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

We present the first lattice QCD calculation of the universal axial γ W-box contribution □_γ 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 □_γ W^VA=3.65(8)_lat(1)_PT×10^-3. Consequently, this yields a slightly higher value of |V_ud|=0.97386(11)_exp.(9)_RC(27)_NS, reducing the previous 2.1σ tension with the CKM unitarity to 1.8σ. Additionally, we calculate the vector γ W-box contribution to the axial charge g_A, denoted as □_γ W^VV, and explore its potential implications.