Consistency between SU(3) and SU(2) chiral perturbation theory for the nucleon mass

Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the $19$ low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-to-leading order~\cite{Ren:2014vea} is supported by comparing the effective parameters (the combinations of the $19$ couplings) with the corresponding low-energy constants in the SU(2) sector~\cite{Alvarez-Ruso:2013fza}. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref.~\cite{Alvarez-Ruso:2013fza}.