1. Hongyu Fu, Trigger group 01-6-26 The Monte Carlo for Trigger Design of BES3 Scintillating Fibre BEMC Outline: Introduction to BES3 Scin-fibre BEMC Trigger Monte Carlo Procedures Results and Discussion

2. Introdution to BES3 Detector and BEMC Geometry of BEMC – 24 equi-lateral detector modules,aligned along phi, BEMC cross section is regular polygon of 24 sides. – Inner radius is 123.5cm – 160 fibre and 160 Pb layers, thickness=19.2cm

3. Positioning of Other Detectors and Material Layers When doing Monte Carlo with geant,the following detectors and materials are considered: – VC – MDC4 – BTOF – ETOF – ECAL – magnetic iron

4. Geometry of BEMC and BES3

5. Monte Carlo Data Production – Use geant to produce detector simulation data, 8kgauss uniform magnetic field along z – 1cm long fibre section is defined as a hit spot(detector cell) – A hit info includes its deposited energy, time and position information – Position info includes in which module, which fibre layer, which fibre and which fibre section the hit lies Monte Carlo and Data Analysis Procedures

6. The Further Processing of Monte Carlo Data The geant output data merely give energy deposit, time of flight and position info of each hit, not the output signal at detector ends. It is necessary to sample randomly according to different distribution and constants, then group hit info into front- end electronics readout signals and trigger channel signals. – Randomize energy information 1. Sample hit energy to photons, 30photon/MeV to two ends, according to poisson distribution 2. Photons exponentially attenuate to detector ends, =3.0m 3. Group photons into FEE cells, and sample binomially to p.e, PMT quantum efficiency=20% 4. Change p.e to equivalent energy, to convenience analysis and comparison

7. 1. With energy as weight,calculate FEEcell energy deposit centre z and its RMS, randomize z according to gaussian distribution 2. Calculate FEEcell time of flight (tof) similarly, adding light transmission time(calculated with z) in detector, is FEE time readout 1. Phi-direction, 12columns/module 2. R-direction, 8rows/module 3. 12*8=96 FEEcells in one module – Randomization of time and z position – FEEcell division

8. FEEcells in one detector module

9. The Selection of Trigger Cell Size – Make energy of one cluster deposit in one trigger cell as much as possible – Small trigger cell to reduce influence of multi-hit Results and Discussion Selection rules: Two indices are used to decide trigger cell size: – Phi width of energy deposit in fibre of a particle. Use 0.3GeV/c electron, because it has max phi-width of energy deposit. – The ratio of the energy of the trigger cell that has max energy deposit to total energy deposit

10. 0.3GeV/c electron,hit at a module centre, phi-direction energy distribution, 1 event 0.3GeV/c electron,hit at a module centre, phi-direction energy distribution, 1000 event

11. Different trigger cell size, the ratio of the energy of the trigger cell that has max energy deposit to total energy deposit, 0.3GeV/c electron

12. Conclusion: Two trigger cells ( namely 6columns/triggercell ) in one module is a proper selection

13. 24 modules,one module is divided into two trigger cells. Two groups of overlapping trigger cells(u and v) are defined to ensure one cluster energy deposit in one triger cell as much as possible

14. 1.5GeV/c electron, ratio of u and v trigger cell max energy deposit to total energy deposit 1.5GeV/c electron, ratio of only u trigger cell max energy deposit to total energy deposit

15. The Selection of Trigger Threshold Scheme 1.Major factor considered is to compensate light transmission attenuation 2.Two schemes,log AMP scheme and double threshold schme are to be selected The thresholds of each trigger channel are divided into BBT(Bhabha threshold) and LET(low energy threshold).Then a high and a low threshold are set in the LET(or BBT).The high and low thresholds in the following text refer to the two thresholds in the LET. – Double threshold cheme

16. LET threshold logic LET effective threshold curve, two-grade and-or logic give a high and a low curve

17. 1. High and low threshold satisfy E h /E l =exp(L/2 ),L=fibre length, =attenuation length, which makes effective threshold curve have min fluctuation 2. Two curves superpose at z=  L/4, fluctuate exponentially, the fluctuation range is exp(L/4 )=exp(3.85/(4*3.0))=1.38.

18. – Log AMP scheme Principle: log(Ea)+log(Eb)=log(E*exp(-z/ ))+log(E*exp(-(L- z)/ ))=2*log(E)-(L/ )*log(e), independent on z

19. Transfer function: I o =I y *log10(|V in /V x |), V x =1mV Dynamic: 44db Error: (V in = 1mV to 100mV) 0.3db (V in = 0.75mV to 200mV) 1db Two-end errors added according to gaussian distribution, **sqrt(2.) 1db 10 0.05 =1.12 **sqrt(2.) =1.174 0.3db 10 0.015 =1.035 **sqrt(2.) =1.050 Some statistics of AD641 log AMP

20. – Comparison of two schemes 1.1GeV/c gamma,  =90 0, random ,inject at different z, effective threshold=0.085GeV and 0.10GeV/c, ratio of passing threshold events under different threshold scheme, 1000 event per spot

21. 1. When using log AMP, the fluctuation of passing threshold ratio by z is much smaller than double threshold scheme. But if the log AMP error is considered, Both of the errors of the two schemes are labeled as decibel,which means higher threshold has larger error, and is of the same error level. The error of the double threshold scheme can be eliminated by offline calibration, because it is systematic error; but error of log AMP scheme cannot. 2. In comparison, log AMP scheme has no superiority to double threshold scheme. So double threshold scheme is selected. Conclusion:

22. The Selection of Threshold Logic Time Window Because of scattering(not distinct for photon, electron and muon, but distinct for hadrons ), rounding of low transverse momentum charged particles and multihit, many peaks can appear in the same trigger channel at different time and z position. The Peaks that have large lag time are caused by the rounding of low transverse momentum charged particles or scattering, thus need to be excluded. This can be done by setting a time window.

23. Lund_charm event, the effect of scattering and low transverse momentum rounding can be seen

24. Estimation of the longest time from the occurrence of one event to the signal’s coming out at detector ends:  Use heaviest stable particle, namely proton  Have minimum transverse momentum p t that allow partile to arrive BEMC  hit one end of the detector According to these rules,the time can be calculated as ： tofl=14.264ns+22.384ns=36.65ns The Monte Carlo shows a peak at time 32ns to 33ns in the following picture. – Calculation of time window and its Monte Carlo value

25. 0.6GeV/c gamma, z=0,  =139 0, far- end FEE readout signal time spectrum, 1000 events.

26. The time window of one trigger channel

27. Main Conclusions – Trigger channels: 2 trigger channel per module, two groups of trigger channels(u and v) – Double threshold scheme – 35ns time window for trigger logic