No abstract

We reexamine critically the chiral expansion for the baryon magnetic moments including the contributions from loops which involve intermediate octet and decuplet baryons. We find that, contrary to some claims, the nonanalytic loop contributions of orders m 1/2 s and m s ln m s are of the same general size because of large coupling factors for the latter, and that the decuplet contributions are as large as the octet contributions and must be included in a consistent calculation. There is no clear evidence of the convergence of the chiral series. The adequacy of the theory will not be established until dynamical models are able to calculate the contributions from the counterterms that largely hide the loop effects in fits to the data.

We recently derived explicit solutions of the leading-order Dokshitzer-Gribov-Lipatov-AltarelliParisi (DGLAP) equations for the Q 2 evolution of the singlet structure function Fs(x, Q 2 ) and the gluon distribution G(x, Q 2 ) using very efficient Laplace transform techniques. We apply our results here to a study of the HERA data on deep inelastic ep scattering as recently combined by the H1 and ZEUS groups. We use initial distributions F γp 2 (x, Q 2 0 ) and G(x, Q 2 0 ) determined for x < 0.1 by a global fit to the HERA data, and extended to x = 1 using the shapes of those distributions determined in the CTEQ6L and MSTW2008LO analyses from fits to other data. Our final results are insensitive at small x to the details of the extension. We obtain the singlet quark distribution Fs(x, Q 2 0 ) from F γp 2 (x, Q 2 0 ) using small non-singlet quark distributions taken from either the CTEQ6L or the MSTW2008LO analyses, evolve Fs and G to arbitrary Q 2 , and then convert the results to individual quark distributions. Finally, we show directly from a study of systematic trends in a comparison of the evolved F γp 2 (x, Q 2 ) with the HERA data, that the assumption of leading-order DGLAP evolution is inconsistent with those data.

We analyze the connections between the quark model (QM) and the description of hadrons in the low-momentum limit of heavy-baryon effective field theory in QCD. By using a three-flavor-index representation for the effective baryon fields, we show that the ``nonrelativistic'' constituent QM for baryon masses and moments is completely equivalent through O(m_s) to a parametrization of the relativistic field theory in a general spin--flavor basis. The flavor and spin variables can be identified with those of effective valence quarks. Conversely, the spin-flavor description clarifies the structure and dynamical interpretation of the chiral expansion in effective field theory, and provides a direct connection between the field theory and the semirelativistic models for hadrons used in successful dynamical calculations. This allows dynamical information to be incorporated directly into the chiral expansion. We find, for example, that the striking success of the additive QM for baryon magnetic moments is a consequence of the relative smallness of the non-additive spin-dependent corrections.Comment: 25 pages, revtex, no figure

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.