Model-dependence of the $\gamma Z$ dispersion correction to the parity-violating asymmetry in elastic $ep$ scattering

Abstract

We analyze the dispersion correction to elastic parity violating electron-proton scattering due to $\gamma Z$ 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 $(0.0054\pm 0.0020)$. This should be compared to the value of the proton's weak charge of $\qwp=0.0713\pm0.0008$ that includes SM 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 $(0.0767\pm 0.0008\pm 0.0020_{\gamma Z})$. 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.

25 pages, 17 figures, 4 tables; revised version accepted for publication in PRC

References in corpus (8)

• Two-Photon Physics in Hadronic Processes
• Low Energy Precision Test of Supersymmetry
• Measurement of Strange Quark Contributions to the Vector Form Factors of the Proton at Q**2=0.22 (GeV/c)**2
• Empirical Fit to Inelastic Electron-Deuteron and Electron-Neutron Resonance Region Transverse Cross Sections
• Testing the Standard Model by precision measurement of the weak charges of quarks
• The Two-Photon-Exchange and γZ-Exchange Corrections to parity-Violating Elastic Electron-Proton Scattering
• Analyzing power in elastic scattering of the electrons off a spin-0 target
• Dispersive contributions to $e^{+}p/e^{-}p$ cross section ratio in forward regime

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