Deep-inelastic scattering and the operator product expansion in lattice QCD

TL;DR

This paper presents a lattice QCD method using a fictitious heavy quark to directly compute moments of deep-inelastic structure functions, overcoming previous operator mixing issues and enabling practical analysis of quark distributions.

Contribution

The authors introduce a novel lattice QCD approach employing a fictitious heavy quark to directly calculate structure function moments, addressing operator mixing and renormalization challenges.

Findings

Enables calculation of higher moments of structure functions.

Applicable to various quark and meson distribution functions.

Practical with current computational resources.

Abstract

We discuss the determination of deep-inelastic hadron structure in lattice QCD. By using a fictitious heavy quark, direct calculations of the Compton scattering tensor can be performed in Euclidean space that allow the extraction of the moments of structure functions. This overcomes issues of operator mixing and renormalisation that have so far prohibited lattice computations of higher moments. This approach is especially suitable for the study of the twist-two contributions to isovector quark distributions, which is practical with current computing resources. While we focus on the isovector unpolarised distribution, our method is equally applicable to other quark distributions and to generalised parton distributions. By looking at matrix elements such as $<\pi^\pm| T [V^\mu(x) A^{\nu}(0)]|0>$ (where $V^\mu$ and $A^\nu$ are vector and axial-vector heavy-light currents) within the same formalism, moments of meson distribution amplitudes can also be extracted.