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

• Main Authors: Shiells, K, Blunden, P. G, Melnitchouk, W
• Format: Journal Article
• Language: English
• Published: 02-12-2020
• Subjects: Physics - High Energy Physics - Experiment; Physics - High Energy Physics - Phenomenology; Physics - Nuclear Theory
• DOI: 10.48550/arxiv.2012.01580

Phys. Rev. D 104, 033003 (2021) 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.