Nucleon polarizabilities in covariant baryon chiral perturbation theory with explicit $\Delta$ degrees of freedom

TL;DR

This paper calculates nucleon polarizabilities using covariant chiral perturbation theory with explicit $$ degrees of freedom, providing predictions and analyzing the role of the $$ resonance in effective field theory.

Contribution

It introduces a covariant $$-full approach to compute nucleon polarizabilities up to order $^3 + q^4$, comparing results with experimental data and assessing the $$'s significance.

Findings

Predictions for nucleon polarizabilities agree with experimental data.

Explicit $$ degrees of freedom improve the effective field theory description.

Heavy-baryon approach shows limitations in convergence for polarizability calculations.

Abstract

We compute various nucleon polarizabilities in chiral perturbation theory implementing the $\Delta$-full ($\Delta$-less) approach up to order $\epsilon^3 + q^4$ ($q^4$) in the small-scale (chiral) expansion. The calculation is carried out using the covariant formulation of $\chi$PT by utilizing the extended on-mass shell renormalization scheme. Except for the spin-independent dipole polarizabilities used to fix the values of certain low-energy constants, our results for the nucleon polarizabilities are pure predictions. We compare our calculations with available experimental data and other theoretical results. The importance of the explicit treatment of the $\Delta$ degree of freedom in the effective field theory description of the nucleon polarizabilities is analyzed. We also study the convergence of the $1/m$ expansion and analyze the efficiency of the heavy-baryon approach for the nucleon polarizabilities.