Momentum-dependent quark mass in two-point correlators.

Abstract

A momentum-dependent quark mass may be incorporated into a quark model in a manner consistent with dynamically broken chiral symmetry. We use this to study the high ${\mathit{Q}}^{2}$ behavior of the vector, axial vector, scalar, and pseudoscalar two-point correlation functions. Expanding the results to order 1/${\mathit{Q}}^{6}$, we show the correspondence between the dynamical quark mass and the vacuum condensates which appear in the operator product expansion (OPE) of QCD. We recover the correct leading logarithmic ${\mathit{Q}}^{2}$ dependence of the various terms in the OPE, but we also find substantial subleading corrections which are numerically huge in a specific case. We conclude by using the vector minus axial vector correlator to estimate the ${\mathrm{\ensuremath{\pi}}}^{+\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\pi}}}^{0}$ electromagnetic mass difference.