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

Abstract

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 non-hadronic kinematics may also be extracted. Our method involves constructing a finite-volume Euclidean four-point function, whose corresponding spectral function 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 semi-leptonic D and B decay rates.

Three-body unitarity versus finite-volume π+π+π+ spectrum from lattice QCD

“…Scattering amplitudes cannot be directly computed as infinite-volume limits of finite-volume observables. However, even without fully resolving the three-body dynamics explicitly, methods exist that take into account the contribution of three-body states [15][16][17][18]. These methods connect finite-volume data with infinite volume properties using either the optical potential or by extracting the spectral density from a correlator.…”

Short-distance matrix elements for D0 -meson mixing from Nf=2+1 lattice QCD

“…D 97, 034513 (2018) 034513-29 relevant for D 0 mixing. More recently, Hansen, Meyer, and Robaina proposed a new method to extract the spectral function for multi-hadron transition rates from finite-volume four-point correlation functions [114]. In the coming years, these new approaches may be implemented in numerical lattice-QCD calculations and lead to more quantitative estimates of long-distance contributions to neutral D-meson mixing.…”

Three-body spectrum in a finite volume: The role of cubic symmetry

“…Note that, as shown in Refs. [28,29], without mapping out the full three-body dynamics explicitly, one can access certain bulk properties of the scattering amplitude (including intermediate three-body channels). For example, the use of an optical potential [29] allows one to access resonances in a finite volume even in the presence of multiple channels and particles.…”