Criterion for dynamical chiral symmetry breaking

TL;DR

This paper investigates the conditions under which dynamical chiral symmetry breaking occurs, linking it to the stability of the vacuum via a generalized Hamiltonian and analyzing the effects of long-range and short-range interactions.

Contribution

It establishes a criterion for chiral symmetry breaking based on the stability analysis of a related quantum-mechanical Hamiltonian, including bounds on critical coupling values.

Findings

Weak long-range attraction can cause symmetry breaking.

Scale invariance leads to a critical coupling for instability.

An upper bound for critical coupling in short-range interactions.

Abstract

The Bethe-Salpeter equation is related to a generalized quantum-mechanical Hamiltonian. Instability of the presumed vacuum, indicated by a tachyon, is related to a negative energy eigenstate of this Hamiltonian. The variational method shows that an arbitrarily weak long-range attraction leads to chiral symmetry breaking, except in the scale-invariant case when the instability occurs at a critical value of the coupling. In the case of short-range attraction, an upper bound for the critical coupling is obtained.