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

We investigate the nucleon self energy through the sixth chiral order in the covariant $SU(2)$ chiral perturbation theory (χPT) 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 σπ 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± 1.7 MeV. It is found that the EOMS scheme exhibits quite satisfactory convergence behavior through O(q⁶) around physical point. We also predict the pion mass dependence of the nucleon mass to the accuracy of O(q⁶), which is in satisfactory agreement with the recent lattice results over a wide range of pion mass.