Parity-violating electroweak asymmetry in $\vec{e}p$ scattering

We have measured the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from protons. Significant contributions to this asymmetry could arise from the contributions of strange form factors in the nucleon. The measured asymmetry is $A=-15.05\pm 0.98\left(\mathrm{stat}\right)\pm 0.56\left(\mathrm{syst}\right)\mathrm{ppm}$ at the kinematic point $⟨{\theta }_{\mathrm{lab}}⟩=12.3°$ and $⟨Q^2⟩=0.477{(\mathrm{GeV}∕c)}^2$. Based on these data as well as data on electromagnetic form factors, we extract the linear combination of strange form factors $G_E^s+0.392G_M^s=0.014\pm 0.020\pm 0.010$, where the first error arises from this experiment and the second arises from the electromagnetic form factor data. This paper provides a full description of the special experimental techniques employed for precisely measuring the small asymmetry, including the first use of a strained GaAs crystal and a laser-Compton polarimeter in a fixed target parity-violation experiment.

Figure 1

Schematic overview of the HAPPEX experiment.

Figure 2

Schematic diagram of the polarized source laser system showing the seed laser, diode amplifier, and components to steer, focus, and attenuate the beam and define its polarization. BS: beamsplitter. BCS: beam combiner and splitter.

Figure 3

Schematic diagram of the helicity control electronics. The helicity signal drives the high voltage on the Pockels cell. The system is electrically isolated from the rest of the lab (dashed box).

Figure 4

Timing diagram of important control signals related to the beam helicity.

Figure 5

Window-to-window beam jitter as measured by a BPM is plotted along the $x$ axis. On the $y$ axis is plotted the beam position as predicted by nearby BPMs. The residuals are smaller than $1\mu \mathrm{m}$.

Figure 6

Noise in pulse pair asymmetries versus beam current and raster size. The width of asymmetries is extrapolated to $15\mathrm{Hz}$, $100\mu \mathrm{A}$ to check if it is consistent (within the dashed bars) with expectation. A value above this indicates target density fluctuations that increase the noise. For reasonably large raster patterns we saw little noise at $94\mu \mathrm{A}$.

Figure 7

Schematic of the focal plane detector. The scattered electrons strike a lead-acrylic shower counter whose light is collected by a PMT and integrated over a helicity period.

Figure 8

Focal plane detector response versus angle of incident particle with respect to the long axis of the focal plane detector, measured using cosmic rays.

Figure 9

Circuit diagram of one channel of the custom 16 bit integrating ADC.

Figure 10

(Color online) Layout of the Hall A Møller polarimeter.

Figure 11

(Color online) Oblique view of the Compton polarimeter. The beam enters from the left and is bent down into a chicane where it intersects the laser activity. The activity is on the bench in the middle of the chicane. The photon detector for backscattered photons is on the bench just upstream of the last chicane magnet.

Figure 12

Counting rate normalized to beam current versus vertical position of the electron beam for the Compton polarimeter. The sensitivity to beam position differences is proportional to the derivative of this curve. The arrow points to where we run.

Figure 13

(Color online) Compton spectrum as measured by the photon calorimeter. The curve is a fit of the Compton cross section convoluted with a Gaussian resolution of the calorimeter [see Eq. (20)].

Figure 14

Incident linear polarization is nearly circularly polarized by the Pockels cell. The error phase $\mathrm{\Delta }$ causes the polarization ellipses for the two helicities to have their major and minor axes rotated by 90° from each other, causing helicity-correlated transmission through an optical element with an analyzing power. The analyzer is assumed to have differing transmission coefficients for light linearly polarized along the axes $x^{\prime }$ and $y^{\prime }$.

Figure 15

Intensity asymmetry as a function of rotatable half-wave plate orientation. The error bars on some points are smaller than the symbols.

Figure 16

Dependence of position differences measured by two BPMs at the $5\mathrm{MeV}$ point in the Injector (a)–(d) on the orientation of the rotatable half-wave plate. The position differences show a strong correlation with the intensity asymmetry (e). The error bars on some data points are smaller than the symbols.

Figure 17

Beam modulation to calibrate sensitivity. (Top) Typical coil and energy vernier modulation values as a function of time. Four modulation pulses each about $3\mathrm{s}$ long are seen: the first is a horizontal correlation coil, the next two are vertical coils, and the fourth is the energy vernier. (Middle) Horizontal position at target versus time for the same data. The position responds to modulation of the horizontal coil and energy vernier but not to modulation of the vertical coils. (Bottom) Čerenkov detector response versus time for the same data. Sensitivity to position and energy modulation is small compared to counting statistics.

Figure 18

Raw asymmetries for 1999 running period, in ppm, broken down by data set. The circles are for the left spectrometer, triangles for the right spectrometer. The step pattern represents the effect of insertion∕removal of the half-wave plate between data sets combined with a Pockels cell reconfiguration between data sets 16 and 17; see text. The amplitude of the step is the average value of the asymmetry over the entire run.

Figure 19

(Color online) Histogram of $6.5\times {10}^7$ window pair asymmetries for 1999 running period, normalized by the square root of beam intensity, with mean value subtracted off, in ppm. Curve is a Gaussian fit.

Figure 20

(Color online) Histogram of 827 run asymmetries for 1999 running period, with mean subtracted off and normalized by statistical error. Curve is a Gaussian fit with width $\sigma =0.98$.

Figure 21

Representative sensitivity coefficients $a_j=(\partial d∕\partial B_j)∕2⟨d⟩$ versus data set for 1999 run, for energy-sensitive position (top row), horizontal positions on the beamline $7.5\mathrm{m}$ and $1.3\mathrm{m}$ upstream of the target (second and third rows), and vertical positions at $7.5\mathrm{m}$ and $1.3\mathrm{m}$ (fourth and fifth rows). Left and right columns correspond to the two detectors. Units in all cases are $\mathrm{ppm}∕\mu \mathrm{m}$. Coefficients are seen to be stable at the level of estimated errors.

Figure 22

Helicity-correlated position differences for 1999 run versus data set, for energy-sensitive position (top plot), horizontal positions at locations on the beamline $7.5\mathrm{m}$ and $1.3\mathrm{m}$ upstream of the target (second and third plots), and vertical positions at $7.5\mathrm{m}$ and $1.3\mathrm{m}$ (fourth and fifth plots). The closed (open) circles correspond to positive (negative) polarization of the electron beam in the experimental hall. The data are plotted without correction for sign of the electron beam polarization.

Figure 23

Detector correction coefficients for 1999 run versus data set. Note that corrections are generally consistent with zero at the level of the estimated errors. The data are plotted without correction for polarization sign.

Figure 24

(Color online) (Top) Residuals from fit of BCM1 to Unser data, as a fraction of the BCM1 pulse height at $32\mu \mathrm{A}$, versus beam current. (Bottom) Same for fit of BCM2 to Unser.

Figure 25

(Color online) (Top) Residuals from fit of detector 1 ot BCM1 data, as a fraction of the detector 1 pulse height at $32\mu \mathrm{A}$, versus beam current. (Bottom) Same for fit of detector 2 to BCM1.

Figure 26

(Color online) Polarization of the JLab electron beam measured by the Møller (solid squares) and the Compton (open circles) polarimeters during the entire 1999 run (upper plot) and July portion (lower plot) where the Compton polarimeter was available. The error bar on the leftmost Møller point in the upper plot is its total error (dominated by systematic error 3.2% relative) while all other points show only the statistical error, which for Møller data is smaller than the symbol (0.2% relative).

Figure 27

(Color online) Results of scan of spectrometer magnetic fields to measure the probability to rescatter into the detector versus the fractional difference from the nominal momentum setting. Inset: the ratio of inelastic to elastic cross sections at the HAPPEX kinematics, ${(d\sigma ∕d\mathrm{\Omega }dE)}_{\mathrm{inel}}∕{(d\sigma ∕d\mathrm{\Omega })}_{\mathrm{elast}}$.

Figure 28

(Top) Reconstructed vertical angle at the target, from triggered data; background from rescattering of inelastic electrons indicated by hatched area. (Bottom) The ratio of observed to predicted rescattering background versus $Q^2$; the ratio is 1 in the region of our kinematics $[Q^2=0.48{(\mathrm{GeV}∕c)}^2]$. The line is a guide to the eye.

Figure 29

Typical $Q^2$ spectrum measured during HAPPEX. In the inset is a missing mass spectrum from the same data.

Figure 30

(Color online) Plot of $G_E^s$ versus $G_M^s$ at $Q^2=0.477{(\mathrm{GeV}∕c)}^2$. The band is the allowed region derived from our results. The width of the band is the total error computed in quadrature. The points are estimates from various models that make predictions at our $Q^2$. The numbers in Ref. [25] are plotted twice due to an ambiguity in the predicted sign. This plot is similar to Fig. 4 in [7] except that the central value and error bars have both reduced slightly, and three new models shown in circles have since been published.