Finite temperature sum rules in the vector channel at finite momentum

TL;DR

This paper derives exact finite-temperature sum rules for vector channel spectral functions at nonzero momentum and demonstrates their use as constraints in lattice QCD spectral fits across different temperatures.

Contribution

It generalizes existing sum rules to finite momentum and temperature, providing a new tool for analyzing spectral functions in lattice QCD.

Findings

Sum rules are derived for finite temperature vector spectral functions at nonzero momentum.

Sum rules are validated as effective constraints in lattice spectral fits.

Application to lattice data at various temperatures shows consistency with theoretical predictions.

Abstract

Exact sum rules for the longitudinal and transverse part of the vector channel spectral functions at nonzero momentum are derived in the first part of the paper. The sum rules are formulated for the finite temperature spectral functions, from which the vacuum component has been subtracted, and represent a generalization of previous work in which sum rules were derived only for the zero-momentum limit. In the second part of the paper, we demonstrate how the sum rules can be used as constraints in spectral fits to lattice data at various temperatures, with the latest dynamical lattice QCD data at zero momentum.