# The vacuum energy density of QCD with nf=3 Quark Flavors

#### Abstract

An equivariant BRST-construction is used to define the continuum SU(3) gauge theory on a finite torus. I corroborate previous results using renormalization group techniques by explicitly computing the measure on the moduli-space of the model with 3 quark flavors to two loops. I find that the correction to the maximum of the one-loop effective action is indeed of order g in the critical covariant gauge. The leading logarithmic corrections from higher loops are also shown to be suppressed by at least one order of g. I therefore can relate the expectation value κ = −〈Tr γ̄〉 of the moduli γ̄ to the asymptotic scale parameter of the modified minimal subtraction scheme. An immediate consequence is the non-perturbative result 〈Θμμ〉 = − 3 8π κ = − (3 exp 2) 45/3π2 Λ MS = −0.2228 . . .Λ MS for the expectation value of the trace of the energy momentum tensor of QCD with three quark flavors. This relation compares favorably with phenomenological estimates of 〈Θμμ〉 from QCD sumrules for the charmonium system and Λ (3) MS from τ -decay. PACS: 11.15.-q 11.15.Bt 11.15.Tk 11.15.Bx NYU-TH–98/02/22 February 1998 e-mail : ms68@scires.nyu.edu offers to continue this research are welcome.

### Cite this paper

@inproceedings{Schaden1998TheVE, title={The vacuum energy density of QCD with nf=3 Quark Flavors}, author={Martin Schaden}, year={1998} }