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

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.