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arXiv · 2012.01580

Electroweak axial structure functions and improved extraction of the $V_{ud}$ CKM matrix element

K. Shiells·P. G. Blunden·W. Melnitchouk
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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.

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K. Shiells, P. G. Blunden, W. Melnitchouk. 2020-12-02. Electroweak axial structure functions and improved extraction of the $V_{ud}$ CKM matrix element. https://doi.org/10.1103/physrevd.104.033003

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