Quark condensate for various heavy flavors

TL;DR

This paper calculates the quark condensate for various heavy flavors using the world-line formalism and stochastic vacuum model, revealing significant deviations from conventional formulas especially for charm quarks.

Contribution

It introduces a novel calculation of the heavy-quark condensate considering the diminishing quark mass and non-confining interactions, highlighting limitations of traditional formulas.

Findings

The quark condensate decreases by 64% when reducing the quark mass to the inverse correlation length.

The conventional heavy-quark condensate formula is invalid for the c-quark and has up to 23% correction for the b-quark.

The condensate is independent of non-confining non-perturbative interactions under certain gluonic correlator parametrizations.

Abstract

The quark condensate is calculated within the world-line effective-action formalism, by using for the Wilson loop an ansatz provided by the stochastic vacuum model. Starting with the relation between the quark and the gluon condensates in the heavy-quark limit, we diminish the current quark mass down to the value of the inverse vacuum correlation length, finding in this way a 64%-decrease in the absolute value of the quark condensate. In particular, we find that the conventional formula for the heavy-quark condensate cannot be applied to the c-quark, and that the corrections to this formula can reach 23% even in the case of the b-quark. We also demonstrate that, for an exponential parametrization of the two-point correlation function of gluonic field strengths, the quark condensate does not depend on the non-confining non-perturbative interactions of the stochastic background Yang-Mills fields.