Intrinsic Single Photon Time Resolution (SPTR)
As described in subsection 5.2.4, typicalSiPMsensors showSPTRofσsptr(see Table 5.1). Hence, the detection time of each photon is by convenience smeared by a Gaussian distribution with this width.
The detection time of a photon is given by
tdetection=tinteraction+∆tdecay+∆tpropagation+∆telectronics delay±measueremen∆tsptr. (9.10) 9.2.5 Sensor and Readout Electronic Response
The response of the sensors and readout electronics to the photons is simulated in multiple steps. In a first step,SiPMdark counts and crosstalk between channels are added to each sensor.
It is possible to simulate the electrical response of the sensors by summing a template single photon response waveform for each photon at its detection timetdetection. Figure B.6a shows the used template waveform and Figure B.6b shows an example event consisting of summed waveforms. This simulation of the full waveform is computationally expensive. Hence, in the baseline configuration, theToAis determined by the detection time of the first photon passing the set threshold level. For a threshold level of 0.5 photoelectrons, this is the first detected photon, whereas for a threshold of 1.5 photoelectron the detection time of the second photon is selected.
Events within theASIC’s deadtime of 40 ns are merged and flagged as piled up. The advant-age of the full waveform mode is that the influence of pileup to theToAis modelled. Because of the small signals and usage of fast scintillators, this procedure is not required for the simu-lation of the fibre sub-detector.
9.3 Simulation Settings and Validation
Whenever possible, the simulation settings are chosen according to measured values. Table 9.1 summarizes settings motivated by vendor specifications and measurements. The simulated number of photons and cluster size distributions with these unbiased settings agree well with measurements done with ribbons consisting of Kuraray SCSF-78MJ and NOL-11 fibres.
Test beam-likesimulation conditions are compared to theDRS4based test beam measure-ments to validate the simulation’s settings. In thetest beam-likesimulation conditions, posit-ively charged pions with a momentum of 160 MeV/c and isotropically distributed momentum direction are generated in the centre of the Mu3e experiment simulation. Only particles which cross the fibre ribbons in the ribbon centre within±1 cm around the centre and with angles below 20◦ with respect to the ribbon’s normal are selected. The former guarantees constant attenuation and photon propagation distances. A variation of the propagation distance results in a smearing of thetleft-trightdistribution. The employed restriction of incident angles results in variations of path lengths below 6.5 %. The photon yield is proportional to the deposited energy which in turn is proportional to the path length of aMIPin the active volume of a fibre.
Hence, the variations in path length translate directly to variations in light yield.
CHAPTER 9. THE SCINTILLATING FIBRE DETECTOR IN THE MU3E SIMULATION FRAMEWORK
Table 9.1:Simulation settings for round KuraraySCSF-78MJfibres andMuTRiGreadout. The abbre-viationexp.indicates that these values are obtained by measurements, whereas those labelled with vendorare references to data sheets.
setting value reference
scintillation decay time τdecay 2.8 ns Table 7.1(vendor) photon yield Y 8000 photon /MeV Table 7.1(vendor) fibres capture efficiency εcapture 5.4 % subsection 4.2.1(vendor) fibre attenuation length Λattenuation 1.395 m [80](exp.)
fibre crosstalk 2 % [124](exp.)
SiPM PDE εpde 40 % section 5.3(vendor)
SiPM SPTR σsptr 85 ps Table 5.1(exp.)
SiPMchannel crosstalk 4 % Table 11.3(exp.)
SiPMpixel crosstalk 2 % Table 11.3(exp.)
DAQjitter σjitter 200 ps
Validation of Simulated Number of Photons per Particle Crossing
Figure 9.7 shows the simulated sum of detected photons per ribbon side in a cluster induced by a single particle crossing. The distributions are fitted with the same model, a convolution of a Landau and a Poisson distribution, as described in Figure 7.3.4. To validate the simula-tion settings, the distribusimula-tion fromtest beam-likesimulation configuration is compared to the results obtained in theDRS4based measurement in a test beam (see Figure 7.15). TheirMPVs
agree better than to 5 %, and the simulated and measured distributions roughly coincide. Fur-thermore, the simulated fibre ribbon efficiencies for test beam-likesimulation configuration of (95.4±0.2) % in an AND configuration, (95.8±0.2) % in an OR configuration respectively, agree within 1.5 % with the measured values.
Validation of Distribution of Simulated Cluster Sizes
Figure 9.8 shows the simulated cluster size distribution of clusters induced by a single particle crossing. The distributions are fitted with the same model as described above. The distribution from thetest beam-likesimulation configuration is compared to the result obtained in aDRS4
based measurement during a test beam (see Figure 7.14). The simulated cluster sizes, with no explicit tuning to this data set, yield a distribution with a 13 % reducedMPVbut with a correct shape.
Validation of Simulated Time Resolution
To reproduce the time resolution measured in test beams and in lab measurements an ad-ditional DAQtime jitter of 200 ps is added to the simulation. Figure 9.9 shows the resulting distribution of the cluster time differencetleft−tright between the ribbon sides in alab-like
9.3. SIMULATION SETTINGS AND VALIDATION
0 5 10 15 20 25 30 35 40
number of photons
probability
testbeam, mpv: 22.6 simulation testbeam, mpv: 22.5 simulation experiment, mpv: 17.0
Figure 9.7:Simulated number of photons fortest beam-like( ) and experiment-like ( ) simulation configuration of one ribbon side.DRS4based test beam measurement ( ) of a 4 layer ribbon consist-ing ofSCSF-78fibres is shown for comparison.
0 2 4 6 8 10 12 14
cluster size [col]
counts
testbeam, mpv: 3.94 simulation testbeam, mpv: 3.40 simulation experiment, mpv: 3.43
Figure 9.8:Simulated cluster size distribution fortest beam-like( ) and experiment-like ( ) simula-tion configurasimula-tion of one ribbon side.DRS4based test beam measurement ( ) are shown for compar-ison.
CHAPTER 9. THE SCINTILLATING FIBRE DETECTOR IN THE MU3E SIMULATION FRAMEWORK
mean 1 ps
core 339 ps
base 720 ps Ncore/Nbase 4.68
single 396 ps
exp gauss 2684 ps
exp gauss 291 ps fwhm/2.35 366 ps
4 2 0 2 4
tleft tright [ns]
5 0 5
modeldata datamax [%] counts
Figure 9.9:Simulated time resolution forlab-likeparticle crossings in a 4 layer ribbon consisting of round KurarySCSF-78MJfibres.lab-likesimulation settings correspond to the irradiation of the ribbon by positrons from a 90Sr source at the fibre ribbon centre.