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arXiv · 2308.16755

Lattice QCD Calculation of Electroweak Box Contributions to Superallowed Nuclear and Neutron Beta Decays

Peng-Xiang Ma·Xu Feng·Mikhail Gorchtein·Lu-Chang Jin·Keh-Fei Liu·Chien-Yeah Seng·Bi-Geng Wang·Zhao-Long Zhang
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Abstract

We present the first lattice QCD calculation of the universal axial $\gamma W$-box contribution $\square_{\gamma W}^{VA}$ to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of $|V_{ud}|$ from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon 4-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at $\square_{\gamma W}^{VA}=3.65(8)_{\mathrm{lat}}(1)_{\mathrm{PT}}\times10^{-3}$. Consequently, this yields a slightly higher value of $|V_{ud}|=0.97386(11)_{\mathrm{exp.}}(9)_{\mathrm{RC}}(27)_{\mathrm{NS}}$, reducing the previous $2.1\sigma$ tension with the CKM unitarity to $1.8\sigma$. Additionally, we calculate the vector $\gamma W$-box contribution to the axial charge $g_A$, denoted as $\square_{\gamma W}^{VV}$, and explore its potential implications.

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Peng-Xiang Ma, Xu Feng, Mikhail Gorchtein, Lu-Chang Jin, Keh-Fei Liu, Chien-Yeah Seng, Bi-Geng Wang, Zhao-Long Zhang. 2023-08-31. Lattice QCD Calculation of Electroweak Box Contributions to Superallowed Nuclear and Neutron Beta Decays. https://arxiv.org/abs/2308.16755

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