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.

We investigate the connection between relativistic potential models for quark-antiquark bound states and the nonrelativistic models that have been used successfully to fit and predict the spectra of relativistic systems, as in the work of Martin. We use Martin's operator inequality p 2 + m 2 ≤ (p 2 + M 2 + m 2 )/2M to motivate the approximation of the relativistic kinetic energy terms in the spinless Salpeter equation by expressions of the nonrelativistic form M + ǫ + p 2 /2M for each quark. To investigate the validity of the resulting approximation numerically, we generate energy spectra for qq mesons composed of two light or two heavy quarks using the spinless Salpeter equation with the linear-plus-Coulomb potential typical of phenomenological fits to qq data, and then fit the lowest few states of each type using the effective Schrödinger description with the same potential. We find good fits to the lowest four calculated cc and the lowest three ss states either taking M fixed at the value M q = p 2 + m 2 q that minimizes the Martin bound, or allowing M q to vary in the fit. The energies of the lowest few cs states are then predicted with similar accuracy. The reasons for the success of the nonrelativistic approximation are identified, and explain the success of Martin's nonrelativistic predictions for the spectra of relativistic light-heavy mesons. However, we note that the agreement between the nonrelativistic and relativistic wave functions is not good, a point of potential concern for the calculation of transition matrix elements.

We show that the detection of neutrinos from a typical ␥ ray burst requires a kilometer-scale detector. We argue that large bursts should be visible with the neutrino telescopes under construction. We emphasize the three techniques by which neutrino telescopes can perform this search: by triggering on ͑i͒ bursts of muons from muon neutrinos, ͑ii͒ muons from air cascades initiated by high energy ␥ rays and ͑iii͒ showers made by relatively low energy (Ӎ100 MeV͒ electron neutrinos. The timing of neutrino-photon coincidences may yield a measurement of the neutrino mass to order 10 Ϫ4 -10 Ϫ5 eV. ͓S0556-2821͑96͒01616-5͔PACS number͑s͒: 95.55.Fw

We analyze the structure of meson loop corrections to the O(m s ) expressions for the baryon masses and magnetic moments in heavy-baryon chiral perturbation theory ͑HBChPT͒, and show in detail how the bulk of the corrections are absorbed into redefinitions of the unknown parameters of the O(m s ) chiral expansion. To effect this analysis, we use the three-flavor-index representation of the effective baryon fields and HBChPT developed in a preceding paper, and a decomposition of the corrections in terms of effective one-, two-, and three-quark operators. The results show why the loop corrections have so little effect on fits to the masses and moments, and do not seriously disrupt the Gell-Mann-Okubo relations for the masses and the Okubo relation for the moments even though individual loops can be quite large. We also examine the momentum structure of the residual loop corrections, and comment on limits on their validity in HBChPT. The structural analysis can be generalized straightforwardly to other problems in HBChPT using the three-flavor-index representation of the effective baryon fields, and provides a fairly simple way to determine what parts of the loop corrections are actually significant in a given setting.