First-Principles Calculation of Electroweak Box Diagrams from Lattice QCD

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 fennions at the physical pion mass with multiple lattice spacings and volumes, we obtain the axial yW-box correction to the semileptonic pion decay, square(VA)(gamma W)vertical bar(pi) = 2.830(11)(stat) (26)(syst) x 10(-3), with the total uncertainty controlled at the level of similar to 1%. 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 vertical bar V-ud vertical bar.