Limitations of the heavy-baryon expansion as revealed by a pion-mass dispersion relation

TL;DR

This paper examines the limitations of the heavy-baryon expansion in chiral perturbation theory using a pion-mass dispersion relation, revealing convergence issues and its inadequacy for certain nucleon properties like polarizability.

Contribution

It demonstrates the limitations of the heavy-baryon expansion through a pion-mass dispersion relation, highlighting issues with convergence and applicability to nucleon polarizability.

Findings

Heavy-baryon loops show stronger cutoff dependence after renormalization.

The expansion's convergence weakens with increasing cutoff.

Heavy-baryon expansion fails to reproduce large soft contributions to polarizability.

Abstract

The chiral expansion of nucleon properties such as mass, magnetic moment, and magnetic polarizability are investigated in the framework of chiral perturbation theory, with and without the heavy-baryon expansion. The analysis makes use of a pion-mass dispersion relation, which is shown to hold in both frameworks. The dispersion relation allows an ultraviolet cutoff to be implemented without compromising the symmetries. After renormalization, the leading-order heavy-baryon loops demonstrate a stronger dependence on the cutoff scale, which results in weakened convergence of the expansion. This conclusion is tested against the recent results of lattice quantum chromodynamics simulations for nucleon mass and isovector magnetic moment. In the case of the polarizability, the situation is even more dramatic as the heavy-baryon expansion is unable to reproduce large soft contributions to this quantity. Clearly, the heavy-baryon expansion is not suitable for every quantity.