Chiral effective-field theory with a resonance and heavy fields

TL;DR

This paper discusses incorporating the Δ(1232) resonance into chiral effective-field theory, addressing power counting issues, formulating a new dispersion relation, and examining proton magnetic polarizability determination from scattering data.

Contribution

It introduces a new dispersion relation linking power counting with analytic properties and clarifies conceptual issues in including resonances in chiral effective-field theory.

Findings

Formulated a novel dispersion relation in pion-mass squared.

Highlighted the connection between power counting and analytic properties.

Addressed controversy in proton magnetic polarizability measurements.

Abstract

Several conceptual points concerning the inclusion of the $\Delta$(1232) resonance in the framework of chiral effective-field theory are discussed, with an emphasis on the problem of power counting in the baryon sector in general. I also formulate a new dispersion relation in the pion-mass squared (or, the quark mass) and make a link between the power counting and the analytic properties of chiral expansion. A controversy regarding the determination of the proton's magnetic polarizability from Compton-scattering data is stressed here as well.