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 $< \bar \psi \psi > \$ or $< \bar \psi \Gamma \psi \bar \psi \Gamma \psi >$. 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 $< \bar \psi \psi >$.

Alexander von Humboldt-Fellow

Presented by E. Katznelson