Model dependence of theγZdispersion correction to the parity-violating asymmetry in elasticepscattering

Abstract

We analyze the dispersion correction to elastic parity violating electron-proton scattering due to γZ exchange. In particular, we explore the theoretical uncertainties associated with modeling contributions of hadronic intermediate states. Taking into account constraints from low-and high-energy, parity-conserving electroproduction measurements, choosing different models for contributions from the non-resonant processes, and performing the corresponding flavor rotations to obtain the electroweak amplitude, we arrive at an estimate of the uncertainty in the total contribution to the parity-violating asymmetry. At the kinematics of the Q-Weak experiment, we obtain a correction to the asymmetry equivalent to a shift in the proton weak charge of (0.0054 ± 0.0020). This should be compared to the value of the proton's weak charge of Q p W = 0.0713 ± 0.0008 that includes Standard Model contributions at tree level and one-loop radiative corrections. Therefore, we obtain a new Standard Model prediction for the parity-violating asymmetry in the kinematics of the Q-Weak experiment of (0.0767 ± 0.0008 ± 0.0020γZ ). The latter error leads to a relative uncertainty of 2.8% in the determination of the proton's weak charge, and is dominated by the uncertainty in the isospin structure of the inclusive cross section. We argue that future parity-violating inelastic ep asymmetry measurements at low-to-moderate Q 2 and W 2 could be exploited to reduce the uncertainty associated with the dispersion correction. Because the corresponding shift and error bar decrease monotonically with decreasing beam energy, a determination of the proton's weak charge with a lower-energy experiment or measurements of "isotope ratios" in atomic parity-violation could provide a useful cross check on any implications for physics beyond the Standard Model derived from the Q-Weak measurement.

Modification of electromagnetic structure functions for theγZ-box diagram

“…It is important to note that Gorchtein et al [6] do not use the Christy-Bosted background in their analysis. For the background they instead use the average of two Generalized Vector Dominance (GVD) models [19,20], isospin rotated for application to the γZ-box and extrapolated down to the resonance region.…”

“…Gorchtein et al [6] constructed their C res expressions using photoproduction amplitudes listed in the Particle Data Group [12]. Thus, their corrective prefactors lack Q 2 -dependence.…”

“…These data will be insufficient to produce a model-independent fit, but provide a first step in testing the validity of the modifications [9]. Rislow and Carlson [5] 5.7 ± 0.9 Gorchtein et al [6] 5.4 ± 2.0 Hall et al [7] 5.60 ± 0.36…”

“…III we showed that there is little difference between modifying the Christy-Bosted resonance fits using our constituent quark model [5] or photoproduction amplitudes from the Particle Data Group (as in [6]). Differences arise between [5] and [6] because of the treatments of the resonance region background. We continue modifying the Christy-Bosted background fit while Gorchtein et al modify two GVD fits to low Q 2 , high W 2 data and extrapolate them down to the resonance region.…”

First result from Qweak

“…It can also be expressed in terms of the weak vector couplings of the light quarks, Q p w = −2(2C 1u + C 1d ) which are again functions of the mixing angle. These expressions are modified beyond tree level by loop corrections [3], however after recent theoretical work on the troublesome Z box term [4][5][6][7][8], these are now sufficiently under control, and the standard model predictions for Q p w and for C 1u and C 1d are robust. The experimental observable is the parity-violating asymmetry, the difference over the sum of the elastic scattering cross section for electrons with positive and negative helicity,…”