A parametrization of the baryon octet and decuplet masses

We construct a general parametrization of the baryon octet and decuplet masses including the three-body terms using the unit operator and the symmetry-breaking factors, $M^d=\textrm{diag}\,(0,1,0)$ and $M^s=\textrm{diag}\,(0,0,1)$, in conjunction with the spin operators. Our parametrization which is equivalent to the usual chiral description is the first general parametrization in the context of effective field theory in the ``quark" representation, where it has the minimal number of operators needed to describe all the octet and decuplet masses. We show that at two-loop level in the heavy-baryon chiral effective field theory, contributions of the three-body terms are cancelled and the general expression for baryon masses is reduced to the independent one- and two body operators. Our parametrization is particularly useful to an analysis of the baryon mass splittings due to both hypercharge-breaking and isospin-breaking effects.