QCD Sum Rules and Spontaneous Breakdown of Chiral Symmetry

Abstract

In this talk we present some results from a Monte-Carlo simulation of a special set of four fermion correlation functions at small lattice spacing in the Susskind formalism. In a previous article [l] a number of identities were derived for meson (i.e. four fermion) correlation functions whose short distance behaviour is governed by chiral symmetry order parameters like \( \) or \( \). In the continuum limit these relations correspond to a set of so-called odd sum rules for two point functions involving the set of currents and quark densities of the form \( \bar \psi \psi ,\bar \psi {\gamma _5}\psi ,\psi {\gamma _\mu }\psi ,\bar \psi {\gamma _5}{\gamma _\mu }\psi \) and \(\bar \psi {\sigma _{\mu v}}\psi \) . Of particular interest are \(\psi (x){\gamma _5}{\gamma _\mu }\psi (x)\psi (y){\gamma _5}\psi (y)\) and \(\psi {\sigma _\mu }_v\psi \bar \psi {\gamma _\mu }\psi \) because the Wilson operators product expansion (OPE) tells us that in the short distance and chiral limit these are directly proportional to the order parameter \( \).