---
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.'
author:
- Philipp Gubler
- Daisuke Satow
title: Finite temperature sum rules in the vector channel at finite momentum 
---

Introduction {#sec:intro}
============

Hadrons, whose dynamics is governed by quantum chromodynamics (QCD), are deconfined at high temperature ($T$), where quarks and gluons are expected to be the fundamental degrees of freedom. Such matter is called quark-gluon plasma, and is experimentally investigated by heavy ion collision experiments. In analyzing the experimental data, electromagnetic (EM) probes such as dilepton spectra are particularly useful [@Adare:2014fwh] because once generated in the medium, they are expected to reach the detector without further 