arXiv subjects
Publications and source records attributed to G. Krein.
Chiral loop corrections for hadronic properties are considered in a constituent quark model. It is emphasized that the correct implementation of such corrections requires a sum over intermediate hadronic states. The leading non-analytic corrections are very important for baryon magnetic moments and explain the failure of the sum rule $(μ_{Σ^{+}}+2μ_{Σ^{-}})/μ_Λ=-1$ predicted by the constituent quark model.
The quark-meson-coupling model is used to study droplet formation from the liquid-gas phase transition in cold asymmetric nuclear matter. The critical density and proton fraction for the phase transition are determined in the mean field approximation. Droplet properties are calculated in the Thomas-Fermi approximation. The electromagnetic field is explicitly included and its effects on droplet properties are studied. The results are compared with the ones obtained with the NL1 parametrization of the non-linear Walecka model.
Generalized nucleon polarizabilities for virtual photons can be defined in terms of electroproduction cross sections as function of the 4-momentum transfer $Q^2$. In particular, the sum of the generalized electric and magnetic polarizabilities $Σ=α+β$ and the spin polarizability $γ$ can be expressed by virtual photon absorption cross sections integrated over the excitation energy. These quantities have been calculated within the framework of the recently developed unitary isobar model for pion photo- and electroproduction on the proton, which describes the available experimental data up to an excitation energy of about 1 GeV. Our results have been compared to the predictions of chiral perturbation theory.
We show that the implementation of chiral symmetry in recent studies of the hadron spectrum in the context of the constituent quark model is inconsistent with chiral perturbation theory. In particular, we show that the leading nonanalytic (LNA) contributions to the hadron masses are incorrect in such approaches. The failure to implement the correct chiral behaviour of QCD results in incorrect systematics for the corrections to the masses.
The mean field description of nuclear matter in the quark-meson coupling model is improved by the inclusion of exchange contributions (Fock terms). The inclusion of Fock terms allows us to explore the momentum dependence of meson-nucleon vertices and the role of pionic degrees of freedom in matter. It is found that the Fock terms maintain the previous predictions of the model for the in-medium properties of the nucleon and for the nuclear incompressibility. The Fock terms significantly increase the absolute values of the single-particle, four-component scalar and vector potentials, a feature that is relevant for the spin-orbit splitting in finite nuclei.
The spin structure functions g1 and g2 have been calculated in the resonance region and for small and intermediate momentum transfer. The calculation is based on a gauge-invariant and unitary model for one-pion photo- and electroproduction. The predictions of the model agree with the asymmetries and the spin sturcture functions recently measured at SLAC, and the first moments of the calculated spin structure functions fullfil the Gerasimov-Drell-Hearn and Burkhardt-Cottingham sum rules within an error of typically 5-10 %.
The long-standing discrepancy between the Gerasimov-Drell-Hearn sum rule and the analysis of pion photoproduction multipoles is greatly diminished by use of s-wave multipoles that are in accord with the predictions of chiral perturbation theory and describe the experimental data in the threshold region. The remaining difference may be due to contributions of channels with more pions and/or heavier mesons whose contributions to the sum rule remain to be investigated by a direct measurement of the photoabsorption cross sections.
We discuss the consistency of the traditional vector meson dominance (VMD) model for photons coupling to matter, with the vanishing of vector meson-meson and meson-photon mixing self-energies at q^2=0. This vanishing of vector mixing has been demonstrated in the context of rho-omega mixing for a large class of effective theories. As a further constraint on such models, we here apply them to a study of photon-meson mixing and VMD. As an example we compare the predicted momentum dependence of one such model with a momentum-dependent version of VMD discussed by Sakurai in the 1960's. We find that it produces a result which is consistent with the traditional VMD phenomenology. We conclude that comparison with VMD phenomenology can provide a useful constraint on such models.
A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces and shares similarities with the quasiparticle method of Weinberg. Starting with the Fock-space representation of single-hadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, hermitian Hamiltonians with a clear physical interpretation are obtained. Applications and comparisons with other composite-particle formalisms of the recent literature are made using the nonrelativistic quark model.
The binding energy of nuclear matter including exchange and pionic effects is calculated in a quark-meson coupling model with massive constituent quarks. As in the case with elementary nucleons in QHD, exchange effects are repulsive. However, the coupling of the mesons directly to the quarks in the nucleons introduces a new effect on the exchange energies that provides an extra repulsive contribution to the binding energy. Pionic effects are not small. Implications of such effects on observables are discussed.
A forward dispersion calculation is implemented for the spin polarizabilities $γ_1, ... ,γ_4$ of the proton and the neutron. These polarizabilities are related to the spin structure of the nucleon at low energies and are structure-constants of the Compton scattering amplitude at ${\cal O}(ω^3)$. In the absence of a direct experimental measurement of these quantities, a dispersion calculation serves the purpose of constraining the model building, and of comparing with recent calculations in heavy baryon chiral perturbation theory.
The optimized $δ$-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the $λϕ^4$ model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the $δ$ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.
Complex mass poles, or ghost poles, are present in the Hartree-Fock solution of the Schwinger-Dyson equation for the nucleon propagator in renormalizable models with Yukawa-type meson-nucleon couplings, as shown many years ago by Brown, Puff, and Wilets (BPW). These ghosts violate basic theorems of quantum field theory and their origin is related to the ultraviolet behavior of the model interactions. Recently, Krein et.al, proved that the ghosts disappear when vertex corrections are included in a self-consistent way, softening the interaction sufficiently in the ultraviolet region. In previous studies of pion-nucleon scattering using "dressed" nucleon propagator and bare vertices, did by Nutt and Wilets in the 70's (NW), it was found that if these poles are explicitly included, the value of the isospin-even amplitude A+ is satisfied within 20% at threshold. The absence of a theoretical explanation for the ghosts and the lack of chiral symmetry in these previous studies led us to re-investigate the subject using the approach of the linear-sigma model and study the interplay of low-energy theorems for pion-nucleon scattering and ghost poles. For bare interaction vertices we find that ghosts are present in this model as well and that the A+ value is badly described. As a first approach to remove these complex poles, we dress the vertices with phenomenological form factors and a reasonable agreement with experiment is achieved. In order to fix the two cutoff parameters, we use the A+ value for the chiral limit (m_pion -> 0) and the experimental value of the isoscalar scattering length. Finally, we test our model by calculating the phase shifts for the S waves and we find a good agreement at threshold.
We solve the Schwinger-Dyson equation for the nucleon propagator in the vacuum using $π$, $σ$, and $ω$ mesons. For bare interaction vertices (Hartree-Fock approximation) we obtain a pair of complex-conjugated poles (ghost poles) and for vertices dressed by phenomenological form-factors these ghosts disappeared. We use these two different approaches to evaluate the scattering lengths and the phase shifts for the $πN$ scattering at threshold. Our results show that only when the form factors are present is possible to obtain a good agreement with the low-energy observables.
Effective chiral Lagrangians involving constituent quarks, Goldstone bosons and long-distance gluons are believed to describe the strong interactions in an intermediate energy region between the confinement scale and the chiral symmetry breaking scale. Baryons and mesons in such a description are bound states of constituent quarks. We discuss the combined use of the techniques of effective chiral field theory and of the field theoretic method known as Fock-Tani representation to derive effective hadron interactions. The Fock-Tani method is based on a change of representation by means of a unitary transformation such that the composite hadrons are redescribed by elementary-particle field operators. Application of the unitary transformation on the microscopic quark-quark interaction derived from a chiral effective Lagrangian leads to chiral effective interactions describing all possible processes involving hadrons and their constituents. The formalism is illustrated by deriving the one-pion-exchange potential between two nucleons using the quark-gluon effective chiral Lagrangian of Manohar and Georgi. We also present the results of a study of the saturation properties of nuclear matter using this formalism.
Binding energy differences of mirror nuclei for A=15, 17, 27, 29, 31, 33, 39 and 41 are calculated in the framework of relativistic deformed mean-field theory. The spatial components of the vector meson fields and the photon are fully taken into account in a self-consistent manner. The calculated binding energy differences are systematically smaller than the experimental values and lend support to the existency of the Okamoto--Nolen-Schiffer anomaly found decades ago in nonrelativistic calculations. For the majority of the nuclei studied, however, the results are such that the anomaly is significantly smaller than the one obtained within state-of-the-art nonrelativistic calculations.
Starting from the Fock space representation of hadron bound states in a quark model, a change of representation is implemented by a unitary transformation such that the composite hadrons are redescribed by elementary-particle field operators. Application of the unitary transformation to the microscopic quark Hamiltonian gives rise to effective hadron-hadron, hadron-quark, and quark-quark Hamiltonians. An effective baryon Hamiltonian is derived using a simple quark model. The baryon Hamiltonian is free of the post-prior discrepancy which usually plagues composite-particle effective interactions.
The optimized $δ$-expansion is used to study vacuum polarization effects in the Walecka model. The optimized $δ$-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. Vacuum effects on self-energies and the energy density of nuclear matter are studied up to ${\cal O}(δ^2)$. When exchange diagrams are neglected, the traditional Relativistic Hartree Approximation (RHA) results are exactly reproduced and, using the same set of parameters that saturate nuclear matter in the RHA, a new stable, tightly bound state at high density is found.