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We present a new technique for extracting decay and transition rates intofinal states with any number of hadrons. The approach is only sensitive tototal rates, in which all out-states with a given set of QCD quantum numbersare included. For processes involving photons or leptons, differential rateswith respect to the non-hadronic kinematics may also be extracted. Our methodinvolves constructing a finite-volume Euclidean four-point function, whosecorresponding spectral function measures the decay and transition rates in theinfinite-volume limit. This requires solving the inverse problem of extractingthe spectral function from the correlator and also necessitates a smoothingprocedure so that a well-defined infinite-volume limit exists. Both of thesesteps are accomplished by the Backus-Gilbert method and, as we show with anumerical example, reasonable precision can be expected in cases with multipleopen decay channels. Potential applications include nucleon structure functionsand the onset of the deep inelastic scattering regime, as well as semi-leptonic$D$ and $B$ decay rates.

From deep inelastic scattering to heavy-flavor semi-leptonic decays: Total rates into multi-hadron final states from lattice QCD