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}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 15 and improve over world data. To achieve this, asymmetries at the 10^{−4} level need to be 16 measured. A specialized data acquisition (DAQ) system with intrinsic particle identification 17 (PID) was developed and used. The DAQ system of this experiment is presented here with 18 an emphasis on understanding of its PID performance, deadtime effect and the capability 19 of measuring small asymmetries.

20 Key words: Jefferson Lab; Hall A; PVDIS; DAQ 21 PACS: 11.30.Er, 12.15.Mm, 13.60.Hb 14.60.Cd 14.65.Bt 29.30.Aj 29.85.Ca

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

22 1 Introduction

23 The Parity Violating Deep Inelastic Scattering (PVDIS) experiment E08-011 was 24 completed in December 2009 at the Thomas Jefferson National Accelerator Facil-25 ity (JLab). The goal of this experiment [1,2] was to measure to a high precision 26 the parity violating asymmetry in deep inelastic scattering of a polarized electron 27 beam on an unpolarized liquid deuterium target. This asymmetry is sensitive to a 28 combination of the quark weak axial charge 2C_{2u} − C_{2d}, where C_{2q} = 2g_{V}^{e} g_{A}^{q} with 29 q = u, d indicating an up or a down quark, g_{V}^{e} is the electron vector coupling and 30 g_{A}^{q} is the quark axial coupling to the Z^{0} boson.

31 For electron inclusive scattering from an unpolarized target, the electromagnetic 32 interaction is parity conserving and is insensitive to the spin flip of the incom-33 ing electron beam. Only the weak interaction violates parity and the interference 34 between electromagnetic and weak interactions causes a difference between the 35 right- and left-handed electron scattering cross-sections σ_{R} and σ_{L}. The magnitude 36 of this cross-section asymmetry, A_{P V} ≡ (σ_{R} − σ_{L})/(σ_{R} + σ_{L}), is proportional to 37 the four momentum transfer squared Q^{2} for Q^{2} ≪ M_{Z}^{2}, and is in the order of 10^{−4} 38 or 100 parts 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 51 goal is < 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 π^{±} are produced primarily from nucleon resonance decays 57 and carry a parity violation asymmetry corresponding to the Q^{2} at which the res-58 onances are produced, typically a fraction of the asymmetry of electrons with the 59 same scattered momentum. Assuming a fraction f of the detected events are π^{−} 60 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 polarized electron beam with a polarization of ap-68 proximately 90% and a 20-cm long liquid deuterium target. The two High Resolu-69 tion Spectrometers (HRS) [5] were used to detect scattered events. While the stan-70 dard HRS detector package and data acquisition (DAQ) system routinely provide 71 a 10^{4} pion rejection with approximately 99% electron efficiency, they are based on 72 full recording of the detector signals and are limited to event rates up to 4 kHz. This 73 is not sufficient for the high rates expected for the experiment. (The HRS DAQ will 74 be referred to as “standard DAQ” hereafter.)

75 Most previous parity violation experiments– SAMPLE [6] at MIT-Bates, HAPPEX [7– 76 10,13], and PREX [12] at JLab – focused on elastic scatterings from nuclear or nu-77 cleon targets which are typically not contaminated by inelastic backgrounds. Sig-78 nals from the detectors can be integrated and a helicity dependence in the integrated 79 signal can be used to extract the physics asymmetry, and no pion rejection was im-80 plemented. Integrating DAQ was also used at the preceding PVDIS measurement 81 at SLAC [3,4] which resulted in approximately 2% of the integrated signal to be 82 pions. In the Mainz PVA4 experiment [14,15], 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 material used.

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 [17,16] 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 percents.

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

103 2 Detector and DAQ Overview

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

112 For the gas Cherenkov and the lead-glass detector, a full recording of their out-113 put ADC data is not feasible at the expected high rate. Instead their signals are 114 passed through discriminators and logic units to form preliminary electron and 115 pion triggers. Particle identification is fulfilled by the use of discriminators for 116 both the lead-glass and the Cherenkov detectors and proper settings of their thresh-117 olds. These preliminary triggers are then combined with the scintillator triggers 118 and Cherenkov signals to form the final electron and pion triggers, which are then 119 sent to scalers to record the event counts and offline used to form asymmetries 120 A = (n_{R}−n_{L})/(n_{R}+n_{L}), where n_{R(L)} is the integrated rate of the triggers normal-121 ized to the integrated beam charge for the right(R) and left(L) handed spin states 122 (helicity) of the incident electron beam. The scalers that count triggers and beam 123 charge are integrated over the helicity period, which was flipped pseudo-randomly 124 at 30 Hz per the experimental technique used by the HAPPEX experiments [13].

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

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

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

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.

171 lead-glass signals to trigger the high threshold TS discriminators for the electron 172 triggers, pions do not introduce extra counting deadtime for the electron triggers.

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

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

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.

191 Full sampling of analog signals were done using Flash-ADCs (FADCs) at low rates 192 intermittently during the experiment. For one group on the left and one group on 193 the right HRS, the preshower and shower SUM8 outputs, the intermediate logical 194 signals of the DAQ, and the output electron and pion triggers were recorded. These 195 FADC data provide a study of pileup effects to confirm the simulation and to pro-196 vide the input parameters for the simulation, specifically the rise and fall times of 197 the signals and their widths.

198 3 DAQ PID Performance

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

206

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

217 As described in the Introduction, pion contamination in the electron trigger would 218 affect the measured electron asymmetry as A^{m} = (1 − f)A_{e} + fA_{π} where A^{m} 219 and A_{e} are the measured and the true electron asymmetries, respectively, f is the 220 pion contamination fraction in the electron trigger, and A_{π} is the parity violation 221 asymmetry of pion production. As shown in Fig. 4, pion rejection factor from the 222 lead-glass detector was above 50. Combined with the approx. 200 pion rejection 223 factor of the gas Cherenkov detector [5], the total pion rejection achieved during 224 this experiment was above 10^{4}. The pion to electron rate ratios for the two Q^{2} values 225 of this experiment were less than 10:1, thus f < 10/10^{4} = 10^{−3}. Because pions 226 are produced from nucleon resonance decays, the parity violation asymmetry of 227 pion production is expected to be no larger than that of scattered electrons with the 228 same momentum. This was confirmed by asymmetries formed from pion triggers 229 during this experiment. Overall the uncertainty in the electron asymmetry due to 230 pion contamination is less than 10^{−3} and is negligible compared to the 3 − 4% 231 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.

232 4 DAQ Deadtime

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

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

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

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

263 4.1 Group Deadtime Measurement

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

272 (1) The count loss R_{o}/R_{i}: when a detector PMT signal precedes the tagger signal 273 by a time interval δt shorter than the DAQ deadtime but longer than the de-274 layed tagger pulse width, the tagger signal is lost and no coincidence output 275 is formed; 276 (2) The pileup fraction p: when a PMT signal precedes the tagger signal by a time 277 interval δt shorter than the delayed tagger signal width, there would be coin-278 cidence output between the delayed tagger and the electron output triggered 279 by the detector PMT signal. If δt is less than the DAQ deadtime (which is true 280 for this experiment), the tagger itself is lost due to deadtime and the tagger-281 trigger coincidence is a false count and should be subtracted. In the case if 282 δt is longer than the DAQ deadtime (not true for this experiment but could 283 happen in general), the tagger itself also triggers a tagger-trigger coincidence 284 but in this case, there are two tagger-trigger coincidence events, both recorded 285 by the fbTDC if working in the multi-hit mode, and one is a false count and 286 should be subtracted. 287 The pileup effect can be measured because the delay between the coinci-288 dence output and the input tagger would be smaller than when the electron 289 output is caused by the tagger. This effect is illustrated in Fig. 5 and con-290 tributes to both I_{1} and I_{2} region of the fbTDC spectrum. Fractions of I_{1} and 291 I_{2} relative to I_{0} are expected to be I_{1}/I_{0} = Rt_{1} and I_{2}/I_{0} = Rw, respectively, 292 where R is the PMT signal rate, w is the width of the trigger output and t_{1} is 293 the time interval the delayed tagger precedes the tagger’s own trigger output. 294 During the experiment w was set to 15 ns for all groups, t_{1} was measured at 295 the end of the experiment and was found to be between 20 and 40 ns. Data for 296 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)

297 where R_{i} is the input tagger rate, R_{o} is the output tagger-trigger coincidence rate, 298 and p = (I_{1} + I_{2})/I_{0} is a correction factor for pileup effects (see Fig. 5 for defini-299 tion of I_{0,1,2}). The pileup effect was measured using fbTDC spectrum for electron 300 narrow and wide triggers for all groups. Results for the deadtime loss D are shown 301 in Figs. 6 and 7 and compared with simulation. Different beam currents between 302 20 and 100 μA were used in this dedicated deadtime measurement. In order to re-303 duce the statistical fluctuation caused by limited number of trials in the simulation 304 within a realistic computing time, simulations were done at higher rates than the 305 actual measurement.

306 The slope of the tagger loss vs. event rate gives the value of group deadtime in 307 seconds, as shown in Figs. 6 and 7, for group 4 on the left HRS and group 4 on 308 the right HRS, respectively. These data are compared with results from the simu-309 lation. One can see that the deadtime for the wide path is approximately 100 ns as 310 expected. The deadtime for the narrow path, on the other hand, is dominated by 311 the input PMT signal width (typically 60-80 ns) instead of the 30-ns discriminator 312 width. The simulated deadtime agree very well than data for both HRSs and for 313 both wide and narrow paths.

314 4.2 Total Deadtime Evaluation

315 Although the deadtime loss of each group was measured using tagger signals, the 316 dominating term in the total deadtime is from the veto electronics because the to-317 tal trigger rate from scintillators and gas Cherenkov is much higher than individ-318 ual group rates. The difference in total loss between narrow and wide path is thus 319 smaller than that in their group deadtimes. Simulation for the veto deadtime was 320 compared with FADC data and the agreement was found to be at 20% level or bet-321 ter. After subtracting group and veto deadtimes from the total simulated deadtime, 322 the remaining is attributed to the logical OR module. There is no direct measure-323 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.

324 straightforward and can be calculated analytically. The difference between the sim-325 ulation and the analytic results can be used to estimate the uncertainty of the OR 326 deadtime.

327 The simulated deadtime loss of the global electron triggers and its decomposi-328 tion into group, veto, and OR are shown in Table 1. The total deadtime is also 329 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.

330 the final asymmetry results from the wide path triggers are (1.64 ± 0.16)% and 331 (0.931 ± 0.215)%, for Q^{2} = 1.1 and 1.9 (GeV/c)^{2}, respectively. These provide a 332 direct correction to the measured asymmetry and the uncertainties are smaller than 333 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.

334 4.3 Asymmetries

335 The physics asymmetries sought for in this experiment are 90 and 160 ppm, for 336 Q^{2} = 1.1 and 1.9 (GeV/c)^{2}, respectively. The measured asymmetries are about 337 90% of these values due to beam polarization. To understand the systematics of the 338 asymmetry measurement, a half-wave plate (HWP) was inserted in the beamline to 339 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.

340 The measured asymmetries flip sign for each beam HWP change and the magnitude 341 of the asymmetry remain consistent within statistical error bars.

342 The asymmetries can be formed from event counts of each beam helicity pair, 343 with 33-ms of helicity right and 33-ms of helicity left beam, normalized by the 344 beam charge. Figure 9 shows the pull distribution of pair-wise asymmetries with 345 the “pull” defined as

p_{i} ≡ (A_{i} − ⟨A⟩)/δA_{i} ,  (4)

346 where A_{i} is the asymmetry extracted from the i-th beam helicity pair with the HWP 347 states already corrected and δA_{i} = 1/\sqrt{N_{i}^{R} + N_{i}^{L}} its statistical uncertainty with 348 N_{i}^{R(L)} the event counts from the right (left) helicity pulse of the pair, and ⟨A⟩ is the 349 asymmetry averaged over all beam pairs. One can see that the asymmetry spectrum 350 agrees to five orders of magnitude with Gaussian distribution expected from purely 351 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).

352 5 Summary

353 A scaler-based counting DAQ with hardware-based particle identification was suc-354 cessfully implemented in the 6 GeV PVDIS experiment at Jefferson Lab. Asymme-355 tries measured by the DAQ follow Gaussian distributions as expected from purely 356 statistical measurements. Particle identification performance of the DAQ were mea-357 sured during the experiment and corrections are applied to the data on a day-to-day 358 basis. DAQ deadtime was calculated from a full-scale timing simulation and re-359 sults are well understood. Systematic uncertainties from the new DAQ contribute to 360 ≈ 0.2% to the final asymmetry results and are negligible compared to the (3 − 4)% 361 statistical uncertainty and other leading systematic uncertainties.

362 Acknowledgments

363 This work is supported in part by the Jeffress Memorial Trust under Award No. 364 J-836, the U.S. National Science Foundation under Award No. 0653347, and the 365 U.S. Department of Energy under Award No. DE-SC0003885. Notice: Authored 366 by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-367 06OR23177. The U.S. Government retains a non-exclusive, paid-up, irrevocable, 368 world-wide license to publish or reproduce this manuscript for U.S. Government 369 purposes.

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