A dispersion relation for the pion-mass dependence of hadron properties

TL;DR

This paper derives a dispersion relation for how hadron properties depend on the pion mass, verified with chiral perturbation theory, and proposes a method for analyzing other mass dependencies in quantum chromodynamics.

Contribution

It introduces a new dispersion relation for hadron properties as functions of pion mass squared, verified with chiral perturbation theory calculations, and outlines a general method for other mass dependencies.

Findings

Verified the dispersion relation with nucleon and Delta properties in chiral perturbation theory.

Demonstrated the relation's applicability up to order p^3 in chiral expansion.

Outlined a method to derive similar relations for other mass-dependent quantities.

Abstract

We present a dispersion relation in the pion-mass squared, which static quantities (nucleon mass, magnetic moment, etc.) obey under the assumption of analyticity in the entire complex $m_\pi^2$ plane modulo a cut at negative $m_\pi^2$ associated with pion production. The relation is verified here in a number of examples of nucleon and $\Delta$-isobar properties computed in chiral perturbation theory up to order $p^3$. We outline a method to obtain relations for other mass-dependencies, and illustrate it on a two-loop example.