Abstract
We present a comprehensive analysis of the $\gamma W$ interference radiative correction to the neutron $\beta$-decay matrix element. Within a dispersion relations approach, we compute the axial-vector part of the $\gamma W$ box amplitude $\Box^{\gamma W}_{A}$ in terms of the isoscalar part of the $F_3^{\gamma W}$ interference structure function. Using the latest available phenomenology for $F_3^{\gamma W}$ from the nucleon elastic, resonance, deep-inelastic, and Regge regions, we find the real part of the box correction to be $\Box^{\gamma W}_A = 3.90(9) \times 10^{-3}$. This improved correction gives a theoretical estimate of the CKM matrix element $|V_{ud}|^2=0.94805(26)$, which represents a 4$\sigma$ violation of unitarity.
Highlights
Probing the unitarity of the Cabibbo-KobayashiMaskawa (CKM) quark mixing matrix provides a stringent test of the Standard Model of nuclear and particle physics
In this work we have presented a comprehensive new analysis of the γW interference contribution to the neutron β-decay matrix element using a dispersive relations framework that has previously been applied successfully for γZ box corrections
The evaluation of the γW correction relies on knowledge of the isoscalar part of the parity-odd γW structure function, Fð30Þ, which is not directly accessible experimentally, but can be modeled from existing phenomenology
Summary
Probing the unitarity of the Cabibbo-KobayashiMaskawa (CKM) quark mixing matrix provides a stringent test of the Standard Model of nuclear and particle physics. The relevant inner correction ΔVR includes the charged current axial-vector box contribution, denoted by □γAW, involving the exchange of a W boson and a photon between the leptons and hadrons (axial here refers to the coupling of the W to the hadron). [3] using improved phenomenological input, resulting in an ≈2.5σ shortfall of unitarity It was shown by Seng et al [7] that the elastic contribution of □γAW to superallowed nuclear β-decays should take into account the so-called elastic quenching effect, which increases the numerator of Eq (1) by ≈0.07%. Taking all the kinematic regions into account, our analysis gives a total correction □γAW 1⁄4 3.90ð9Þ × 10−3, which is larger than recent results [4,5,6,7], and leads to a discrepancy of ≈4σ with Standard Model unitarity for the top row of the CKM matrix. Appendix contains the details of the derivation of the Fγ3W structure function in the DIS region in terms of leading twist PDFs
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