We analyze the universal radiative correction ∆ V R to neutron and superallowed nuclear β decay by expressing the hadronic γW -box contribution in terms of a dispersion relation, which we identify as an integral over the first Nachtmann moment of the γW interference structure function F (0) 3 . By connecting the needed input to existing data on neutrino and antineutrino scattering, we obtain an updated value of ∆ V R = 0.02467 (22), wherein the hadronic uncertainty is reduced. Assuming other Standard Model theoretical calculations and experimental measurements remain unchanged, we obtain an updated value of |V ud | = 0.97366(15), raising tension with the first row CKM unitarity constraint. We comment on ways current and future experiments can provide input to our dispersive analysis.The unitarity test of the Cabibbo-Kobayashi-Maskawa (CKM) matrix serves as one of the most important precision tests of the Standard Model. In particular, tests of first-row CKM unitarity |V ud | 2 + |V us | 2 + |V ub | 2 = 1 receive the most attention since these matrix elements are known with highest precision, all with comparable uncertainties. The good agreement with unitarity [1] serves as a powerful tool to constrain New Physics scenarios.Currently, the most precise determination of |V ud | comes from measurements of half-lives of superallowed 0 + → 0 + nuclear β decays with a precision of 10 −4 [2]. At tree-level, these decays are mediated by the vector part of the weak charged current only, which is protected against renormalization by strong interactions due to conserved vector current (CVC), making the extraction of |V ud | relatively clean. Beyond tree-level, however, electroweak radiative corrections (EWRC) involving the axial current are not protected, and lead to a hadronic uncertainty that dominates the error in the determination of |V ud |.The master formula relating the CKM matrix element |V ud | to the superallowed nuclear β decay half-life is [2]:where the nucleus-independent Ft-value is obtained from the experimentally measured f t-value by absorbing all nuclear-dependent corrections, and where ∆ V R represents the nucleus-independent EWRC. Currently, an average of the 14 best measured half-lives yields an extraordinarily precise value of Ft = 3072.27(72) s. A similar master formula exists for free neutron β decay [3] depending additionally on the axial-to-vector nucleon coupling ratio λ = g A /g V , and is free of nuclear-structure uncertainties. But the much larger experimental errors in the measurement of its lifetime and the ratio λ [4] makes it less competitive in the extraction of |V ud |. Regardless, if first-row CKM unitarity is to be tested at a higher level of precision, improvement in the theoretical estimate of ∆ V R by reducing hadronic uncertainties is essential. The best determination of ∆ V R = 0.02361(38) was obtained in 2006 by Marciano and Sirlin [5] (in the following, we refer to their work as [MS]). They were able to reduce the hadronic uncertainty by a factor of 2 over their earlier calculatio...

both a high degree of experimental precision and robust theoretical computations used to extract CKM matrix elements from experimental observables.Here, we focus on the hadronic and nuclear theory relevant to tests of the first row CKM unitarity condition : |V ud | 2 + |V us | 2 + |V ub | 2 = 1. The matrix element |V ud | = 0.97420 ± 0.00021 [2] is the main contributor to the first row unitarity, and is relevant for charged pion, neutron, and nuclear β-decay. Currently, the most precise determination of the value of V ud is obtained with the superallowed 0 + -0 + nuclear β decays. Since both initial and final nuclei have no spin, only the vector current interaction with the nucleus contributes at leading order. The conservation of the vector current (CVC) protects the vector coupling from being renormalized by the strong interaction and makes 0 + -0 + nuclear β decays an especially robust method for determining V ud . Precision tests require, apart from the purely experimental accuracy, an accurate computation of SM electroweak radiative corrections (RC). The present day framework for computing these corrections was formulated in the classic arXiv:1812.03352v3 [nucl-th]

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.

We consider elastic scattering of electrons off a proton target. The parity violating (PV) asymmetry arises at leading order in α due to interference of γ and Z exchange. The radiative corrections to this leading mechanism were calculated in the literature and included in experimental analyses, except for γZ box and cross-box contributions. We present here a dispersion calculation of these corrections in forward kinematics. We demonstrate that at the GeV energies of current PV experiments, such corrections are not suppressed by the small vector weak charge of the electron, as occurs in the atomic PV. Our results suggest that the current theoretical uncertainty in the analysis of the QWEAK experiment might be substantially underestimated, and more accurate account of the dispersion corrections are needed in order to interprete the PV data.PACS numbers: 21.10. Pt, 25.30.Bf, 25.30.Fj, 27.10.+h, 27.80.+w Precision tests of the Standard Model at low energies provide an important tool to search for New Physics and to constrain model parameters. Such tests involve high precision measurements of observables that are typically suppressed or precisely vanish in the Standard Model (SM). Prominent examples of such observables include the electric dipole moment and neutrino magnetic moments. Another important example of a parameter of the nucleon structure suppressed in the SM is the weak charge of the proton, Q p W = 1 − 4 sin 2 θ W . With the value of the weak mixing angle at low momentum transfers sin 2 θ W (0) = 0.23807 ± 0.00017 [1], the SM predicts the proton weak charge of order ≈ 0.05. A precise (4%) measurement of the weak charge of the proton is the aim of the QWEAK experiment at Jefferson Lab [2].In order to achieve the required precision in the QWEAK experiment, the radiative corrections have to be considered. This was done in various works, to mention the most important references [1,3], and the combined estimate of the theoretical uncertainty is currently 2.2%. This level of precision, coupled with a 2% measurement of the parity violating asymmetry, would allow for a 0.3% determination of θ W at low energies. The main difficulty in calculating the radiative corrections originates in the hadronic structure-dependent contributions from the box diagrams with the exchange of γγ, ZZ, W W and γZ. Since the parity conserving amplitude at leading order has a 1 Q 2 pole, the exchange of two photons only leads to a correction that vanishes at Q 2 = 0. This amounts in a contribution ∼ αQ 2 , with α ≈ 1 137 , that can safely be neglected. Parity violating amplitude in the OBE approximation has no such pole, and the respective correction remains finite in the forward direction. The ZZ and W W -boxes were estimated in [1,3] to give a large correction that comes from hard exchanged * Electronic address: mgorshte@indiana.edu † Electronic address: horowit@indiana.edu bosons' momenta in the loop, ∼ M Z (M W ), whereas low momenta contributions are suppressed by an extra power of G F . In this case, all subprocesses inside the...