In this talk, I will present our lattice QCD calculation of the photon–$W $box contributions to pion, kaon, neutron, and superallowed nuclear beta decays. These contributions play an essential role in the determination of the CKM matrix elements $V_{ud}$ and $V_{us}$. I will also discuss a possible extension to the photon–$Z$ box contributions in parity-violating electron–proton scattering, which are directly relevant to precision determinations of the weak mixing angle $\theta_W$.