Extracting the ${\bar q}q$ condensate for light quarks beyond the chiral limit in models of QCD

TL;DR

This paper refines the definition of the non-perturbative light quark condensate in QCD models by including multiple classes of solutions to the Schwinger Dyson Equation, enabling more accurate extraction from the Operator Product Expansion.

Contribution

It introduces a comprehensive approach considering three classes of solutions to better determine the quark condensate beyond the chiral limit in QCD models.

Findings

The physical condensate can be reliably extracted by fitting to the Operator Product Expansion.

The condensate increases with quark mass from zero to about 25 MeV.

Including multiple solution classes stabilizes the condensate determination.

Abstract

It has recently been suggested \cite{Chang:2006bm} that a reliable and unambiguous definition of the non-perturbative massive quark condensate could be provided by considering a non positive-definite class of solutions to the Schwinger Dyson Equation for the quark propagator. In this paper we show that this definition is incomplete without considering a third class of solutions. Indeed, studying these three classes reveals a degeneracy of possible condensate definitions leading to a whole range of values. However, we show that the {\it physical} condensate may in fact be extracted by simple fitting to the Operator Product Expansion, a procedure which is stabilised by considering the three classes of solution together. We find that for current quark masses in the range from zero to 25 MeV or so (defined at a scale of 2 GeV in the $\bar{MS}$ scheme), the dynamically generated condensate increases from the chiral limit in a wide range of phenomenologically successful models of the confining QCD interaction. Lastly, the role of a fourth class of noded solutions is briefly discussed.