Computing neutrino cross sections from Euclidian responses

TL;DR

This paper introduces a method to compute neutrino cross sections directly from Euclidean responses by extracting moments and weighted integrals, avoiding complex inversions, and demonstrates its feasibility with toy models and realistic responses.

Contribution

It presents a novel approach to calculate neutrino cross sections from Euclidean responses, enabling ab-initio computations with controlled uncertainties.

Findings

Feasible extraction of response moments from Euclidean data.

Controlled correction for unphysical region contributions.

Potential for ab-initio neutrino cross section calculations.

Abstract

Energy integrated neutrino cross sections are integrals of nuclear responses weighted with kinematic prefactors. We decompose the prefactors into a limited set of functions of energy transfer and show the relevant integrals are the moments of the responses, and integrals weighted with $1/(a+\omega)^n$ with $n\leq 2$. These can be directly obtained from the Euclidean response, avoiding the need for inversion of the Laplace transform. As a proof of concept we study the procedure with toy-model responses for the quasielastic peak. We show that the different contributions can be straightforwardly organized in terms of relative importance, and how flux-averaged cross sections can be obtained. Using a realistic model for the response and numerical uncertainty we show that it is feasible to obtain the required integrals from the Euclidean response, with large uncertainties only for the third moment. Due to kinematic restrictions, the integrals contain contributions from the unphysical region for neutrino scattering, coming from high-momentum nucleons. We show that (in the absence of two-body currents) robust corrections for this contamination are obtained from the single-nucleon momentum distribution. These results present an opportunity to compute certain neutrino cross sections with ab-initio methods with controlled uncertainties.