification can be reduced by a factor 4 compared to the standard ‘‘offline’’ algorithm and takes only 3.7 ms. This compares
ARTICLE IN PRESS 154
N. Neufeld / Nuclear Instruments and Methods in Physics Research A 553 (2005) 152–156
well with the time-budget available in the ‘‘HLT’’ of 60 ms.3 In the following first a description of the pattern recognition is given, the speeding up of which is the key ingredient to what follows in the next sections: a local algorithm PID based on the treatment of individual tracks and a global PID algorithm, which treats all tracks at once. 3.1. Parameterizing the geometry To relate the position of a photon detected on the hybrid photon detector (HPD [4]) to an angle between track and the emitted Cherenkov photon requires the solution of a quartic equation [5] due to the optics of the RICH system. This is computationally quite expensive. Currently, this is estimated to take up to half a second. This can clearly not be done, even at a low rate, in the trigger within the resources available. To overcome this problem a different approach for estimating the effect of the detector geometry on the Cherenkov rings has been chosen. Fig. 2 shows the hit pixels on the HPD planes, where the crosses mark the impact point of the tracks as if they were reflected. Simulated photons are tracked through the detector to the HPD plane. These photons are emitted at a fixed yC ¼ 30 mrad and uniformly distributed in the azimuthal angle f. Afterwards the effect of the optics on each photon can be determined by calculating the radius r of each photon with respect to the impact of the track they were emitted from. Using the mean radius, r¯, one can plot the distortion of the rings as a function of f. This is shown in Fig. 3. All rings show approximately the same distortion which can be fitted to be dr ¼ A cosð2fÞ ðA 2:5 mmÞ To correct for the optics one has
ray-trace a few photons through the radiator to determine the mean radius. apply the correction: yC ¼ 30r=ð¯r A cosð2fÞÞ mrad.
The resulting resolution on yC is good, 0.7 mrad, to be compared with the expected resolutions from
Fig. 2. Rings of Cherenkov photons, emitted at yC ¼ 30 mrad on the HPD plane (dots). The center of the HPD plane is the origin of the coordinate system. The reflected impact points of tracks are indicated with crosses.
Fig. 3. Ring-distortion as a function of the mean radius.
the radiators, between 0.58 and 2.0 mrad. yC is shown in Fig. 4. 3.2. A track-based (local) particle ID algorithm Each track is taken in turn, and only a ‘‘heavy’’/ ‘‘light’’ differentiation is done.4 A peak search is performed within a 2s window for the signal and 4s window for the background by maximizing
3
This corresponds to the time needed for the algorithm on a reference 1 GHz Pentium III CPU. On a 2007 CPU this time should be between 10 and 20 ms.
4 Everything lighter than a kaon is treated as pion, everything heavier as a kaon.
ARTICLE IN PRESS N. Neufeld / Nuclear Instruments and Methods in Physics Research A 553 (2005) 152–156
155
Table 1 Efficiencies () of local PID for 0ppp100 GeV=c
Rejecting pions Selecting kaons
K –K
p –K
90% 44%
44% 8%
K 1
Efficiency
0.8
0.6
0.4
Fig. 4. Resolution of yC for simulated photons. 0.2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S B= ð1 þ BÞ, where S is the signal and B the background peak, respectively. There are two possible strategies. One aims at rejecting pions by cutting on ðrS=Bmax rtruepion Þ. Here rS=Bmax is the Cherenkov ring radius. This approach has a high efficiency but a rather poor purity. The other strategy selects kaons by taking a band around ðrS=Bmax rtruekaon Þ. This has a worse efficiency for kaons but a greater purity. Table 1 summarizes the performance of the local method.
0
π
0
20
40 60 Momentum (GeV/c)
80
100
Fig. 5. Performance of online global algorithm.
The likelihood is computed first assuming all tracks to be pions. Then each in turn is changed to a kaon. The track which gives the largest increase in likelihood is fixed to be kaon. This is repeated until no further increase can be gained.
3.3. A global particle ID algorithm The main difficulty for any ‘‘local’’ algorithm is the treatment of below-threshold tracks: it is impossible to ‘‘compare’’ the w2 of a ring above the threshold to no ring. This is can be overcome by looking at the overall (‘‘global’’) event likelihood, as is done in the ‘‘offline’’ algorithm [5]. The following are the main steps:
Photon hits are assigned to the track with the closest ring image only within a tunable radius depending on the resolution s of the yC . P The event likelihood is calculated from the w2 of all hit pixels relative to the track they are assigned to. Per ring a term P ¼ en nn =n! is added where n is the number of hits on the ring and n the expected number of hits.
Tuning the K-efficiency to 95% keeps the p misidentification rate at 26%. This is shown in Fig. 5. From the figure it is also clear that the difficulty lies in the low momentum region. Restricting the sample to tracks with momenta 45 GeV=c gives a misidentification rate of 9%. For comparison Fig. 6 shows the performance of the offline algorithm, also tuned to 95% kaon efficiency. It shows that the online method performs very well at considerably lower computational costs: the algorithm takes 3.7 ms5 for all 5 This is time for the algorithm alone, not accounting for the necessary decoding of the raw-data. Including the decoding the total time is 18 ms. It should be noted that most of the decoding will have to be done in any case.
ARTICLE IN PRESS N. Neufeld / Nuclear Instruments and Methods in Physics Research A 553 (2005) 152–156
156
CPUs. Using new very fast techniques for patternrecognition allows even taking advantage of RICH pattern-recognition in the real-time environment of the software trigger. Two algorithms have been developed based on this pattern recognition. Both are fast, the global treatment of all tracks and photons simultaneously is superior in pion rejection efficiency. The availability of fast pion/kaon separation in the HLT will allow a relaxation of other selection cuts and opens the possibility to pursue more inclusive selections.
K
1
Efficiency
0.8
0.6
0.4
0.2
π
0 0
20
40 60 Momentum (GeV/c)
80
100
Fig. 6. Performance of offline global algorithm.
tracks compared to almost 250 ms for the offline procedure.
4. Conclusions LHCb has a powerful three-level trigger system to select the rare CP-violating decays of B hadrons at the LHC. Maximum flexibility is achieved by running most of the trigger on general-purpose
References [1] LHCb Collaboration, Reoptimized Detector Design and Performance, No. 2003-030 in CERN/LHCC, CERN, Geneva, Switzerland, 2003. [2] LHCb Collaboration, Trigger System Technical Design Report, No. 2003-031 in CERN/LHCC, CERN, Geneva, Switzerland, 2003. [3] LHCb Collaboration, Online System Technical Design Report, No. 2001-040 in CERN/LHCC, CERN, Geneva, Switzerland, 2001. [4] N. Kanaya, Performance study of the pixel hybrid photon detectors for the LHCb RICH, in: these proceedings, 2004. [5] R. Forty, O. Schneider, RICH Pattern Recognition, Technical Report LHCb-98-040, CERN (1998).