Abstract
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}.
Highlights
Chiral perturbation theory (ChPT) provides a model independent framework to explore the nonperturbative regime of strong interactions [3,4,5,6]
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, providing support to the assumption made in Ref. [2] that the SU(2) baryon chiral perturbation theory can be applied to study n f = 2 + 1 lattice quantum chromodynamics (QCD) simulations as long as the strange quark mass is close to its physical value
In order to better constrain the large number of unknown low energy constants (LECs), the strong isospin breaking effects on the octet baryon masses are taken into account
Summary
Chiral perturbation theory (ChPT) provides a model independent framework to explore the nonperturbative regime of strong interactions [3,4,5,6]. [2], nucleon masses from the n f = 2 + 1 lattice simulations of BMW [52], PACS-CS [18], LHPC [19], HSC [20], NPLQCD [24], MILC [53], and RBC-UKQCD [54] were analyzed in SU(2) BChPT with the EOMS scheme as well, with the assumption that the LECs depend only weakly on the strange quark mass around its physical value.
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