Quark Condensate from Renormalization Group Optimized Spectral Density

TL;DR

This paper employs a renormalization group optimized perturbation method to compute the nonperturbative QCD spectral density and chiral quark condensate, providing stable multi-loop approximations and comparing with other recent determinations.

Contribution

It introduces a RGOPT approach to calculate the QCD spectral density and quark condensate, achieving stable multi-loop results and estimating theoretical uncertainties.

Findings

Quark condensate for n_f=2: -(0.833-0.845) times the QCD scale

Quark condensate for n_f=3: -(0.814-0.838) times the QCD scale

Results are consistent with lattice and spectral sum rule determinations.

Abstract

Our renormalization group consistent variant of optimized perturbation, RGOPT, is used to calculate the nonperturbative QCD spectral density of the Dirac operator and the related chiral quark condensate $\langle \bar q q \rangle$, for $n_f=2$ and $n_f=3$ massless quarks. Sequences of approximations at two-, three-, and four-loop orders are very stable and give $\langle \bar q q \rangle^{1/3}_{n_f=2}(2\, {\rm GeV}) = -(0.833-0.845) \bar\Lambda_2 $, and $ \langle \bar q q \rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) = -(0.814-0.838) \bar\Lambda_3 $ where the range is our estimated theoretical error and $\bar\Lambda_{n_f}$ the basic QCD scale in the $\rm \bar{MS}$-scheme. We compare those results with other recent determinations (from lattice calculations and spectral sum rules).