Nucleon mass in covariant baryon chiral perturbation theory at leading two-loop order

TL;DR

This paper extends covariant baryon chiral perturbation theory to two-loop order to accurately compute the nucleon mass, showing excellent convergence and agreement with lattice QCD data, thus enhancing its predictive power.

Contribution

It provides the first complete two-loop order (O(p^5)) calculation of the nucleon mass in relativistic BChPT, ensuring proper power counting and renormalization scale independence.

Findings

Small higher-order contributions (~8 MeV) indicate good convergence.

Excellent agreement with lattice QCD data for pion masses up to 300 MeV.

Establishes two-loop relativistic BChPT as a precision tool for nucleon studies.

Abstract

We calculate the nucleon mass within a manifestly relativistic formulation of baryon chiral perturbation theory (BChPT), extending the framework to leading two-loop order ($\mathcal{O}(p^5)$). By employing dimensional counting analysis and rigorously verifying the extended on-mass-shell scheme at this order, we obtain a complete chiral representation of the nucleon mass that preserves analyticity, respects proper power counting, and maintains renormalization-scale independence. The resulting expression exhibits excellent convergence, with $\mathcal{O}(p^5)$ contributions remaining small ($\sim 8~\rm{MeV}$). This formulation provides a robust foundation for chiral extrapolation, demonstrating remarkable agreement with lattice QCD data across a wide range of pion masses ($M_\pi \lesssim 300~\rm{MeV}$). The success of this calculation establishes two-loop relativistic BChPT as a precision tool for studying nucleon structure and related properties.