The $\epsilon$-regime of dilaton chiral perturbation theory

TL;DR

This paper introduces the $\\epsilon$-regime of dilaton chiral perturbation theory, computing key quantities like the dilaton mass and spectral density, revealing a simple scaling relation to ordinary chiral perturbation theory.

Contribution

It presents the first detailed analysis of the $\\epsilon$-regime in dilaton chiral perturbation theory, establishing a universal scaling relation with ordinary chiral perturbation theory.

Findings

Chiral condensate and spectral density relate via a simple scaling.

Results agree with universal predictions in the $\\epsilon$-regime.

Derived expressions for dilaton mass and topological susceptibility.

Abstract

The $\epsilon$-regime of dilaton chiral perturbation theory is introduced. We compute the dilaton mass, the chiral condensate and the topological susceptibility in the $\epsilon$-regime, as a function of the fermion mass. The microscopic spectral density of the Dirac operator is obtained from dilaton chiral perturbation theory. Our main result is that the chiral condensate and the spectral density are related to their counterparts from ordinary chiral perturbation theory via a simple scaling relation. This relation originates from the mass dependence of the dilaton potential, and is valid in both the $\epsilon$-regime and the $p$-regime. In the $\epsilon$-regime, moreover, all results agree with the universal predictions to leading order in $\epsilon$.