1 A Counting Data Acquisition System for Measuring 2 Parity Violation Asymmetry in Deep Inelastic 3 Scattering

4 R. Subedi^{a}^{1} , D. Wang^{a}, K. Pan^{b}, X. Deng^{a}, R. Michaels^{c}, 5 P. E. Reimer^{d}, A. Shahinyan^{e}, B. Wojtsekhowski^{c}, X. Zheng^{a,∗}

6 ^{a}University of Virginia, Charlottesville, VA 22904, USA

7 ^{b}Massachusetts Institute of Technology, Cambridge, MA 02139, USA

8 ^{c}Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA

9 ^{d}Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA

10 ^{e}Yerevan Physics Institute, Yerevan, Armenia

11 Abstract

12 An experiment that measured the parity violating asymmetry in deep inelastic scattering 13 was completed at the Thomas Jefferson National Accelerator Facility in experimental Hall 14 A. From this asymmetry one can extract a combination of the quark weak axial charge. To 15 achieve this, asymmetries at the 10^{−4} level need to be measured. A specialized data acqui-16 sition (DAQ) system with intrinsic particle identification (PID) was developed and used. 17 The DAQ system of this experiment is presented here with an emphasis on understanding 18 of its PID performance, deadtime effect and the capability of measuring small asymmetries.

19 Key words: Jefferson Lab; Hall A; PVDIS; DAQ 20 PACS: 11.30.Er, 12.15.Mm, 13.60.Hb 14.60.Cd 14.65.Bt 29.30.Aj 29.85.Ca

21 1 Introduction

22 The Parity Violating Deep Inelastic Scattering (PVDIS) experiment E08-011 was 23 completed in December 2009 at the Thomas Jefferson National Accelerator Facil-

1 Present address: George Washington University, 725 21^{st} St, NW, Washington, DC 20052, USA

∗ Corresponding author. E-mail: xiaochao@jlab.org; Telephone: 001-434-243-4032; Fax: 001-434-924-4576

Preprint submitted to Elsevier Science 21 September 2012

24 ity (JLab). The goal of this experiment [1,2] was to measure with high precision 25 the parity violating asymmetry in deep inelastic scattering of a polarized electron 26 beam on an unpolarized liquid deuterium target. This asymmetry is sensitive to a 27 combination of the quark weak axial charge 2C_{2u} − C_{2d}, where C_{2q} = 2g_{V}^{e} g_{A}^{q} with 28 q = u, d indicating an up or a down quark, g_{V}^{e} is the electron vector coupling and 29 g_{A}^{q} is the quark axial coupling to the Z^{0} boson.

30 For electron inclusive scattering from an unpolarized target, the electromagnetic 31 interaction is parity conserving and is insensitive to the spin flip of the incom-32 ing electron beam. Only the weak interaction violates parity and causes a differ-33 ence between the right- and the left-handed electron scattering cross-sections σ_{R} 34 and σ_{L}. The dominant contribution to the parity violation asymmetry, A_{P V} ≡ 35 (σ_{R} − σ_{L})/(σ_{R} + σ_{L}), arises from the interference between electromagnetic and 36 weak interactions and is proportional to the four momentum transfer squared Q^{2} 37 for Q^{2} ≪ M_{Z}^{2}. The magnitude of the asymmetry is in the order of 10^{−4} or 100 parts 38 per million (ppm) at Q^{2} = 1 (GeV/c)^{2}.

39 The PVDIS asymmetry from a deuterium target is

A_{P V} = (−\frac{G_{F} Q^{2}}{4\sqrt{2}πα}) (2g_{A}^{e}Y_{1} \frac{F_{1}^{γZ}}{F_{1}^{γ}} + g_{V}^{e} Y_{3} \frac{F_{3}^{γZ}}{F_{1}^{γ}} ) ,  (1)

40 where Q^{2} is the negative of the four-momentum transfer squared, G_{F} is the Fermi 41 weak coupling constant, α is the fine structure constant, Y_{1} and Y_{3} are kinematic 42 factors, x is the Bjorken scaling variable, and F_{1,3}^{γ(Z)} are deuteron structure functions 43 that can be evaluated from the parton distribution functions and the quark-Z^{0} vector 44 and axial couplings g_{V,A}^{q}. From this asymmetry one can extract the quark weak 45 vector and axial charges C_{1,2q}, which can be written as

C_{1u} = 2g_{A}^{e}g_{V}^{u} = −\frac{1}{2} + \frac{3}{4} sin^{2} θ_{W} , C_{2u} = 2g_{V}^{e} g_{A}^{u} = −\frac{1}{2} + 2 sin^{2} θ_{W} ,
C_{1d} = 2g_{A}^{e}g_{V}^{d} = \frac{1}{2} − \frac{2}{3} sin^{2} θ_{W} , C_{2d} = 2g_{V}^{e} g_{A}^{d} = \frac{1}{2} − 2 sin^{2} θ_{W} ,

46 in the tree-level Standard Model with θ_{W} the weak mixing angle.

47 The goal of JLab E08-011 is to measure the PVDIS asymmetries to statistical pre-48 cisions of 3% and 4% at Q^{2} = 1.1 and 1.9 (GeV/c)^{2}, respectively, and under the 49 assumption that hadronic physics corrections are small, to extract the quark axial 50 weak charge combination (2C_{2u}−C_{2d}). In addition, the systematic uncertainty goal 51 is less than 3%. For this experiment, the expected asymmetries are 91 and 160 ppm 52 respectively at the two Q^{2} values. To achieve the required precision, an event rate 53 capability of up to 500 kHz is needed.

54 The main challenge of deep inelastic scattering experiments is the separation of 55 scattered electrons from charged pion background in the spectrometer and detector 56 system. Charged pions are produced primarily from nucleon resonance decays and 57 could carry a parity violation asymmetry corresponding to the Q^{2} at which the 58 resonances are produced, typically a fraction of the asymmetry of electrons with 59 the same scattered momentum. Assuming a fraction f of the detected events are 60 π^{−} and 1 − f are electrons, the measured asymmetry is

A_{m} = fA_{π} + (1 − f)A_{e},  (2)

61 where A_{e} is the desired electron scattering asymmetry and A_{π} is the asymmetry of 62 the pion background. To extract A_{e} to a high precision, one needs to either minimize 63 the pion contamination f to a negligible level, or to correct the measured asymme-64 try for the asymmetry of pions, which itself needs to be measured precisely. For 65 the PVDIS experiment, the goal was to reach f < 10^{−3}. Since the expected π to 66 electron ratio varies between (1 − 10) : 1, a 10^{4} pion rejection was needed.

67 The experiment used a 100 μA electron beam with a polarization of approximately 68 90% and a 20-cm long liquid deuterium target. The two High Resolution Spec-69 trometers (HRS) [3] were used to detect scattered events. While the standard HRS 70 detector package and data acquisition (DAQ) system routinely provide a 10^{4} pion 71 rejection with approximately 99% electron efficiency, they are based on full record-72 ing of the detector signals and are limited to event rates up to 4 kHz [3]. This is not 73 sufficient for the high rates expected for the experiment. (The HRS DAQ will be 74 referred to as “standard DAQ” hereafter.)

75 Most previous parity violation experiments– SAMPLE [4] at MIT-Bates, HAPPEX [5– 76 9], and PREX [10] at JLab – focused on elastic scattering from nuclear or nucleon 77 targets that are typically not contaminated by inelastic backgrounds. Signals from 78 the detectors can be integrated and a helicity dependence in the integrated signal 79 can be used to extract the physics asymmetry, and no pion rejection was imple-80 mented. An integrating DAQ was also used at the preceding PVDIS measurement 81 at SLAC [11,12] in which approximately 2% of the integrated signal was attributed 82 to pions. In the Mainz PVA4 experiment [13,14], particles were detected in a total 83 absorption calorimeter and integrated energy spectrum was recorded. Charged pi-84 ons and other background were separated from electrons in the offline analysis of 85 the energy spectrum, and the pion rejection is in the order of 100:1 based on the 86 characteristics of the calorimeter.

87 High performance particle identification can usually be realized in a counting-based 88 DAQ where each event is evaluated individually. In the G0 experiment [15,16] at 89 JLab, a superconducting spectrometer with 2π azimuthal angle coverage was used 90 to detect elastically scattered protons at the forward angle and elastic electrons at 91 the backward angle. At the forward angle, protons were identified using time-of-92 flight. At the backward angle, pions were rejected from electrons using an Aerogel 93 Cherenkov counter and a pion rejection factor of 125 was reported. The deadtime 94 correction of the counting system was at the order of a few percent.

95 While the PVDIS experiment can fully utilize existing spectrometers and detectors 96 at JLab, upon examining all existing techniques for PV measurements it became 97 clear that a custom electronics and DAQ are needed to control the systematic un-98 certainties due to data collection to below 1%. In this paper we describe a counting-99 based, cost effective DAQ which limited the pion contamination of the data sample 100 to a negligible level of f < 10^{−3}. Basic information of the detector package and 101 the DAQ setup will be presented first, followed by analysis focused on electron 102 detection efficiency, pion rejection, corrections due to counting deadtime, and the 103 statistical quality of the asymmetry measurement.

104 2 Detector and DAQ Overview

105 The design goal of the DAQ is to record data up to 1 MHz with hardware-based PID 106 and well measured and understood deadtime effects. The following detectors in the 107 HRS were used to characterize scattered particles: Two scintillator planes provided 108 the main trigger, while a CO_{2} gas Cherenkov detector and a double-layer segmented 109 lead-glass detector provided particle identification information. The vertical drift 110 chambers (as the tracking detector) were used during calibration runs and turned 111 off during production data taking because they were not expected to endure the 112 high event rates.

113 For the gas Cherenkov and the lead-glass detector, a full recording of their out-114 put ADC data is not feasible at the expected high rate. Instead their signals are 115 passed through discriminators and logic units to form preliminary electron and 116 pion triggers. Particle identification is fulfilled by the use of discriminators for 117 both the lead-glass and the Cherenkov detectors and proper settings of their thresh-118 olds. These preliminary triggers are then combined with the scintillator triggers 119 and Cherenkov signals to form the final electron and pion triggers, which are then 120 sent to scalers to record the event counts and offline used to form asymmetries 121 A = (n_{R}−n_{L})/(n_{R}+n_{L}), where n_{R(L)} is the integrated rate of the triggers normal-122 ized to the integrated beam charge for the right(R) and left(L) handed spin states 123 (helicity) of the incident electron beam. The scalers that count triggers and beam 124 charge are integrated over the helicity period, which was flipped pseudo-randomly 125 at 30 Hz per the experimental technique used by the HAPPEX experiments [9].

126 For HRS the two layers of the lead-glass detector are called “preshower” and 127 “shower” detectors, respectively. The preshower blocks in the Right HRS (the spec-128 trometer located to the right side of the beamline when viewed along the beam 129 direction) has 48 blocks arranged in a 2 × 24 array, with the longest dimension 130 of the blocks aligned perpendicular to the particle trajectory. For the two blocks 131 in each row, only the ends facing outward are read out by photo-multiplier tubes 132 (PMTs) and the other ends of the two blocks were facing each other and not read 133 out. Therefore the preshower detector had 48 output channels. All preshower blocks 134 were individually wrapped to prevent light leak. The preshower and the shower de-135 tectors in the Left HRS are similar to the preshower detector on the Right HRS 136 except that for each detector there are 34 blocks arranged in a 2 × 17 array. The 137 shower detector in the Right HRS had 75 blocks arranged in a 5 × 15 array with the 138 longest dimension of the blocks aligned along the trajectory of scattered particles. 139 PMTs are attached to each block of the Right shower detector on one end only, 140 giving 75 output channels.

141 Because the lead-glass detectors in the Left and Right HRS were different, design 142 of the lead-glass-based triggers of the DAQ is also different, as shown in Fig. 1. As 143 a compromise between the amount of electronics needed and the rate in the front 144 end logic modules, the lead-glass blocks in both the preshower and the shower de-145 tectors were divided into 6 (8) groups for the Left (Right) HRS, with each group 146 consisting 8 blocks. On the Right HRS only 60 of the 75 shower blocks were used 147 while the 15 blocks on the edge were not read out. The reduction on the HRS 148 acceptance due to not using these side blocks is negligible. Signals from the 8 149 blocks in each group were added using a custom-made analog summing unit called 150 “SUM8 modules”, then passed to discriminators. The geometry and the position of 151 each preshower group were carefully chosen to match those of the corresponding 152 shower group to maximize electron detection efficiency. On the Left HRS adjacent 153 groups in both preshower and shower had overlapping blocks, while for the Right 154 HRS only preshower blocks were overlapping. To allow overlap between adjacent 155 groups, signals from preshower blocks on the Right HRS and from both preshower 156 and shower blocks on the Left HRS were split into two identical copies using pas-157 sive splitters.

158 A schematic diagram for the DAQ electronics for the Right HRS is shown in Fig. 2. 159 The electron and pion triggers were formed by passing shower (SS) and preshower 160 (PS) signals or their sums, called total shower (TS) signals, through discriminators 161 with different thresholds. For electron triggers, logical ANDs of the PS discrimi-162 nator and the TS discriminator outputs were used. For pion triggers, low threshold 163 discriminators on the TS signal alone were used to reject background. These signals 164 were then combined with signals from scintillators and the gas Cherenkov (called 165 electron or pion “VETO” signals) to form electron or pion triggers for each shower 166 and preshower group. The electron VETO signals required the gas Cherenkov to 167 be triggered, while the pion VETO required the opposite. The electron or pion trig-168 gers from all six groups on the Left HRS (eight groups for the Right HRS) were 169 then ORed together to form the global electron or pion triggers for the Left (Right) 170 HRS. All triggers – electron and pions from each group, as well as the final global 171 triggers – were counted using scalers. Because pions do not produce large enough 172 lead-glass signals to trigger the high threshold TS discriminators for the electron 173 triggers, pions do not introduce extra counting deadtime for the electron triggers.

Fig. 1. [Color online] Grouping scheme (side-view) for the double-layer lead-glass detectors for the Left and the Right HRS. Scattered particles enter the detector from the left. The colored vertical bars represent the range of each group.

174 In order to monitor the counting deadtime of the DAQ, two identical paths of elec-175 tronics were constructed. The only difference between the two paths is in the dis-176 criminator output width, set at 30 ns and 100 ns for the “narrow” and the “wide” 177 paths, respectively. The scalers are rated for 250 MHz (4 ns deadtime) and therefore 178 do not add to the deadtime. In addition, since the output width of all logic modules 179 were set to 15 ns, the deadtime of the DAQ for each group is dominated by the 180 deadtime of the discriminators.

181 The SUM8 modules used for summing all lead-glass signals also served as fan-out 182 modules, providing exact copies of the input PMT signals. These copies were sent 183 to the standard HRS DAQ for calibration. During the experiment, data were col-184 lected at low rates using reduced beam currents with both DAQs functioning, such 185 that a direct comparison of the two DAQs can be made. The vertical drift chambers 186 were used during these low rate DAQ studies. Outputs from all discriminators, sig-187 nals from the scintillator and the gas Cherenkov, and all electron and pion triggers 188 were sent to Fastbus TDCs (fbTDC) and were recorded in the standard DAQ. Data 189 from these fbTDCs were used to align amplitude spectrum and its timing. They 190 also allow the study of the Cherenkov or lead-glass performance for the new DAQ 191 triggers.

192 Full sampling of analog signals were done using Flash-ADCs (FADCs) at low rates 193 intermittently during the experiment. For one group on the left and one group on

Fig. 2. [Color online] Electronics diagram for the Right HRS DAQ used by the PVDIS experiment. The Sum8’s, discriminators and logic modules for two groups are shown, as well as the location of tagger signal inputs, setup of the VETO circuit using scintillator and gas Cherenkov signals, the logic units for combining triggers from all eight groups into final triggers, and the scalers. Electronics for the Left HRS are similar except for the grouping scheme.

194 the right HRS, the preshower and shower SUM8 outputs, the intermediate logical 195 signals of the DAQ, and the output electron and pion triggers were recorded. These 196 FADC data provide a study of pileup effects to confirm the simulation and to pro-197 vide the input parameters for the simulation, specifically the rise and fall times of 198 the signals and their widths.

199 3 DAQ PID Performance

200 PID performance of the DAQ system was studied with calibration runs taken at low 201 beam currents using fbTDC signals along with ADC data of all detector signals 202 recorded by the standard DAQ. Events that triggered the DAQ would appears as a 203 timing peak in the corresponding fbTDC data of the standard DAQ and a cut on this 204 peak can be used to select those events. Figure 3 shows the preshower vs. shower 205 signals for group 2 on the Left HRS. A comparison between no fbTDC cut and with 206 cut on the fbTDC signal of the electron wide trigger from this group clearly shows

the hardware PID cuts.

Fig. 3. [Color online] Preshower vs. Shower ADC data (sum of 8 blocks each) for group 2 on the Left HRS, without the fbTDC cut (left panel) and with cut on the group 2 electron wide trigger fbTDC signal (right panel). It clearly shows the thresholds on the preshower and the total shower signals, indicating the DAQ is selecting the correct events as electrons. The events near the vertical axis, around ADC channels (200,1000), are electrons that deposited energy in overlapping blocks between group 2 and group 1 (or group 3) and are recorded by the other group.

207

208 Electron efficiency and pion rejection factors of the lead-glass detector on the Left 209 HRS are shown in Fig. 4 as functions of the location of the hit of the particle in 210 the preshower detector. PID performance on the Right HRS is similar. Electron 211 efficiency from wide groups are slightly higher than narrow groups because there 212 is less event loss due to timing mis-alignment when taking the coincidence between 213 the preshower and the total shower discriminator outputs. Variations in the electron 214 efficiency across the spectrometer acceptance effectively influence the kinematics 215 (Q^{2}) of the measurement. For this reason, low-rate calibration data were taken daily 216 during the experiment to monitor the DAQ PID performance and corrections are 217 applied to data.

218 As described in the Introduction, pion contamination in the electron trigger would 219 affect the measured electron asymmetry as A^{m} = (1 − f)A_{e} + fA_{π} where A^{m} 220 and A_{e} are the measured and the true electron asymmetries, respectively, f is the 221 pion contamination fraction in the electron trigger, and A_{π} is the parity violation 222 asymmetry of pion production. As shown in Fig. 4, pion rejection factor from the 223 lead-glass detector was above 50. Combined with the approx. 200 pion rejection 224 factor of the gas Cherenkov detector [3], the total pion rejection achieved during 225 this experiment was above 10^{4}. The pion to electron rate ratios for the two Q^{2} values 226 of this experiment were less than 10:1, thus f < 10/10^{4} = 10^{−3}. Because pions 227 are produced from nucleon resonance decays, the parity violation asymmetry of 228 pion production is expected to be no larger than that of scattered electrons with the 229 same momentum. This was confirmed by asymmetries formed from pion triggers 230 during this experiment. Overall the uncertainty in the electron asymmetry due to 231 pion contamination is less than 10^{−3} and is negligible compared to the 3 − 4% 232 statistical uncertainty.

Fig. 4. [Color online] Electron detection efficiency (left) and pion rejection factor (right) vs. vertical (dispersive) hit position of the particle in the preshower detector for the narrow electron triggers in the Left HRS. A one-hour run was used in this evaluation. For electron efficiencies, the total efficiency is shown by the red curve, while blue shaded area indicates events that are recorded by the two adjacent groups. The average electron efficiency across the detector for this one-hour run is (94.626 ± 0.002)% and the average pion rejection factor is 75.3 ± 1.1. The error bars are statistical only. PID performance for the wide path and the Right HRS are similar.

233 4 DAQ Deadtime

234 Deadtime is the amount of time after an event during which the system is unable 235 to record another event. Identifying the exact value of the deadtime is always a 236 challenge in counting experiments. By having a narrow and wide path, we can 237 observe the trend in the deadtime – the wider path should have higher deadtime. By 238 matching the observed trend with our simulation we can benchmark and confirm 239 the simulation result of our deadtime. In addition, dividing lead-glass blocks into 240 groups greatly reduces the deadtime loss in each group compared to summing all 241 blocks together and forming only one final trigger.

242 To illustrate the importance of the deadtime, consider its effect on the asymmetry 243 A. For a simple system with only one contribution to the deadtime δ, the observed 244 asymmetry A_{O} is related the the true asymmetry A according to A_{O} = (1−δ)A. In 245 this experiment δ was on the order of 0.02 (dependent on the rate). To achieve a 3% 246 accuracy on the asymmetry, δ must be known with a ≤ 30% relative accuracy, so 247 that it becomes a negligible systematic error. The DAQ we deployed was, however, 248 more complex, having the three contributions to the deadtime, as listed below and 249 shown in Fig. 2:

250 (1) The “group” deadtime: deadtime due to discriminators and logical AND mod-251 ules used to form group triggers; 252 (2) The “veto” deadtime: deadtime from electronics that used scintillator and 253 Cherenkov signals to form the “gate” signals which were sent to the AND 254 module of each group to form group electron and pion triggers. 255 (3) The “OR” deadtime: deadtime due to the logical OR module when combining 256 all group triggers.

257 The final deadtime is a combination of all three. In order to evaluate the DAQ 258 deadtime, a full-scale simulation was developed as follows: The analog signals for 259 preshower, shower, scintillator and gas Cherenkov as recorded by ADCs from low-260 current runs are fed to the simulation as inputs. The simulation takes into account all 261 electronics and delay cables of the DAQ and calculate digital outputs from discrim-262 inators, all AND and OR modules. For the preshower and shower SUM8 outputs, 263 FADC data were used to determine the signal width.

264 4.1 Group Deadtime Measurement

265 In order to study the group deadtime, a high rate pulser signal (“tagger”) was mixed 266 with all preshower and total shower signals using analog summing modules, see 267 Figs. 2 and 5. In the absence of all detector signals, a tagger pulse produces without 268 loss an electron trigger output, and a “tagger-trigger coincidence” pulse between 269 this output and the delayed tagger – the tagger itself with an appropriate delay to 270 account for the DAQ response time. When high-rate detector signals are present, 271 however, some of the tagger pulses would not be able to trigger the DAQ due to 272 deadtime. The relative loss in the tagger output w.r.t. the tagger input has two com-273 ponents:

274 (1) The count loss R_{o}/R_{i}: when a detector PMT signal precedes the tagger signal 275 by a time interval δt shorter than the DAQ deadtime but longer than the de-276 layed tagger pulse width, the tagger signal is lost and no coincidence output 277 is formed; 278 (2) The pileup fraction p: when a PMT signal precedes the tagger signal by a time 279 interval δt shorter than the delayed tagger signal width, there would be coin-280 cidence output between the delayed tagger and the electron output triggered 281 by the detector PMT signal. If δt is less than the DAQ deadtime (which is true 282 for this experiment), the tagger itself is lost due to deadtime and the tagger-283 trigger coincidence is a false count and should be subtracted. In the case if 284 δt is longer than the DAQ deadtime (not true for this experiment but could 285 happen in general), the tagger itself also triggers a tagger-trigger coincidence 286 but in this case, there are two tagger-trigger coincidence events, both recorded 287 by the fbTDC if working in the multi-hit mode, and one is a false count and 288 should be subtracted. 289 The pileup effect can be measured because the delay between the coinci-290 dence output and the input tagger would be smaller than when the electron 291 output is caused by the tagger. This effect is illustrated in Fig. 5 and con-292 tributes to both I_{1} and I_{2} region of the fbTDC spectrum. Fractions of I_{1} and 293 I_{2} relative to I_{0} are expected to be I_{1}/I_{0} = Rt_{1} and I_{2}/I_{0} = Rw, respectively, 294 where R is the PMT signal rate, w is the width of the trigger output and t_{1} is 295 the time interval the delayed tagger precedes the tagger’s own trigger output. 296 During the experiment w was set to 15 ns for all groups, t_{1} was measured at 297 the end of the experiment and was found to be between 20 and 40 ns. Data for 298 I_{1,2} extracted from fbTDC agree very well with the expected values.

The fractional loss of tagger events due to DAQ deadtime is evaluated as

D = 1 − (1 − p)(R_{o}/R_{i}),  (3)

299 where R_{i} is the input tagger rate, R_{o} is the output tagger-trigger coincidence rate, 300 and p = (I_{1} + I_{2})/I_{0} is a correction factor for pileup effects (see Fig. 5 for defini-301 tion of I_{0,1,2}). The pileup effect was measured using fbTDC spectrum for electron 302 narrow and wide triggers for all groups. Results for the deadtime loss D are shown 303 in Figs. 6 and 7 and compared with simulation. Different beam currents between 304 20 and 100 μA were used in this dedicated deadtime measurement. In order to re-305 duce the statistical fluctuation caused by limited number of trials in the simulation 306 within a realistic computing time, simulations were done at higher rates than the 307 actual measurement.

308 The slope of the tagger loss vs. event rate gives the value of group deadtime in 309 seconds, as shown in Figs. 6 and 7, for group 4 on the left HRS and group 4 on 310 the right HRS, respectively. These data are compared with results from the simu-311 lation. One can see that the deadtime for the wide path is approximately 100 ns as 312 expected. The deadtime for the narrow path, on the other hand, is dominated by 313 the input PMT signal width (typically 60-80 ns) instead of the 30-ns discriminator 314 width. The simulated deadtime agree very well than data for both HRSs and for 315 both wide and narrow paths.

316 4.2 Total Deadtime Evaluation

317 Although the deadtime loss of each group was measured using tagger signals, the 318 dominating term in the total deadtime is from the veto electronics because the to-319 tal trigger rate from scintillators and gas Cherenkov is much higher than individ-320 ual group rates. The difference in total loss between narrow and wide path is thus 321 smaller than that in their group deadtimes. Simulation for the veto deadtime was 322 compared with FADC data and the agreement was found to be at 20% level or bet-323 ter. After subtracting group and veto deadtimes from the total simulated deadtime, 324 the remaining is attributed to the logical OR module. There is no direct measure-325 ment of the logical OR deadtime, but the effect of the logical OR module is quite

from signals triggered by tagger itself from signals triggered by PMT signals (pile-ups) I_{0}  I_{1}  I_{2}

Fig. 5. [Color online] Top: schematic diagram for the tagger setup and signal timing sequence. Bottom: fbTDC spectrum for the relative timing between tagger-trigger coincidence and the input tagger, in 0.5-ns bins. The fbTDC module works in the multi-hit mode. Two different scenarios are shown: 1) Main peak I_{0}: when there is no PMT signal preceding the tagger, the tagger triggers the DAQ and forms a tagger-trigger coincidence. 2) Pileup events I_{1} and I_{2}: when there is a PMT signal preceding the tagger by a time interval shorter than the delayed tagger width, the PMT signal triggers the DAQ and forms a tagger-trigger coincidence signal with the delayed tagger.

326 straightforward and can be calculated analytically. The difference between the sim-327 ulation and the analytic results can be used to estimate the uncertainty of the OR 328 deadtime.

329 The simulated deadtime loss of the global electron triggers and its decomposi-330 tion into group, veto, and OR are shown in Table 1. The total deadtime is also 331 shown in Fig. 8 as a function of the total event rate. The deadtime corrections to

Fig. 6. [Color online] Deadtime loss in percent vs. event rate from the tagger method for group 4 on the Left HRS. Top: actual deadtime loss from tagger measurements; Bottom: simulated deadtime loss of the tagger. The tagger fractional count loss 1 − R_{o}/R_{i} (red) and the pileup correction p (black) are combined to form the total group deadtime D (blue). These data were taken (or simulated) at a Q^{2} of 1.1 (GeV/c)^{2}. To minimize the statistical uncertainty while keeping the computing time reasonable, the simulation used higher event rates than the tagger measurement. The total group deadtime can be determined from the linear fit slope coefficients: tagger data narrow p_{1} = (61.5 ± 0.2) × 10^{−9} s, wide p_{1} = (99.9 ± 0.3) × 10^{−9} s, simulation narrow p_{1} = (62.5 ± 1.4) × 10^{−9} s, wide p_{1} = (102 ± 1.3) × 10^{−9} s. Group 4 is from the central blocks of the lead-glass detector and has the highest rate among all groups.

332 the final asymmetry results from the wide path triggers are (1.64 ± 0.16)% and 333 (0.931 ± 0.215)%, for Q^{2} = 1.1 and 1.9 (GeV/c)^{2}, respectively. These provide a 334 direct correction to the measured asymmetry and the uncertainties are smaller than 335 the 30% limit originally designed for this experiment.

Fig. 7. [Color online] Deadtime loss in percent vs. event rate from the tagger method for group 4 on the Right HRS. Top: tagger data; Bottom: simulation. These data were taken (or simulated) at a Q^{2} of 1.9 (GeV/c)^{2}. The total group deadtime can be determined from the linear fit slope coefficients: tagger data narrow p_{1} = (71.1 ± 0.9) × 10^{−9} s, wide p_{1} = (107 ± 1.2) × 10^{−9} s, simulation narrow p_{1} = (73.9 ± 1.5) × 10^{−9} s, wide p_{1} = (115 ± 1.5) × 10^{−9} s. Group 4 is from the central blocks of the lead-glass detector and has the highest rate among all groups. See Fig. 6 caption for details.

336 4.3 Asymmetries

337 The physics asymmetries sought for in this experiment are 90 and 160 ppm, for 338 Q^{2} = 1.1 and 1.9 (GeV/c)^{2}, respectively. The measured asymmetries are about 339 90% of these values due to beam polarization. To understand the systematics of the 340 asymmetry measurement, a half-wave plate (HWP) was inserted in the beamline to 341 flip the laser helicity in the polarized source during half of the data taking period.

Table 1 Simulated DAQ deadtime loss (in percent) and fractional contributions from group, veto, and OR deadtimes. The fractional deadtime from OR is calculated as one minus those from group and veto, and its uncertainty is estimated from the difference between simulation and the analytical results. The uncertainty of the total deadtime is the uncertainties from group, veto and OR added in quadrature.

Q^{2}  Path  fractional contribution  Total deadtime
(GeV/c)^{2}  Group  Veto  OR  loss at 100μA
1.1  narrow (20.6 ± 2.1)% (51.3 ± 1.9)% (28.1 ± 8.6)% (1.45 ± 0.13)%
wide (29.5 ± 2.4)% (45.3 ± 1.7)% (25.3 ± 9.0)% (1.64 ± 0.16)%
1.9  narrow (2.9 ± 0.2)% (80.6 ± 18.5)% (16.5 ± 12.3)% (0.885 ± 0.196)%
wide (4.3 ± 0.4)% (76.6 ± 17.5)% (19.1 ± 15.1)% (0.931 ± 0.215)%

Fig. 8. [Color online] Simulated deadtime loss of the global electron trigger for the Left (left) and the Right (right) HRS. The error bars shown are due to statistical uncertainty of the simulation. See Table 1 for final uncertainty evaluation.

342 The measured asymmetries flip sign for each beam HWP change and the magnitude 343 of the asymmetry remain consistent within statistical error bars.

344 The asymmetries can be formed from event counts of each beam helicity pair, 345 with 33-ms of helicity right and 33-ms of helicity left beam, normalized by the 346 beam charge. Figure 9 shows the pull distribution of pair-wise asymmetries with 347 the “pull” defined as

p_{i} ≡ (A_{i} − ⟨A⟩)/δA_{i} ,  (4)

348 where A_{i} is the asymmetry extracted from the i-th beam helicity pair with the HWP 349 states already corrected and δA_{i} = 1/\sqrt{N_{i}^{R} + N_{i}^{L}} its statistical uncertainty with 350 N_{i}^{R(L)} the event counts from the right (left) helicity pulse of the pair, and ⟨A⟩ is the 351 asymmetry averaged over all beam pairs. One can see that the asymmetry spectrum 352 agrees to five orders of magnitude with Gaussian distribution expected from purely 353 statistical fluctuations.

Fig. 9. [Color online] Pull distribution [Eq.(4)] for the global electron narrow trigger for Q^{2} = 1.1 (top) and Q^{2} = 1.9 (GeV/c)^{2} (bottom).

354 5 Summary

355 A scaler-based counting DAQ with hardware-based particle identification was suc-356 cessfully implemented in the 6 GeV PVDIS experiment at Jefferson Lab. Asymme-357 tries measured by the DAQ follow Gaussian distributions as expected from purely 358 statistical measurements. Particle identification performance of the DAQ were mea-359 sured during the experiment and corrections are applied to the data on a day-to-day 360 basis. DAQ deadtime was calculated from a full-scale timing simulation and re-361 sults are well understood. Systematic uncertainties from the new DAQ contribute to 362 ≈ 0.2% to the final asymmetry results and are negligible compared to the (3 − 4)% 363 statistical uncertainty and other leading systematic uncertainties.

364 Acknowledgments

365 This work is supported in part by the Jeffress Memorial Trust under Award No. 366 J-836, the U.S. National Science Foundation under Award No. 0653347, and the 367 U.S. Department of Energy under Award No. DE-SC0003885. Notice: Authored 368 by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-369 06OR23177. The U.S. Government retains a non-exclusive, paid-up, irrevocable, 370 world-wide license to publish or reproduce this manuscript for U.S. Government 371 purposes.

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