Universal Properties of Chiral Simmetry Breaking

Abstract

We discuss chiral symmetry breaking critical points from the perspective of PCAC, correlation length scaling and the chiral equation of state. A scaling theory for the ratio $R_{\pi }$ of the pion to sigma masses is presented. The Goldstone character of the pion and properties of the longitudinal and transverse chiral susceptibilities determine the ratio $R_{\pi }$ which can be used to locate critical points and measure critical indices such as $\delta$. We show how PCAC and correlation length scaling determine the pion mass' dependence on the chiral condensate and lead to a practical method to measure the anomalous dimension $\eta$. These tools are proving useful in studies of the chiral transition in lattice QED and the quark-gluon plasma transition in lattice QCD.

19 pages, 4 figures. CERN-TH.6630/92 ILL-(TH)-92-18

References in corpus (3)

• The Four-Fermi Model in Three Dimensions at Non-Zero Density and Temperature
• Monopole Percolation and The Universality Class of the Chiral Transition in Four Flavor Noncompact Lattice QED
• Spectroscopy, Equation Of State And Monopole Percolation In Lattice QED With Two Flavors

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