The EMU Cathode-Strip Signal Time Shape and Cross-talk: Test-Beam Data vs. Simulation

• Motivation
  • Validation of the simulation (currently done in ORCA) is a part of the CMS Physics TDR, Vol. 1 [1].
  • The importance of a realistic simulation of the CSC input signals and electronics response (the coordinate and time resolution, L1 trigger primitives, pile-up, neutron background, etc.).
  • The old (prototype) front-end electronics parameters are still in use in the ORCA simulation [2].
  • New parameters which match the final cathode-amplifier design and pulser cross-talk data are now available (see notes [3] and [4] by S. Durkin et al.).
  
  
• Conditions
  • Test-beam data - from the CERN H2 beamline, 150 GeV/c muons, 25 ns structured beam, Oct. 2004, Run 554, Track-Finder Trigger.
  • Simulation - ORCA_8_7_1, OSCAR_3_7_0 (using the CMS detector geometry since the test-beam geometry is not available yet), single muon track with Pt = 100 GeV/c, generated flat in Eta and Phi, demand 1.3 < EtaGen < 1.6 (~ as in the beam test), take hits only from CSC ME234/2, the data are in: cmsuaf.fnal.gov:/uscms_data/d1/lpcmuon/simplegun/mup*_100/.
  • Demand one anode hit and one cathode comparator hit per CSC layer in the test-beam data. Demand one muon track in the ORCA simulation.
  
  
• Fitting the cathode output pulse
  • The output pulse from every cathode front-end channel is sampled every 50 ns and stored in a Switch Capacitor Array (SCA). Eight consecutive SCA samples are digitized and read out whenever there is a LCT*L1A (Local Charged Track trigger * Level-1 Accept signal) coincidence. The first 50 ns time bin is defined to be in coincidence with the L1A signal ( Fig.1 , see more details in the note [5] by A. Korytov).
    
    
  • The SCA values around the maximum SCA can be well fitted by using a semi-Gaussian function S(t) (see note [6] by S. Durkin). Here, S(t) is used in the form:
    
    

    SCA(t)		= Q * S(t)
    S(t)		= 0.2133 * [(t - Ts) / T0] ** 4 * exp[-(t - Ts) / T0] ,	(1)

    
    where Q is the charge on the strip, Ts is the arrival time of the pulse, and 4 * T0 is the peaking time (S(t) = 1 with normalizing coefficient 0.2133 at t - Ts = 4 * T0, see Fig.1). We demand t - Ts > 0. Due to the 25 ns beam structure and the 50 ns SCA sampling period, a signal can have 2 possible positions in time (2 possible Ts values), depending on whether the muon comes with an odd or even L1 Accept. Note in Fig.1 the two pulses 25 ns apart and having their maximum SCA in the same time bin at t = 250 ns. The Ts value also depends on the DMB clock settings, which can be different from CSC to CSC. In addition, Ts is smeared by the CSC drift time.
    
    
  • As described in the note [6] by S. Durkin, the fitting procedure uses the SCA(t) values from 3 cathode strips, with the middle strip having the maximum SCA(t). However, instead of using 3 time bins centered on the time bin with the maximum charge deposition, 4 time bins are used here, making a total of 12 analyzed bins. Table 1 below gives an example of the SCA(t) pedestal-subtracted ADC counts in 8 time bins and 3 strips taken from one event in layer 2 of the ME3/2 chamber from Run 554 of the test beam. The SCA(t) values in time bins at t = 125, 175, 225 and 275 ns (shown in blue) were used in the fit. Notice that the maximum SCA for the middle strip (shown in red) is at t = 225 ns. The ADC counts in the first time bin for each strip are used as pedestals (with RMS = 2.7 in test-beam events and RMS = 4.0 in the ORCA simulation).
    
    Table 1. SCA(t) for 3 cathode strips.
    

    Strip \ t, ns	25	75	125	175	225	275	325	375
    Left	0	0	41	110	88	41	18	5
    Middle	0	3	112	420	512	370	214	122
    Right	0	1	33	85	57	16	6	3

    
    Adding one more time bin at a lower time (t = 125 ns) to the fit significantly reduces the correlation between the Ts and T0 error matrix elements.
    The function used for fitting the ADC counts in the 12 SCA time bins from the 3 cathode strips of a given CSC layer in each event was the following:
    
    

    SCA_left(t)		= Q_left		* S(t) + Ct * Fc(t) * ( 0		+		Q_middle		)
    SCA_middle(t)		= Q_middle		* S(t) + Ct * Fc(t) * ( Q_left		+		Q_right		)	(2)
    SCA_right(t)		= Q_right		* S(t) + Ct * Fc(t) * ( Q_middle		+		0		)

    
    where Ct is the cross-talk coefficient and Fc(t) is the cross-talk function describing the time dependence of the strip-to-strip cross-talk (see pulser data analysis). For both the test-beam and the simulation data, the fitted parameters are Q_left, Q_middle, Q_right, T0, Ts and Ct, giving a total number of degrees of freedom of 6. To obtain a good measurement of the cross-talk coefficient, Ct, additional cuts were imposed on the hits in both the test-beam and simulation events. Hits with a large signal and with the muon passing close to the center of the middle strip were selected, yielding a ~10% selection efficiency. The cuts were:
    
    R = SCA_middle_max / (SCA_left_max + SCA_middle_max + SCA_right_max)
    R > 0.7 and SCA_middle_max > 200 for the test-beam events
    R > 0.7 and SCA_middle_max > 150 for the ORCA simulation events
    
    
  
  
• Results
  • A summary of the results is given in Table 2.
    
    Table 2. Measured Parameters.
    

    Data \ Parameters	T0, ns	Ct	Ts
    Beam test	34.2 +/- 1.3(RMS)	0.099 +/- 0.014(RMS)	Ts
    ORCA simulation	34.2 +/- 1.7(RMS)	0.084 +/- 0.022(RMS)	Ts
    Pulser data, Fig. 3	34.1 - 36.0	0.095 - 0.098	65 - 109 ns

    
    
    The peaking time, T0, is about the same in all 3 types of data and in all chambers with the same gas gap ( ME1/2, ME2/2, ME3/2). It is less in the ME1/1 chamber because of its smaller gas gap.
    
    The cross-talk coefficient measured in the test-beam data is the same for all chambers with the same strip geometry ( ME2/2, ME3/2) but is less in ME1/2 since its strip geometry and capacitance are different from those in ME23/2. The mean of the Ct distribution from the ORCA simulation is lower than in both the test-beam and pulser data, likely due to the simplified cross-talk description in ORCA.
    
    
  • Arrival time (Ts)
    The distribution of the arrival time, Ts, for one ME3/2 CSC layer ( Ts) shows 2 peaks 25 ns apart and smeared by the drift time in that layer. Averaging the Ts values over 4-6 layers of a CSC on an event-by-event basis, allows us to reduce this smearing and measure the cathode beam-crossing time with high accuracy (see details in note [7] by S. Durkin). The corresponding distributions are given for ME1/2, ME2/2 and ME3/2. For these distributions the restrictions on R and SCA_middle_max were removed. The difference in the peak widths is due to the position of the first SCA time bin used in the fit. When the pulse-shape data are sampled and fitted using a limited number of points, the fit is sensitive to the positions of the points. For example, when the corresponding SCA is sampled at the beginning of the pulse (in its sloping part), it contributes less to the fit, making the fit less sensitive to the value of Ts. Such cases are characterized by a low SCA(tmax-2)/Q value (compare ME2/2 and ME3/2).
    
    The cathode beam-crossing time was compared with the first anode-discriminator-hit time in note [7], and good agreement was found.
    
    
  • Restoring the pulse shape by use of Ts
    The Ts-dependence of SCA(t) can be eliminated by subtracting the Ts value from the time of all 8 SCA samples for a given cathode strip in each event. Since the value of Ts can vary due to the drift time, the SCA measures each pulse at a different time. Therefore, such a subtraction will give the restored pulse shape, measured with much finer time resolution than the original 8 time bins (see ME3/2, the data are from the middle strip). Averaging SCA(t - Ts)/Q for each 6.25 ns time bin in ME3/2 gives the detailed pulse shape. It looks almost the same in the data for ME1/2 - ME3/2. A similar procedure was done for the ORCA-simulated and pulser data (see here) and their comparison with the ME2/2 test-beam data shows reasonable agreement.
    
    Note that ORCA presently makes use of an old cathode-amplifier single-electron response function provided by R. Wilkinson (private communication). A new function, buckeye_single_electron_ave, available in [3] (see README), is compared with the old one here. For this comparison, a table of buckeye_single_electron_ave function values was used (provided by S. Durkin), with the data in the plot shifted by -20 ns to compensate for the delay in the rise of the pulse (S. Durkin, private communication).
    
    
  • Measuring cross-talk in data with subtracted Ts.
    Previously, in pulser (see [4]) and test-beam data (see talk by Y. Zheng), analysis of the cross-talk versus time curve gave the ratio of the SCA value of one side strip to the sum of the central strip SCA value and both side-strip SCA values for any given time bin. It was shown in [4] (see Fig. 3) that the slope of the pulser cross-talk distribution agreed well with the slope of the cross-talk obtained by fitting test-beam hits to the Gatti distribution. However, a systematic offset in time was observed and this was attributed to an insufficient understanding of the Gatti shape used in the test-beam fits.
    
    Figures ME2/2, ORCA and Pulser show, in a similar manner, the cross-talk distributions from this analysis, using the subtracted-Ts values. To eliminate the contribution of the induced pulse caused by the track-hit charge on the side-strip SCA, the fitted values of Q_left*S(t) and Q_right*S(t) were subtracted from the corresponding SCA value in each of the 3 time bins. This was done in order to have a direct comparison with the pulser data, where only the central strip was pulsed. Again, the restrictions on R and SCA_middle_max were used to obtain reliable cross-talk measurements.
    
    The corresponding cross-talk-averaged ratios are presented here. There is reasonable agreement between the cross-talks from the test-beam and pulser data, both having a slope about (1.2*10**-3)/ns. However, the cross-talk in the ORCA simulation is different from both the test-beam and pulser data.
    
  
  
• Conclusions
  • The SCA shapes of the cathode-strip output pulses in the ORCA simulation and in real data are very similar (see here). There is good agreement, with only rather small differences, in the shapes of the old and new cathode-amplifier single-electron response functions. However, for consistency, the new single-electron response function should replace the old one in the ORCA simulation.
    
    
  • The cross-talks as measured in the test-beam and pulser data are similar (see the figure here). However, the cross-talk in the ORCA simulation should be updated by using the functions from [3] .
  
  (Thanks to S. Durkin for very helpful discussions and for providing the tables of pulser data and values for the single-electron response function.)