Light quark mass dependence of nucleon mass to two-loop order

TL;DR

This paper calculates the nucleon mass dependence on light quark mass using two-loop covariant chiral perturbation theory, verifying the EOMS scheme's convergence and matching lattice results.

Contribution

It provides a two-loop order analysis of nucleon mass dependence on quark mass within covariant chiral perturbation theory, confirming the EOMS scheme's effectiveness.

Findings

EOMS scheme shows good convergence up to order q^6.

Predicted nucleon mass in chiral limit: 856.6 MeV.

Results agree with recent lattice QCD data.

Abstract

We investigate the nucleon self energy through the sixth chiral order in the covariant $SU(2)$ chiral perturbation theory ($\chi$PT) in the single baryon sector. The validity of the extended on-mass-shell (EOMS) renormalization scheme is explicitly verified to two-loop order, manifested by the miraculous cancellation of all nonlocal divergences and power-counting-breaking (PCB) terms that are nonanalytic in pion mass. Using the $\sigma_{\pi N}$ term determined from the latest lattice simulation to constrain some unknown higher-order low energy constants (LECs), we predict the nucleon mass in the chiral limit to be $856.6\pm 1.7$ MeV. It is found that the EOMS scheme exhibits quite satisfactory convergence behavior through ${\cal O}(q^6)$ around physical point. We also predict the pion mass dependence of the nucleon mass to the accuracy of ${\cal O}(q^6)$, which is in satisfactory agreement with the recent lattice results over a wide range of pion mass.