First-principles calculation of electroweak box diagrams from lattice QCD

Understand

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 $\sim1$\%.