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

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 ($\sim 8\mathrm{MeV}$). This formulation provides a robust foundation for chiral extrapolation, demonstrating remarkable agreement with lattice QCD data across a wide range of pion masses ($M_{\pi }\lesssim 300\mathrm{MeV}$). The success of this calculation establishes two-loop relativistic BChPT as a precision tool for studying nucleon structure and related properties.

Comments: 6 pages, 1 figure, proceeding for the 21st International Conference on Hadron Spectroscopy and Structure (HADRON2025)