Thermal QCD sum rules in the $\rho^0$ channel revisited

R. Hofmann; Th. Gutsche; A. Faessler

doi:doi:10.1007/s100520000461

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2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C 17, 651-662
DOI 10.1007/s100520000461

Thermal QCD sum rules in the $\rho^0$ channel revisited

R. Hofmann - Th. Gutsche - A. Faessler

Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany

Received: 16 November 1999 / Revised version: 20 May 2000 /
Published online: 23 October 2000 - Springer-Verlag 2000

Abstract
From the hypothesis that at zero temperature the square root of the spectral continuum threshold s₀ is linearly related to the QCD scale $\Lambda$ we derive in the chiral limit and for temperatures considerably smaller than $\Lambda$ scaling relations for the vacuum parts of the Gibbs averaged scalar operators contributing to the thermal operator product expansion of the $\rho^0$ current-current correlator. The scaling with $\lambda\equiv \sqrt{s_0(T)/s_0(0)}$ , s₀ being the T-dependent perturbative QCD continuum threshold in the spectral integral, is simple for renormalization group invariant operators, and becomes nontrivial for a set of operators which mix and scale anomalously under a change of the renormalization point. In contrast to previous works on thermal QCD sum rules with this approach the gluon condensate exhibits a sizable T-dependence. The $\rho$ -meson mass is found to rise slowly with temperature which coincides with the result found by means of a PCAC and current algebra analysis of the $\rho^0$ correlator.