Pion-mass dispersion relation in the baryon sector

TL;DR

This paper derives a dispersion relation in the complex pion-mass squared plane that constrains static baryon properties, providing insights into differences between heavy-baryon and relativistic approaches in chiral perturbation theory.

Contribution

It introduces a novel dispersion relation in the complex pion-mass squared plane applicable to baryon static quantities, enhancing understanding of theoretical differences.

Findings

Dispersion relation constrains baryon masses, magnetic moments, polarizabilities.

Highlights differences between heavy-baryon and relativistic calculations.

Provides a new analytical tool in chiral perturbation theory.

Abstract

By looking at the complex plane of the pion-mass squared we establish a dispersion relation which the static quantities, such as baryon masses, magnetic moments, polarizabilities, should obey. This dispersion relation yields insight into the differences between the heavy-baryon and relativistic calculations in the baryon sector of chiral perturbation theory.