Constraints on Chiral Perturbation Theory Parameters from QCD Inequalities

TL;DR

This work uses fundamental QCD positivity constraints (Weingarten and Witten inequalities) to bound the parameters of chiral perturbation theory. By translating these inequalities into both coordinate- and momentum-space formulations, the authors derive key relations such as $2 m_q(μ) \le B_0(μ) Z(μ)$ and $m_π^2 \le B_0(μ)^2 Z(μ)$, linking explicit and spontaneous chiral symmetry breaking to low-energy constants. They further explore renormalization effects, generalized chiral perturbation theory, and momentum-derivative versions of the bounds, showing that current EFT parameter values satisfy the constraints while highlighting how the inequalities can inform or constrain the chiral expansion. Additional results propose new inequality avenues for Wilson-line correlators and stress-tensor traces, with no known violations found. The study provides a rigorous, QCD-grounded framework for testing and constraining chiral EFTs.

Abstract

We explore some of the constraints imposed by positivity of the QCD measure (Weingarten's inequalities) on the parameters defining chiral perturbation theory. We find, in particular, that $2 m_q (μ)\leq B_0(μ) Z(μ)$. The use of further properties of the exact fermion propagator yields information on some higher order parameters.