Erratum: Effective field theory and the quark model. II. Structure of loop corrections [Phys. Rev. D65, 034019 (2002)]

Abstract

Professor G. Morpurgo recently pointed out to us that he had derived the generalized Gell-Mann-Okubo relation given in Eq. ͑3.38͒ of our paper in Ref. ͓1͔ below, Eq. ͑2͒. His derivation was in the context of his general parametrization method for determining the spin and symmetry-breaking structure of the baryon masses and moments. The parameter T in his expression is equivalent to our matrix element ␣ M M .We would remark that, as discussed in our paper, the matrix element ␣ M M is calculable dynamically at one loop, so is not to be used as an adjustable parameter in fitting the baryon masses in the chiral loop expansion. Our approaches differ in that respect. The calculated and experimental values of ␣ M M are in reasonable agreement for the baryon octet. Although there is some evidence for a contribution of order m 3 s in the decuplet, this appears to be very small if electromagnetic corrections to the masses are eliminated as in Professor Morpurgo's treatment.The detailed structure found in our analysis is of course consistent with the general parametrization method even though, as discussed in Ref. ͓2͔ below, the latter is finally presented in the language of the constituent quark model. Our results for the baryon magnetic moments in terms of seven parameters are similar to those derived in Morpurgo's papers.We would like to thank Professor Morpurgo for pointing out his earlier work, and for his comments.

Estimates of isospin breaking contributions to baryon masses

“…However, we used a spin-and flavorindex or "quark" representation of the effective octet and decuplet baryon fields and the electromagnetic and mesonic interactions rather than the usual matrix expressions for the fields. The connection of this representation to the usual effective-field methods was discussed in detail in [4,5]. It has been applied in past analyses of the splittings between baryon isospin multiplets [4,5,6], and of the baryon magnetic moments [5,7].…”

“…The connection of this representation to the usual effective-field methods was discussed in detail in [4,5]. It has been applied in past analyses of the splittings between baryon isospin multiplets [4,5,6], and of the baryon magnetic moments [5,7]. 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.…”

“…where 4) and the ellipsis represents terms that can be absorbed into the structures that already appear in our analysis of intermultiplet mass splittings in [5].…”

“…that appeared in our earlier analysis of intermultiplet mass splittings [4,5], but involve the replacement of (one) matrix M s by M d and have coefficients proportional to the mass difference (m d − m u ) rather than m s . As shown below, terms of this form arise in QCD-based dynamical models from a colormagnetic interaction [13], and can give IB contributions to the intramultiplet mass splittings comparable to those from electromagnetic interactions [14,15] [32].…”

“…The procedures needed to convert Eq. (1.1) to an expression in terms of effective baryon fields in the matrix representation are described in detail in [4,5], but will not be needed here.…”