New Formulation ofγZBox Corrections to the Weak Charge of the Proton

Abstract

We present a new formulation of one of the major radiative corrections to the weak charge of the proton -that arising from the axial-vector hadron part of the γZ box diagram, ℜe ✷ A γZ . This formulation, based on dispersion relations, relates the γZ contributions to moments of the F γZ 3 interference structure function. It has a clear connection to the pioneering work of Marciano and Sirlin, and enables a systematic approach to improved numerical precision. Using currently available data, the total correction from all intermediate states is ℜe ✷ A γZ = 0.0044(4) at zero energy, which shifts the theoretical estimate of the proton weak charge from 0.0713(8) to 0.0705(8). The energy dependence of this result, which is vital for interpreting the Q weak experiment, is also determined.As modern parity-violating (PV) experiments press to ever improving levels of precision, they remain a vital complement to direct tests of the Standard Model at the high energy frontier. The classic example of this, involving precise measurements of parity violation in atoms, led to a remarkably accurate determination of sin 2 θ W . A complementary PV electron-proton scattering measurement underway by the Q weak Collaboration [1] at Jefferson Lab has the potential to increase the mass scale associated with new physics to 2 TeV or higher, provided that the critical radiative corrections are under control. In this Letter we present a new formulation of the important γZ radiative corrections which allows for their controlled, systematic evaluation.Including electroweak radiative corrections, the proton weak charge is defined, at zero electron energy E and zero momentum transfer, as [2]where sin 2 θ W (0) is the weak mixing angle at zero momentum, and the corrections ∆ρ, ∆ e and ∆ ′ e are given in [2] and references therein. The contributions ✷ W W and ✷ ZZ arise from the W W and ZZ box and crossed-box diagrams, and can be computed perturbatively. They are expected to be energy independent for electron scattering in the GeV range. By contrast, the γZ interference correction ✷ γZ (E) depends on physics at both short and long distance scales.In the classic work of Marciano and Sirlin (MS) [3], ✷ γZ (0) was evaluated in a quark model-inspired loop calculation using either a "perturbative" (p) or a "nonperturbative" (np) ansatz,where v e (M 2 Z ) = (1 − 4ŝ 2 ), andŝ 2 ≡ sin 2 θ W (M 2 Z ) = 0.23116 in the MS scheme [4].The perturbative ansatz [3]is the free quark model result, with m a hadronic mass scale, and shows the leading-log behavior. For the nonperturbative ansatz, B np = K m + L m is the sum of a long-distance part, L m , and a short-distance part, K m , withHere m is a mass scale representing the onset of asymptotic behavior at large loop momenta, and the factor (1 − α s (u)/π) is the lowest-order correction induced by the strong interactions. In Ref.[3] L m is taken to be the elastic nucleon (Born) contribution, which is evaluated to be 2.04 using the same dipole form factors for both the electromagnetic and axial-vector coupling. MS...

ConstrainedγZinterference corrections to parity-violating electron scattering

“…At the energy of the Q weak experiment, however, both terms provide significant contributions. The A γZ corrections were first computed some time ago by Marciano and Sirlin [7,8] and were updated recently within a dispersion relation framework by Blunden et al [19,20], with reduced errors. The vector hadron correction, V γZ , which is subject to significantly larger uncertainty, will be the focus of the rest of this analysis.…”

Measurements of Parity-Violating Asymmetries in Electron-Deuteron Scattering in the Nucleon Resonance Region

“…These results provide a test of local quark-hadron duality in the nucleon electroweak γZ interference structure functions and are compared to the theoretical models of Matsui, Sato, and Lee [34], Gorchtein, Horowitz, and Ramsey-Musolf [35], and the Adelaide-JLab-Manitoba collaboration [36]. These results also provide constraints for nucleon resonance models relevant for calculating background corrections to elastic PVES [35][36][37][38][39][40].…”

Modification of electromagnetic structure functions for theγZ-box diagram

“…Blunden et al [10] split their Re A γZ analysis into elastic (W 2 = M 2 ), resonance (W 2 π ≤ W 2 ≤ 4 GeV 2 ), and deep inelastic scaling (W 2 > 4 GeV 2 ) regions. To allow for an easier comparison between our analysis and theirs, we used the same energy regions.…”

“…If added in quadrature, the uncertainty reduces to 1 × 10 −3 . The total γZ-box value from Blunden et al [10] is…”