A parametrization of the baryon octet and decuplet masses

Abstract

We construct a general parametrization of the baryon octet and decuplet mass operators including the three-body terms using the unit operator and the symmetrybreaking factors M d = diag (0, 1, 0) and M s = diag (0, 0, 1) in conjunction with the spin operators. Our parametrization has the minimal number of operators needed to describe all the octet and decuplet masses. Investigating the likely size of the three-body terms, we find that contributions of the three-body hypercharge splittings are comparable to those from the one-and two-body isospin splittings and that contributions of the three-body isospin splitting operators are very small. We prove that, in dynamical calculations, one must go to three loops to get the three-body terms. We also find that the suggested hierarchy of sizes for terms in the most general expression for baryon masses that involve multiple factors of M d and/or M s does not hold strictly for dynamical calculations in heavy baryon chiral perturbation theory: terms of a given order in a meson loop expansion may appear both with the expected factors of M d and M s , and with one factor more.PACS numbers: 13.40.Dk,11.30.Rd § The connection of this representation to the usual effective-field methods was discussed in detail in [18,19]. The results in each case can be summarized in terms of a set of effective interactions that have the appearance of interactions between quarks in the familiar semirelativistic or nonrelativistic quark models for the baryons [29, 30, 31], but the corresponding matrix elements can be translated back to expressions in terms of the relativistic effective baryon fields.

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