Speaker
Description
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.
