Description
Precise tests of CKM unitarity provide a probe of physics beyond the Standard Model. Using the most precise determinations—$V_{ud}$ from superallowed nuclear $\beta$ decays and $V_{us}$ from leptonic and semileptonic decays—the first‑row sum $|V_{ud}|^{2}+|V_{us}|^{2}+|V_{ub}|^{2}$ deviates from unity by $2\text{–}3\,\sigma$. This tension emphasizes the need for further reductions in both experimental and theoretical uncertainties. On the theoretical side, the leading uncertainty stems from radiative corrections to the relevant decays. We perform a lattice QCD calculation of the radiative corrections to meson leptonic decays with the infinite‑volume reconstruction (IVR) method. Compared with the traditional $\mathrm{QED}_{L}$ approach, IVR reduces the systematic uncertainties due to the finite‑volume effects from $\sim\!40\%$ to $0.08\%$. We also compute the branching ratios for the radiative leptonic decays $\pi\to \ell\nu_\ell\gamma$ and $K\to \ell\nu_\ell\gamma$ and compare the lattice results with existing experimental data.
