Towards fully non-perturbative computation of inelastic $\ell N$ scattering cross sections from lattice QCD

TL;DR

This paper introduces a non-perturbative lattice QCD method to calculate inelastic lepton-nucleon scattering cross sections, especially at low energies where perturbative techniques fail, enabling more accurate predictions for neutrino experiments.

Contribution

The authors develop a novel lattice QCD framework to compute inelastic scattering cross sections directly, applicable at low energies relevant for neutrino-nucleon interactions, extending previous approaches used for B meson decays.

Findings

Method successfully computes the hadronic tensor on the lattice.

Framework can be generalized to other inelastic processes.

Provides a pathway for first-principles predictions of neutrino cross sections.

Abstract

We propose a fully non-perturbative method to compute inelastic lepton-nucleon ($\ell N$) scattering cross sections using lattice QCD. The method is applicable even at low energies, such as the energy region relevant for the recent and future neutrino-nucleon ($\nu N$) 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. 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, S. Hashimoto, arXiv:2005.13730]. It can be generalized to compute the $\ell N$ scattering cross sections and their moments, as well as the virtual correction to the nuclear $\beta$-decay. Necessary quark-line contractions for two current insertions corresponding to the Compton amplitude to be computed on the lattice are summarized.