Chiral Representation of the Nucleon Mass at Leading Two-loop Order

TL;DR

This paper presents a detailed two-loop order calculation of the nucleon mass within relativistic baryon chiral perturbation theory, providing a precise chiral representation that aligns well with lattice QCD data.

Contribution

It offers the first complete two-loop order chiral expansion of the nucleon mass, validating the extended-on-mass-shell scheme and demonstrating good convergence up to 350 MeV pion mass.

Findings

The $ ext{O}(p^5)$ contribution is about 10 MeV.

The chiral expansion accurately describes lattice QCD data.

The expansion shows good convergence up to 350 MeV pion mass.

Abstract

We calculate the nucleon mass in a manifestly relativistic baryon chiral perturbation theory up to the leading two-loop order. Through dimensional counting analysis, we perform the chiral expansion and verify the validity of the extended-on-mass-shell scheme at the two-loop level. As a result, we obtain the complete chiral representation of the nucleon mass up to $\mathcal{O}(p^5)$, which preserves the original analytic properties and satisfies the correct power counting. The obtained chiral result is well-suited for chiral extrapolation and provides an excellent description of lattice QCD data across a broad range of pion masses. We find that the $\mathcal{O}(p^5)$ contribution is small, approximately $10$ MeV, and varies only mildly with increasing pion mass, demonstrating good convergence of the nucleon mass up to pion masses of about 350 MeV at two-loop order.