Many ongoing and upcoming experiments in particle physics aim, through precision measurements, to observe phenomena inconsistent with the Standard model. To be successful, comparably precise theoretical calculations are necessary, even when the challenge of nonperturbative quantum chromodynamics (QCD) is involved. Fortunately, an established method exists to meet this demand: lattice QCD. The Fermilab Lattice and MILC Collaborations have been especially successful in carrying out calculations required for quark-flavor experiments, such as reducing the total theoretical uncertainty on leptonic decay amplitudes down to the sub-percent level with all sources of error under control. 

A next, and more crucial step, is to improve the precision of semileptonic decay amplitudes to this level. They play a central role in many phenomenological applications. For example, recent measurements give hints of (previously unobserved) lepton-flavor violation. The Belle II experiment at the KEK Laboratory in Japan and the LHCb experiment at the CERN Laboratory in Switzerland are pursuing new measurements that will result in unprecedented precision for many relevant observables, including probes of lepton-flavor universality. Their interpretation as tests of the Standard Model or discovery of new physics requires theoretical calculations more precise than those done to date. This project targets semileptonic decays with a B or D meson in the initial states and a pion or kaon in the final state, for which the transition matrix elements—known as form factors—for the vector, scalar, and tensor currents will be computed. Leadership-class computational resources are essential to reduce the theoretical uncertainties to the target level.