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 11 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 in-32 teraction is parity conserving and is insensitive to the spin flip of the incoming elec-33 tron beam. Only the weak interaction violates parity. Taking the difference of the 34 left- and right-handed electron scattering cross-sections, one can isolate the parity 35 violating contribution. The parity violating asymmetry for deep inelastic electron 36 scattering from a deuterium target, A_{P V}, can be written as

A_{P V} ≡ \frac{σ_{R} − σ_{L}}{σ_{R} + σ_{L}} = (−\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)

37 where σ_{R}(L) is the cross section for right-(left-)handed incident electrons, Q^{2} is the 38 negative of the four-momentum transfer squared, G_{F} is the Fermi weak coupling 39 constant, α is the fine structure constant, Y_{1} and Y_{3} are kinematic factors, and x is 40 the Bjorken scaling variable. In the quark parton model,

F_{1}^{γZ} = ∑ g_{V}^{q} Q_{q} [q(x) + q̄(x)]  (2)
F_{3}^{γZ} = ∑ g_{A}^{q}Q_{q} [q(x) − q̄(x)]  (3)
F_{1}^{γ} = \frac{1}{2} ∑ Q_{q}^{2} [q(x) + q̄(x)]  (4)

41 where Q_{q} is the electric charge of quarks and q(x), q̄(x) are quark distribution 42 functions. Rewriting g_{A(V)}^{e}g_{V (A)}^{q} as C_{1(2)q}, and assuming R^{γ} = R^{γZ} = 0 where 43 R^{γ(Z)} = σ_{L}^{γ(Z)}/σ_{T}^{γ(Z)} is the ratio of the longitudinal to transverse cross section of 44 the virtual photon exchange (γ^{∗} − Z interference), one has Y_{1} = 1 and

A_{P V} = (\frac{3G_{F} Q^{2}}{πα^{2}\sqrt{2}} ) ×
\frac{2C_{1u}[1 + R_{C}(x)] − C_{1d}[1 + R_{S}(x)] + Y_{3}(2C_{2u} − C_{2d})R_{V} (x)}{5 + R_{S}(x) + 4R_{C}(x)} , (5)

45 where R_{V,C,S} are related to quark distributions. The magnitude of the asymmetry 46 is in the order of 10^{−4}, or 100 parts per million (ppm) at Q^{2} = 1 (GeV/c)^{2}. The 47 tree-level Standard Model effective weak coupling constants C_{1,2q} are

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} ,

48 with θ_{W} the weak mixing angle. The goal of JLab E08-011 is to measure the PVDIS 49 asymmetries to statistical precisions of 3% and 4% at Q^{2} = 1.1 and 1.9 (GeV/c)^{2}, 50 respectively. In addition, the systematic uncertainty goal is < 3%, and under the 51 assumption that hadronic physics corrections are small, our goal is to extract from 52 these asymmetries the effective coupling constant combination (2C_{2u} − C_{2d}). The 53 magnitudes of the asymmetries are expected to be 90 and 170 ppm for the two 54 measured kinematics of Q^{2} = 1.1 and 1.9 (GeV/c)^{2}, respectively. To achieve the 55 required precision, a rate capability of up to 500 kHz is needed. Although this is 56 not the first time the PVDIS asymmetries are measured, the only preceding PVDIS 57 measurement have been carried out at SLAC [3,4] in the late 1980’s, with approx-58 imately 9% statistical and 9% systematic uncertainties. The increased precision of 59 this experiment required better controls of all systematic uncertainties.

60 The experiment used a 100 μA polarized electron beam with a polarization of ap-61 proximately 90% and a 20-cm long liquid deuterium target. The two High Reso-62 lution Spectrometers (HRS) [5] were used to detect scattered electrons. Similar to 63 other deep inelastic scattering experiments, the main challenge of the measurement 64 is to separate electrons from charged pion background due to electro- or photo-65 production. While the standard HRS detector package and data acquisition (DAQ) 66 system routinely provide a good particle identification (PID), they are based on 67 full recording of the detector signals and are limited to event rates up to 4 kHz. 68 This is not sufficient for the high rates expected for the experiment. The HRS DAQ 69 will be referred to as “standard DAQ” hereafter. For previous JLab parity violation 70 experiments [7,8] focusing on elastic scattering from nuclear or nucleon targets, 71 integrating DAQ could be used because elastic scattering typically is not contami-72 nated by backgrounds. For the SLAC PVDIS experiment, an integrating DAQ was 73 used with the input being the lead-glass detector signals. However, about 2% of 74 the integrated signal was from the pion background. This would cause a system-75 atic uncertainty comparable in size to our statistical uncertainty and a better data 76 collection method must be found.

77 2 Detector and DAQ Overview

78 The design goal of the experiment is to record data up to 1 MHz with hardware-79 based PID and well measured and understood deadtime effects. The following de-80 tectors in the HRS were used: Two scintillator planes provided the main trigger, 81 while a CO_{2} gas Cherenkov detector and a double-layer segmented lead-glass de-82 tector provided particle identification information. The vertical drift chambers (as 83 the tracking detector) were used during calibration runs and turned off during pro-84 duction data taking because they were not expected to endure the high event rates.

85 For the gas Cherenkov and the lead-glass detector, a full recording of their out-86 put ADC data is not feasible at the expected high rate. Instead their signals are 87 passed through discriminators and logic units to form preliminary electron and 88 pion triggers. Particle identification is fulfilled by the use of discriminators for 89 both the lead-glass and the Cherenkov detectors and proper settings of their thresh-90 olds. These preliminary triggers are then combined with the scintillator triggers 91 and Cherenkov signals to form the final electron and pion triggers, which are then 92 sent to scalers to record the event counts and offline used to form asymmetries 93 A = (n_{R}−n_{L})/(n_{R}+n_{L}), where n_{R(L)} is the integrated rate of the triggers normal-94 ized to the integrated beam charge for the right(R) and left(L) handed spin states 95 (helicity) of the incident electron beam. The scalers that count triggers and beam 96 charge are integrated over the helicity period, which was flipped pseudo-randomly 97 at 30 Hz per the experimental technique used by the HAPPEX experiments [9].

98 For HRS the two layers of the lead-glass detector are called “preshower” and 99 “shower” detectors, respectively. The preshower blocks in the Right HRS (the spec-100 trometer located to the right side of the beamline when viewed along the beam 101 direction) has 48 blocks arranged in a 2 × 24 array, with the longest dimension 102 of the blocks aligned perpendicular to the particle trajectory. For the two blocks 103 in each row, only the ends facing outward are read out by photo-multiplier tubes 104 (PMTs) and the other ends of the two blocks were facing each other and not read 105 out. Therefore the preshower detector had 48 output channels. All preshower blocks 106 were individually wrapped to prevent light leak. The preshower and the shower de-107 tectors in the Left HRS are similar to the preshower detector on the Right HRS 108 except that for each detector there are 34 blocks arranged in a 2 × 17 array. The 109 shower detector in the Right HRS had 75 blocks arranged in a 5 × 15 array with the 110 longest dimension of the blocks aligned along the trajectory of scattered particles. 111 PMTs are attached to each block of the Right shower detector on one end only, 112 giving 75 output channels.

113 Because the lead-glass detectors in the Left and Right HRS were built differently, 114 design of the lead-glass-based triggers of the DAQ is also different, as shown in 115 Fig. 1. As a compromise between the amount of electronics needed and the rate in 116 the front end logic modules, the lead-glass blocks in both the preshower and the 117 shower detectors were divided into 6 (8) groups for the Left (Right) HRS, with 118 each group consisting 8 blocks. On the Right HRS only 60 of the 75 shower blocks 119 were used while the 15 blocks on the edge were not read out. The reduction on the 120 HRS acceptance due to not using these side blocks is negligible. Signals from the 8 121 blocks in each group were added using a custom-made analog summing unit called 122 “SUM8 modules”, then passed to discriminators. The geometry and the position of 123 each pre-shower group was carefully chosen to match those of the corresponding 124 shower group to maximize electron detection efficiency. On the Left HRS adjacent 125 groups in both preshower and shower had overlapping blocks, while for the Right 126 HRS only preshower blocks were overlapping. To allow overlap between adjacent 127 groups, signals from preshower blocks on the Right HRS and from both preshower 128 and shower blocks on the Left HRS were split into two identical copies using pas-129 sive splitters.

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.

130 A schematic diagram for the DAQ electronics for the Right HRS is shown in Fig. 2. 131 The electron and pion triggers were formed by passing shower (SS) and preshower 132 (PS) signals or their sums, called total shower (TS) signals, through discriminators 133 with different thresholds. For electron triggers, logical ANDs of the PS discrimi-134 nator and the TS discriminator outputs were used. For pion triggers, low threshold 135 discriminators on the TS signal alone were used to reject background. These signals 136 were then combined with signals from scintillators and the gas Cherenkov (called 137 electron or pion “VETO” signals) to form electron or pion triggers for each shower 138 and preshower group. The electron VETO signals required the gas Cherenkov to 139 be triggered, while the pion VETO required the opposite. The electron or pion trig-140 gers from all six groups on the Left HRS (eight groups for the Right HRS) were 141 then ORed together to form the global electron or pion triggers for the Left (Right) 142 HRS. All triggers – electron and pions from each group, as well as the final global 143 triggers – were counted using scalers. Because pions do not produce large enough

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.

144 lead-glass signals to trigger the high threshold TS discriminators for the electron 145 triggers, pions do not introduce extra counting deadtime for the electron triggers.

146 In order to monitor the counting deadtime of the DAQ, two identical paths of elec-147 tronics were constructed. The only difference between the two paths is in the dis-148 criminator output width, set at 30 ns and 100 ns for the “narrow” and the “wide” 149 paths, respectively. The scalers are rated for 250 MHz (4 ns deadtime) and therefore 150 do not add to the deadtime. In addition, since the output width of all logic modules 151 were set to 15 ns, the deadtime of the DAQ for each group is dominated by the 152 deadtime of the discriminators.

153 The SUM8 modules used for summing all lead-glass signals also served as fan-out 154 modules, providing exact copies of the input PMT signals. These copies were sent 155 to the standard HRS DAQ for calibration.During the experiment, data were col-156 lected at low rates using reduced beam currents with both DAQs functioning, such 157 that a direct comparison of the two DAQs can be made. The vertical drift chambers 158 were used during these low rate DAQ studies. Outputs from all discriminators, sig-159 nals from the scintillator and the gas Cherenkov, and all electron and pion triggers 160 were sent to Fastbus TDCs (fbTDC) and were recorded in the standard DAQ. Data 161 from these fbTDCs were used to align amplitude spectrum and its timing. They 162 also allow the study of the Cherenkov or lead-glass performance for the new DAQ 163 triggers.

164 Full sampling of analog signals were done using Flash-ADCs (FADCs) at low rates 165 intermittently during the experiment. For one group on the left and one group on 166 the right HRS, the preshower and shower SUM8 outputs, the intermediate logical 167 signals of the DAQ, and the output electron and pion triggers were recorded. These 168 FADC data provide a study of pileup effects to confirm the simulation and to pro-169 vide the input parameters for the simulation, specifically the rise and fall times of 170 the signals and their widths.

171 3 DAQ PID Performance

172 PID performance of the DAQ system was studied with calibration runs taken at low 173 beam currents using fbTDC signals along with ADC data of all detector signals 174 recorded by the standard DAQ. Events that triggered the DAQ would appears as a 175 timing peak in the corresponding fbTDC data of the standard DAQ and a cut on this 176 peak can be used to select those events. Figure 3 shows the preshower vs. shower 177 signals for group 2 on the Left HRS. A comparison between no fbTDC cut and with 178 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.

179

180 Electron efficiency and pion rejection factors of the lead-glass detector on the Left 181 HRS are shown in Fig. 4 as functions of the location of the hit of the particle in 182 the preshower detector. PID performance on the Right HRS is similar. Electron 183 efficiency from wide groups are slightly higher than narrow groups because there 184 is less event loss due to timing mis-alignment when taking the coincidence between 185 the preshower and the total shower discriminator outputs. Variations in the electron 186 efficiency across the spectrometer acceptance effectively influence the kinematics 187 (Q^{2}) of the measurement. For this reason, low-rate calibration data were taken daily 188 during the experiment to monitor the DAQ PID performance and corrections are 189 applied to data.

190 Pion contamination in the electron trigger would affect the measured electron asym-191 metry as A_{e}^{m} = (A_{e}^{true} + fA_{π})/(1 + f) where A_{e}^{m} and A_{e}^{true} are the measured and 192 the true electron asymmetries, respectively, f is the pion contamination fraction in 193 the electron trigger, and A_{π} is the parity violation asymmetry of pion production. 194 As shown in Fig. 4, pion rejection factor from the lead-glass detector was above 195 50. Combined with the approx. 200 pion rejection factor of the gas Cherenkov de-196 tector [5], the total pion rejection achieved during this experiment was above 10^{4}. 197 The pion to electron rate ratios for the two Q^{2} values of this experiment were less 198 than 10:1, thus f < 10/10^{4} = 10^{−3}. Because pions are produced from nucleon 199 resonance decays, the parity violation asymmetry of pion production is expected 200 to be no larger than that of scattered electrons with the same momentum. This was 201 confirmed by asymmetries formed from pion triggers during this experiment. Over-202 all the uncertainty in the electron asymmetry due to pion contamination is less than 203 10^{−3} and is negligible compared to the 3 − 4% 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 averge 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.

204 4 DAQ Deadtime

205 Deadtime is the amount of time after an event during which the system is unable 206 to record another event. Identifying the exact value of the deadtime is always a 207 challenge in counting experiments. By having a narrow and wide path, we can 208 observe the trend in the deadtime – the wider path should have higher deadtime. By 209 matching the observed trend with our simulation we can benchmark and confirm 210 the simulation result of our deadtime. In addition, dividing lead-glass blocks into 211 groups greatly reduces the deadtime loss in each group compared to summing all 212 blocks together and forming only one final trigger.

213 To illustrate the importance of the deadtime, consider its affect on the asymmetry 214 A. For a simple system with only one contribution to the deadtime δ, the observed 215 asymmetry A_{O} is related the the true asymmetry A according to A_{O} = (1−δ)A. In 216 this experiment δ was on the order of 0.02 (dependent on the rate). To achieve a 3% 217 accuracy on the asymmetry, δ must be known with a ≤ 30% relative accuracy, so 218 that it becomes a negligible systematic error. The DAQ we deployed was, however, 219 more complex, having the three contributions to the deadtime, as listed below and 220 shown in Fig. 2:

221 (1) The “group” deadtime: deadtime due to discriminators and logical AND mod-222 ules used to form group triggers; 223 (2) The “veto” deadtime: deadtime from electronics that used scintillator and 224 Cherenkov signals to form the “gate” signals which were sent to the AND 225 module of each group to form group electron and pion triggers. 226 (3) The “OR” deadtime: deadtime due to the logical OR module when combining 227 all group triggers.

228 The final deadtime is a combination of all three. In order to evaluate the DAQ 229 deadtime, a full-scale simulation was developed as follows: The analog signals for 230 preshower, shower, scintillator and gas Cherenkov as recorded by ADCs from low-231 current runs are fed to the simulation as inputs. The simulation takes into account all 232 electronics and delay cables of the DAQ and calculate digital outputs from discrim-233 inators, all AND and OR modules. For the preshower and shower SUM8 outputs, 234 FADC data were used to determine the signal width.

235 4.1 Group Deadtime Measurement

236 In order to study the group deadtime, a high rate pulser signal (“tagger”) was mixed 237 with all preshower and total shower signals using analog summing modules, see 238 Figs. 2 and 5. In the absence of all detector signals, a tagger pulse produces without 239 loss an electron trigger output, and a “tagger-trigger coincidence” pulse between 240 this output and the delayed tagger – the tagger itself with an appropriate delay to 241 account for the DAQ response time. When high-rate detector signals are present, 242 however, some of the tagger would not be able to trigger the DAQ due to deadtime. 243 The relative loss in the tagger output w.r.t. the tagger input has two components:

244 (1) The count loss R_{o}/R_{i}: when a detector PMT signal precedes the tagger signal 245 by a time interval δt shorter than the DAQ deadtime but longer than the de-246 layed tagger pulse width, the tagger signal is lost and no coincidence output 247 is formed; 248 (2) The pileup fraction p: when a PMT signal precedes the tagger signal by a time 249 interval δt shorter than the delayed tagger signal width, there would be coin-250 cidence output between the delayed tagger and the electron output triggered 251 by the detector PMT signal. If δt is less than the DAQ deadtime (which is true 252 for this experiment), the tagger itself is lost due to deadtime and the tagger-253 trigger coincidence is a false count and should be subtracted. In the case if 254 δt is longer than the DAQ deadtime (not true for this experiment but could 255 happen in general), the tagger itself also triggers a tagger-trigger coincidence 256 but in this case, there are two tagger-trigger coincidence events, both recorded 257 by the fbTDC if working in the multi-hit mode, and one is a false count and 258 should be subtracted. 259 The pileup effect can be measured because the delay between the coinci-260 dence output and the input tagger would be smaller than when the electron 261 output is caused by the tagger. This effect is illustrated in Fig. 5 and con-262 tributes to both I_{1} and I_{2} region of the fbTDC spectrum. Fractions of I_{1} and 263 I_{2} relative to I_{0} are expected to be I_{1}/I_{0} = Rt_{1} and I_{2}/I_{0} = Rw, respectively, 264 where R is the PMT signal rate, w is the width of the trigger output and t_{1} is 265 the time interval the delayed tagger precedes the tagger’s own trigger output. 266 During the experiment w was set to 15 ns for all groups, t_{1} was measured at 267 the end of the experiment and was found to be between 20 and 40 ns. Data for 268 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}),  (6)

269 where R_{i} is the input tagger rate, R_{o} is the output tagger-trigger coincidence rate, 270 and p = (I_{1} + I_{2})/I_{0} is a correction factor for pileup effects (see Fig. 5 for defini-271 tion of I_{0,1,2}). The pileup effect was measured using fbTDC spectrum for electron 272 narrow and wide triggers for all groups. Results for the deadtime loss D are shown 273 in Figs. 6 and 7 and compared with simulation. Different beam currents between 274 20 and 100 μA were used in this dedicated deadtime measurement. In order to re-275 duce the statistical fluctuation caused by limited number of trials in the simulation 276 within a realistic computing time, simulations were done at higher rates than the 277 actual measurement.

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.

278 The slope of the tagger loss vs. event rate gives the value of group deadtime in 279 seconds, as shown in Figs. 6 and 7, for group 4 on the left HRS and group 4 on 280 the right HRS, respectively. These data are compared with results from the simu-281 lation. One can see that the deadtime for the wide path is approximately 100 ns as 282 expected. The deadtime for the narrow path, on the other hand, is dominated by 283 the input PMT signal width (typically 60-80 ns) instead of the 30-ns discriminator 284 width. The simulated deadtime agree very well than data for both HRSs and for

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.

285 both wide and narrow paths.

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.

286 4.2 Total Deadtime Evaluation

287 Although the deadtime loss of each group was measured using tagger signals, the 288 dominating term in the total deadtime is from the veto electronics because the to-289 tal trigger rate from scintillators and gas Cherenkov is much higher than individ-290 ual group rates. The difference in total loss between narrow and wide path is thus 291 smaller than that in their group deadtimes. Simulation for the veto deadtime was 292 compared with FADC data and the agreement was found to be at 20% level or bet-293 ter. After subtracting group and veto deadtimes from the total simulated deadtime, 294 the remaining is attributed to the logical OR module. There is no direct measure-295 ment of the logical OR deadtime, but the effect of the logical OR module is quite 296 straightforward and can be calculated analytically. The difference between the sim-297 ulation and the analytic results can be used to estimate the uncertainty of the OR 298 deadtime.

299 The simulated deadtime loss of the global electron triggers and its decomposi-300 tion into group, veto, and OR are shown in Table 1. The total deadtime is also

shown in Fig. 8 as a function of the total event rate. The deadtime corrections to

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)%

301

302 the final asymmetry results from the wide path triggers are (1.64 ± 0.16)% and 303 (0.931 ± 0.215)%, for Q^{2} = 1.1 and 1.9 (GeV/c)^{2}, respectively. These provide a 304 direct correction to the measured asymmetry and the uncertainties are smaller than

the 30% limit originally designed for this experiment.

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.

305

306 4.3 Asymmetries

307 The physics asymmetries sought for in this experiment are 90 and 160 ppm, for 308 Q^{2} = 1.1 and 1.9 (GeV/c)^{2}, respectively. The measured asymmetries are about 309 90% of these values due to beam polarization. To understand the systematics of the 310 asymmetry measurement, a half-wave plate (HWP) was inserted in the beamline to 311 flip the laser helicity in the polarized source during half of the data taking period. 312 The measured asymmetries flip sign for each beam HWP change and the magnitude 313 of the asymmetry remain consistent within statistical error bars.

314 The asymmetries can be formed from event counts of each beam helicity pair, 315 with 33-ms of helicity right and 33-ms of helicity left beam, normalized by the 316 beam charge. Figure 9 shows the pull distribution of pair-wise asymmetries with 317 the “pull” defined as

p_{i} ≡ (A_{i} − ⟨A⟩)/δA_{i} ,  (7)

318 where A_{i} is the asymmetry extracted from the i-th beam helicity pair with the HWP 319 states already corrected and δA_{i} = 1/\sqrt{N_{i}^{R} + N_{i}^{L}} its statistical uncertainty with 320 N_{i}^{R(L)} the event counts from the right (left) helicity pulse of the pair, and ⟨A⟩ is the 321 asymmetry averaged over all beam pairs. One can see that the asymmetry spectrum 322 agrees to five orders of magnitude with Gaussian distribution expected from purely 323 statistical fluctuations.

324 5 Summary

325 A scaler-based counting DAQ with hardware-based particle identification was suc-326 cessfully implemented in the 6 GeV PVDIS experiment at Jefferson Lab. Asymme-327 tries measured by the DAQ follow Gaussian distributions as expected from purely 328 statistical measurements. Particle identification performance of the DAQ were mea-329 sured during the experiment and corrections are applied to the data on a day-to-day 330 basis. DAQ deadtime was calculated from a full-scale timing simulation and re-331 sults are well understood. Systematic uncertainties from the new DAQ contribute to 332 ≈ 0.2% to the final asymmetry results and are negligible compared to the (3 − 4)% 333 statistical uncertainty and other leading systematic uncertainties.

Fig. 9. [Color online] Pull distribution [Eq.(7)] for the global electron narrow trigger for Q^{2} = 1.1 (top) and Q^{2} = 1.9 (GeV/c)^{2} (bottom).

334 Acknowledgments

335 This work is supported in part by the Jeffress Memorial Trust under Award No. 336 J-836, the U.S. National Science Foundation under Award No. 0653347, and the 337 U.S. Department of Energy under Award No. DE-SC0003885. Notice: Authored 338 by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-339 06OR23177. The U.S. Government retains a non-exclusive, paid-up, irrevocable, 340 world-wide license to publish or reproduce this manuscript for U.S. Government 341 purposes.

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