Towards fully nonperturbative computations of inelastic ℓN scattering cross sections from lattice QCD

Abstract

We propose a fully nonperturbative method to compute inelastic lepton-nucleon ($\ensuremath{\ell}N$) scattering cross sections using lattice quantum chromodynamics (QCD). The method is applicable even at low energies, such as the energy region relevant for the recent and future neutrino-nucleon scattering experiments, for which perturbative analysis is invalidated. The basic building block is the forward Compton-scattering amplitude, or the hadronic tensor, computed on a Euclidean lattice. A total cross section is constructed from the hadronic tensor by multiplying a phase space factor and integrating over the energy and momentum of final hadronic states. The energy integral that induces a sum over all possible final states is performed implicitly by promoting the phase space factor to an operator written in terms of the transfer matrix on the lattice. The formalism is imported from that of the inclusive semileptonic $B$ meson decay [P. Gambino and S. Hashimoto, Phys. Rev. Lett. 125, 032001 (2020)] and generalized to compute the $\ensuremath{\ell}N$ scattering cross sections and their moments, as well as the virtual correction to the nuclear $\ensuremath{\beta}$ decay.