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]

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