The hadronic tensor from four-point functions on the lattice

TL;DR

This paper develops a lattice QCD method to compute the hadronic tensor across a wide range of momentum transfers, aiding the understanding of lepton-hadron scattering processes.

Contribution

It extends previous lattice calculations by incorporating larger momentum transfers using stochastic sources, enabling more comprehensive structure function analysis.

Findings

Successful calculation of four-point functions over broad kinematic regions

Implementation of stochastic sources improves computational efficiency

Preliminary results show promise for detailed hadronic tensor reconstruction

Abstract

The hadronic tensor is the central non-perturbative object in the calculation of the cross section of lepton-hadron interactions like neutrino-nucleon scattering. It is usually parameterized in terms of structure functions, which encode all necessary information for all kinematic regions. Moreover, the structure functions can be factorized in terms of parton distribution functions (PDFs) and contains information on hadron resonances. On the lattice, we can calculate the corresponding matrix element of two quark-bilinear currents with a relative Euclidean time separation. The reconstruction of the hadronic tensor in Minkowski space requires appropriate dealing with the corresponding inverse problem. In our current work, we extend previous calculations on the nucleon by considering a much larger range of momentum transfers, which is inevitable in the context of structure functions. This can be achieved by using stochastic sources, which allows us to calculate the required four-point functions in a broad kinematic region. We employ a clover fermion ensemble at pion mass $m_\pi = 223~\mathrm{MeV}$ and lattice spacing $a=0.085~\mathrm{fm}$. In these proceedings, we will give an overview of our simulation and present some first preliminary results.