Studying Hadronic Structure of the Photon in Lattice QCD

TL;DR

This paper demonstrates how to compute matrix elements involving photons in lattice QCD, enabling new calculations of photon-related processes and sum rules in quantum chromodynamics.

Contribution

It introduces a method to calculate matrix elements of local quark-gluon operators in photon states using lattice QCD, extending to various photon-involved quantities.

Findings

Matrix element of a local quark-gluon operator in photon state can be calculated in lattice QCD.

Generalization to transition form factors and Compton amplitudes involving space-like photons.

Potential to define generalized sum rules like Drell-Hearn-Gerasimov and Bjorken in lattice QCD.

Abstract

We show that the matrix element of a local quark-gluon operator in the photon state, $<\gamma(k\lambda)|\hat O| \gamma(k\lambda)>$, can be calculated in lattice QCD. The result is generalized to other quantities involving space-like photons, including the transition form factor $\gamma\gamma^*\to \pi^0$ and the virtual-photon-nucleon Compton amplitude $<\gamma^*N |\gamma^*N>$ which can be used to define the generalized Drell-Hearn-Gerasimov and Bjorken sum rules.