From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD

We present a new technique for extracting decay and transition rates into final states with any number of hadrons. The approach is only sensitive to total rates, in which all out-states with a given set of QCD quantum numbers are included. For processes involving photons or leptons, differential rates with respect to the nonhadronic kinematics may also be extracted. Our method involves constructing a finite-volume Euclidean four-point function, with a corresponding spectral function that measures the decay and transition rates in the infinite-volume limit. This requires solving the inverse problem of extracting the spectral function from the correlator and also necessitates a smoothing procedure so that a well-defined infinite-volume limit exists. Both of these steps are accomplished by the Backus-Gilbert method, and, as we show with a numerical example, reasonable precision can be expected in cases with multiple open decay channels. Potential applications include nucleon structure functions and the onset of the deep-inelastic scattering regime, as well as semileptonic D and B decay rates.