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We present the first realistic lattice QCD calculation of the $gamma W$-box diagrams relevant for beta decays. The nonperturbative low-momentum integral of the $gamma W$ loop is calculated using a lattice QCD simulation, complemented by the perturbative QCD result at high momenta. Using the pion semileptonic decay as an example, we demonstrate the feasibility of the method. By using domain wall fermions at the physical pion mass with multiple lattice spacings and volumes, we obtain the axial $gamma W$-box correction to the semileptonic pion decay, $Box_{gamma W}^{VA}big|_{pi}=2.830(11)_{mathrm{stat}}(26)_{mathrm{sys}}times10^{-3}$, with the total uncertainty controlled at the level of $sim1$%. This study sheds light on the first-principles computation of the $gamma W$-box correction to the neutron decay, which plays a decisive role in the determination of $|V_{ud}|$.
We present a lattice QCD calculation of the axial $gamma W$-box diagrams relevant for the kaon semileptonic decays. We utilize a recently proposed method, which connects the electroweak radiative corrections in Sirlins representation to that in chira
We develop a methodology for the computation of the $Kto ell u_ell ell^+ ell^-$ decay width using lattice QCD and present an exploratory study here. We use a scalar function method to account for the momentum dependence of the decay amplitude and ado
In the past year, we calculated with lattice QCD three quantities that were unknown or poorly known. They are the $q^2$ dependence of the form factor in semileptonic $Dto Kl u$ decay, the decay constant of the $D$ meson, and the mass of the $B_c$ mes
The leading-order electromagnetic and strong isospin-breaking corrections to the ratio of $K_{mu 2}$ and $pi_{mu 2}$ decay rates are evaluated for the first time on the lattice, following a method recently proposed. The lattice results are obtained u
As algorithms and computing power have advanced, lattice QCD has become a precision technique for many QCD observables. However, the calculation of nucleon matrix elements remains an open challenge. I summarize the status of the lattice effort by exa