Electroweak box diagrams on the lattice for pion and neutron decay

TL;DR

This paper calculates electroweak box diagram contributions to pion and kaon beta decays using lattice QCD, aiming to improve theoretical precision in CKM matrix element determinations.

Contribution

It provides nonperturbative lattice QCD results for electroweak box diagrams relevant to pion and kaon decays, reducing uncertainties in CKM matrix tests.

Findings

Electroweak box contribution to pion decay: 2.820(28) x 10^{-3}

Electroweak box contribution to kaon decay: 2.384(17) x 10^{-3}

Results help refine CKM matrix unitarity tests.

Abstract

CKM matrix is unitary by construction in the standard model(SM). The recent analyses on the first row of CKM matrix show $ \approx 3\sigma$ tension with unitarity. Nonperturbative calculations of the radiative corrections can reduce the theory uncertainty in CKM matrix elements. Here we compute the electroweak box contribution to the pion and kaon $\beta$ decays using seven $N_f=2+1+1$ HISQ-Clover lattice with various pion mass and lattice spacing. The continuum and chiral limit is taken using the leading dependence on $M_\pi$ and $a$, where $M_\pi$ extrapolation is taken to the physical pion mass and $SU(3)$ symmetric mass for pion and kaon box contribution, respectively. Our results are $ \square_{\gamma W}^{VA} |_{\pi} = 2.820 (28) \times 10^{-3} $ and $ \square_{\gamma W}^{VA} |_{K} = 2.384 (17) \times 10^{-3} $.