PDFs and Neutrino-Nucleon Scattering from Hadronic Tensor

TL;DR

This paper reviews the Euclidean formulation of the nucleon hadronic tensor, explores inverse algorithms for Minkowski space conversion, and presents results on neutrino-nucleon scattering at high momentum transfer, highlighting elastic and inelastic contributions.

Contribution

It introduces a detailed classification of gauge invariant insertions and compares inverse algorithms for the Euclidean to Minkowski conversion in the context of neutrino-nucleon scattering.

Findings

Successful numerical checks of elastic form factors from charge vector currents.

Demonstration of resonance and inelastic contributions at high momentum transfer.

Evaluation of inverse algorithms for the Laplace transform in hadronic tensor analysis.

Abstract

We review the Euclidean path-integral formulation of the nucleon hadronic tensor and classify the gauge invariant and topologically distinct insertions in terms of connected and disconnected insertions and also in terms of leading and higher-twist contributions in the DIS region. Converting the Euclidean hadronic tensor back to the Minkowski space requires solving an inverse problem of the Laplace transform. We have investigated several inverse algorithms and studied the pros and cons of each. We show a result with a relatively large momentum transfer ($Q^2 \sim 4\, {\rm GeV^2}$) to suppress the elastic scattering and reveal the contributions from the resonance and inelastic region of the neutrino-nucleon scattering. For elastic scattering, the hadronic tensor is the the product of the elastic form factors for the two corresponding currents. We checked numerically for the case of two charge vector currents ($V_4$) with the electric form factor calculated from the three-point function and found they agree within errors.