Measurement of parity-violating asymmetry in electron-deuteron inelastic scattering

The parity-violating asymmetries between a longitudinally polarized electron beam and an unpolarized deuterium target have been measured recently. The measurement covered two kinematic points in the deep-inelastic scattering region and five in the nucleon resonance region. We provide here details of the experimental setup, data analysis, and results on all asymmetry measurements including parity-violating electron asymmetries and those of inclusive pion production and beam-normal asymmetries. The parity-violating deep-inelastic asymmetries were used to extract the electron-quark weak effective couplings, and the resonance asymmetries provided the first evidence for quark-hadron duality in electroweak observables. These electron asymmetries and their interpretation were published earlier, but are presented here in more detail.

Figure 1

The electron exchanges either a virtual photon (left) or a virtual $Z^0$ (right) with the target. The interference between these two processes leads to a parity-violating asymmetry between left- and right-handed electrons.

Figure 2

Feynman diagram for contact interactions, used commonly to describe beyond-standard-model interactions.

Figure 3

Previous data on $C_{2q}$, extrapolated to $Q^2=0$. The yellow ellipse represents a simultaneous fit to $C_{1q}$ and $C_{2q}$ using only the SLAC E122 asymmetries [9], reanalyzed using the latest PDF fits (see Appendix pp1). The magenta vertical-line-hatched band represents a fit to the best $C_{1q}$ data [31] and the green slanted-line-hatched ellipse represents the combined fit of the E122 asymmetries and the best $C_{1q}$. The right panel shows an enlarged view with the vertical and the horizontal axes at the same scale. The standard model value is shown as the black dot, where the size of the dot is for visibility.

Figure 4

Schematic floor plan of the 6-GeV PVDIS experiment in Hall A at JLab. The electron beam enters from the left, passes through a series of monitoring devices such as the ARC (that uses the arc session of the beamline) and the eP (that uses electron-proton elastic scattering) for energy measurement, Compton and Møller polarimeters for polarization measurement, the beam charge monitor (BCM) and the beam position monitor (BPM), then scatters from a liquid ${\mathrm{D}}_2$ target in the middle of the hall. The scattered electrons were detected in the HRS pair in inclusive mode.

Figure 5

Schematic diagram of the target ladder arrangement used during the experiment. The electron beam is along the horizontal direction (the $z$ axis) and is incident from the left on the target. The carbon multifoils were located at $z=(-15,-7.5,0,7.5,15)$ cm and the Al dummy foils were located at $z=(-10,10)$ cm. All other solid targets were located at $z=0$ cm and were about 1 inch apart in the vertical direction.

Figure 6

(Bottom) Schematic diagram for the HRS in Hall A of JLab, figure taken from Ref. [54]. (Top) Magnified view of the detector package in the HRS.

Figure 7

Measured standard deviation of the pairwise asymmetries at kinematics DIS#2, for various raster sizes and two beam currents 100 and $115\mu \mathrm{A}$. The curves show the results of the fit $\delta A=p_0{x}^{p_1}+p_2$, where $x$ is the raster size in mm. The parameter $p_2$ represents the purely statistical fluctuation that depends only on the beam current and not the raster size, while the term $p_0{x}^{p_1}$ is an empirical term that describes the size of target boiling. The fit results for 100 $\mu \mathrm{A}$ are $p_0=(1.77\pm 1.94)\times {10}^4, p_1=-2.48\pm 1.85, p_2=27973.0\pm 681.7$; and for 115 $\mu \mathrm{A}$ are $p_0=(9.40\pm 3.78)\times {10}^3, p_1=-1.37\pm 1.09, p_2=25941.0\pm 1433.4$. At a raster size of $4\times 4{\mathrm{mm}}^2$ ($x=4$), the boiling noise is at the level of 569 ppm for 100 $\mu \mathrm{A}$ and 1407 ppm for 115 $\mu \mathrm{A}$ and is negligible compared to the value from purely statistical fluctuations.

Figure 8

Measured standard deviation of the pairwise asymmetries at various beam currents for DIS#1 (top) and DIS#2 (bottom), with a $4\times 4{\mathrm{mm}}^2$ square raster. The curves show the results of the fit $\delta A\propto I^{p_3}$ and its error band. The fit results are $p_3=0.4900\pm 0.0076$ and $p_3=0.4897\pm 0.0072$ for DIS#1 and DIS#2, respectively. These results are in good agreement with pure counting statistics ($\delta A\propto \sqrt{I}$).

Figure 9

Polarization results from the Møller polarimeter measurements taken with a beam energy of 6.067 GeV. The error bars represent the quadratic sum of the statistical and systematic errors. However, for each measurement the statistical uncertainty was on the order of 0.1%, much smaller than the systematic error. An additional measurement was done with a beam energy of 4.867 GeV at the end of the run period, which gave a similar polarization.

Figure 10

Comparison between Compton (black solid circles) and Møller (red open squares) measurements taken during the time period when both polarimeters were available. The beam energy was 6.067 GeV. The error bars for Møller represent the quadratic sum of the statistical and systematic errors, with the statistical error smaller than the systematic by one order of magnitude. For Compton measurement, the statistical errors are plotted with the data points and the systematic error ($1.92\%$ relative) is plotted along the horizontal axis. A constant fit to Compton measurements gave an average of 89.45%, while the average of Møller results was $88.74\%$.

Figure 11

Calibrated beam spot distribution at the target.

Figure 12

Top view of the TCS $(x_{\text{tg}},y_{\text{tg}},z_{\text{tg}})$ and the sieve plane coordinate system $(x_{\mathrm{sieve}},y_{\mathrm{sieve}})$. The $z_{\text{tg}}$ axis is along the HRS central ray, the $y_{\text{tg}}$ axis is pointing to the left, the $x_{\text{tg}}$ axis is pointing vertically down, and the origin of the TCS is the point along the HRS central ray that is the closest to the Hall center. The ${\varphi }_{\text{tg}}$ is the tangent of the in-plane angle and ${\theta }_{\text{tg}}$ is the tangent of the out-of-plane angle (not shown) with respect to the spectrometer central ray. The sieve plane is located at a drift distance $L=1.12$ m from the TCS origin, with the $y_{\mathrm{sieve}}$ axis pointing to the left of the spectrometer entrance and the $x_{\mathrm{sieve}}$ axis pointing vertically down. The pointing of the spectrometer, $D$, describes how much the HRS central ray misses the Hall center, and ${\theta }_0$ is the angle of the HRS central ray with respect to the beamline. Figure reproduced from Refs. [54, 70].

Figure 13

(Top) Vertex reconstruction for Left DIS#1. The number above each foil is $\Delta z_{\mathrm{foil}}\mathrm{data}$, defined as how much the observed foil position misses the expected value. The blue dotted lines are fits to the peak position. For all foils we have $\Delta z_{\mathrm{foil}}\mathrm{data}⩽0.4$ mm. (Bottom) Reconstruction of the sieve hole positions for left RES II. The data are shown as scattered points and are compared to the expected positions (grids). No obvious discrepancy is seen. The axes are oriented such that the sieve hole pattern is as if viewed when facing the spectrometer entrance. Two of the sieve holes are larger than others to allow identifying the center and the orientation of the sieve plate.

Figure 14

Fine tuning of the HRS acceptance in hamc. Event distributions from data are plotted at the collimator (entrance of the HRS $Q_1$), $Q_1$ exit, and entrances and exits of the dipole and $Q_3$. From these distributions, the best estimate of the position and the size of the apertures were determined (black dashed lines and curves). These were then used as aperture or acceptance cuts in hamc. The axes are oriented such that the distributions are as viewed along the particle trajectory, with $y$ the horizontal and $x$ the vertical (dispersive) directions, respectively.

Figure 15

Comparison between hamc (red dashed lines) and data (black solid lines). From top to bottom: target variables—${\theta }_{\text{tg}}, {\varphi }_{\text{tg}}, y_{\text{tg}}$, and ${(\delta p/p)}_{\text{tg}}$—for left HRS DIS#1; $Q^2$ and $x$ for left HRS DIS#1; target variables for right HRS DIS#2; $Q^2$ and $x$ for right HRS DIS#2.

Figure 16

Kinematics of the beam-normal asymmetry background. The incident and the scattered electrons' momenta are ${\vec{k}}_e$ and ${\vec{k}}_e^{\prime }$, and ${\vec{S}}_{\mathrm{V},\mathrm{H},\mathrm{L}}$ denote, respectively, the incident electron's spin polarization components in the vertical, horizontal, and longitudinal directions. The central scattering angle setting of the spectrometer is ${\theta }_0$ and the scattered electron's momentum has an out-of-plane angle denoted by ${\theta }_{\text{tr}}$.

Figure 17

The function $P_{\mathrm{rs}}\left(E\right)$ determined from HAPPEx data.

Figure 18

Kinematics used in hamc to correct energy losses $\delta E$ and $\delta E^{\prime }$ for the incoming and outgoing electrons, respectively. The kinematics reconstructed from the data corresponds to $E_{\mathrm{beam}}$ and $E_{\det }^{\prime }$, while the vertex kinematics corresponds to $E_{\mathrm{vtx}}$ and $E_{\mathrm{vtx}}^{\prime }$.

Figure 19

Simulated vertex kinematics of the two DIS kinematics #1 (left) and #2 (right).

Figure 20

Kinematics coverage of the four resonance measurements (colored contours), compared with the DIS vertex kinematics (black contours).

Figure 21

Event distributions in $W$ (top) and $Q^2$ (bottom) for the six DAQ groups taken at setting RES I. The coverage in $W$ increases monotonously from group 1 to 6. The red dashed histogram shows the global trigger events.

Figure 22

From Ref. [49]: $W$ dependence of the parity-violating asymmetries in $\vec{e}{-}^2\mathrm{H}$ scattering in the nucleon resonance region. The physics asymmetry results $A_{\text{PV}}^{\mathrm{phys}}$ for the four kinematics RES I, II, III, and IV (solid circles, solid squares, solid triangles, and open triangles, respectively), in parts per million (ppm), are scaled by $1/Q^2$ and compared with calculations from Ref. [87] (Theory A, dashed line), Ref. [88] (Theory B, dotted line), Ref. [90] (Theory C, solid line), and the DIS estimation (dash-double-dotted line) using Eq. (32) with the extrapolated CJ PDF [91]. The vertical error bars for the data are statistical uncertainties, while the horizontal error bars indicate the rms values of the $W$ coverage of each bin. The experimental systematic uncertainties are shown as the shaded bands at the bottom. For each of the four kinematics, calculations were performed at the fixed $E_b$ and $Q^2$ values of each of the RES I, II, III, and IV settings and with a variation in $W$ to match the coverage of the data. Theories B and C each have three curves showing the central values and the upper and the lower bounds of the calculation. Uncertainties of the DIS calculation were below 1 ppm and are not visible.

Figure 23

From Ref. [48]: Results on $(2C_{1u}-C_{1d}){|}_{Q^2=0}$ and $(2C_{2u}-C_{2d}){|}_{Q^2=0}$ from the present experiment. The right panel shows an enlarged view with the vertical and the horizontal axis at the same scale. The new results (blue horizontal-line-hatched ellipse) are compared with SLAC E122 (yellow ellipse) [8, 9]. A fit to the latest data on $C_{1q}$ [31] (from PVES and atomic Cs [32, 33, 34, 35]) is shown as the magenta vertical-line-hatched band. The green slanted-line-hatched ellipse shows a fit to the combined result of SLAC E122 and the latest $C_{1q}$, while the red line-cross-hatched ellipse shows a fit to the combined result of SLAC E122, the present experiment, and the latest $C_{1q}$. The standard model value $2C_{2u}-C_{2d}{|}_{Q^2=0}=-0.0950\pm 0.0004$ is shown as the black dot, where the size of the dot is for visibility.

Figure 24

From Ref. [48]: Mass exclusion limits on the electron and quark compositeness and contact interactions obtained from the zero-$Q^2$ values of $2C_{1u}-C_{1d}$ and $2C_{2u}-C_{2d}$ at the 95% confidence level. The yellow (inner) contour shows the limit obtained from SLAC E122 asymmetry results [8, 9] combined with the best $C_{1q}$ values [31]. The red (outer) contour shows the limit with our new results added.