Exact vector channel sum rules at finite temperature and their applications to lattice QCD data analysis

Abstract

We derive three exact sum rules for the spectral function of the electromagnetic current with zero spatial momentum at finite temperature. Two of them are derived in this paper for the first time. We explicitly check that these sum rules are satisfied in the weak coupling regime and examine which sum rule is sensitive to the transport peak in the spectral function at low energy or the continuum at high energy. Possible applications of the three sum rules to lattice computations of the spectral function and transport coefficients are also discussed: We propose an ansatz for the spectral function that can be applied to all three sum rules and fit it to available lattice data of the Euclidean vector correlator above the critical temperature. As a result, we obtain estimates for both the electrical conductivity $\sigma$ and the second order transport coefficient ${\tau }_J$.

7 pages, 3 figures; v2: Fig. 4 is added, several details of formalism in Sec. II are added, explanation of lattice analysis in Sec. III is extended; v3 (published version in PRD): typo fixed, discussion in Sec. III extended

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Cited by in corpus (5)

• Heavy Quarkonium in Extreme Conditions
• Recent Progress in QCD Condensate Evaluations and Sum Rules
• Electrical conductivity of the quark-gluon plasma: perspective from lattice QCD
• Light vector correlator in medium: Wilson coefficients up to dimension 6 operators
• Finite temperature sum rules in the vector channel at finite momentum