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Register a new userFlavor SU(3) breaking effects in the chiral unitary model for meson-baryon scatterings
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T. Hyodo
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We examine flavor SU(3) breaking effects on meson-baryon scattering amplitudes in the chiral unitary model. It turns out that the SU(3) breaking, which appears in the leading quark mass term in the chiral expansion, can not explain the channel dependence of the subtraction parameters of the model, which are crucial to reproduce the observed scattering amplitudes and resonance properties.
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We study s-wave meson-baryon scattering using the chiral unitary model. We consider $1/2^{-}$ baryon resonances as quasibound states of the low lying mesons ($pi,K,eta$) and baryons ($N,Lambda,Sigma,Xi$). In previous works, the subtraction constants which appear in loop integrals were found to largely depend on the channels, and it was necessary to fit these constants to reproduce the data. In order to extend this model to all channels with fewer parameters, we introduce flavor SU(3) breaking interactions in the framework of chiral perturbation theory. It is found, however, that the observed SU(3) breaking in meson-baryon scattering cannot be explained by the present SU(3) breaking interactions. The role and importance of the subtraction constants in the present framework are discussed.
The validity of SU(4)-flavor symmetry relations of couplings of charmed $D$ mesons to light mesons and baryons is examined with the use of $^3{rm P}_0$ quark-pair creation model and nonrelativistic quark model wave functions. We focus on the three-meson couplings $pipirho$, $KKrho$ and $DDrho$ and baryon-baryon-meson couplings $NNpi$, $NLambda K$ and $NLambda_c D$. It is found that SU(4)-flavor symmetry is broken at the level of 30% in the $DDrho$ tree-meson couplings and 20% in the baryon-baryon-meson couplings. Consequences of these findings for DN cross sections and existence of bound states D-mesons in nuclei are discussed.
We study baryon-baryon scattering by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. We derive the corresponding diagrammatic rules paying special attention to complications caused by momentum-dependent interactions and propagators of particles with non-zero spin. We define the effective potential as a sum of two-baryon irreducible contributions of time-ordered diagrams and derive a system of integral equations for the scattering amplitude, which provides a coupled-channel generalization of the Kadyshevsky equation. The obtained leading-order baryon-baryon potentials are perturbatively renormalizable, and the corresponding integral equations have unique solutions in all partial waves. We discuss the issue of additional finite subtractions required to improve the ultraviolet convergence of (finite) loop integrals on the example of nucleon-nucleon scattering in the $^3P_0$ partial wave. Assuming that corrections beyond leading order can be treated perturbatively, we obtain a fully renormalizable formalism which can be employed to study baryon-baryon scattering.
A significant drop of the vector meson masses in nuclear matter is observed in a chiral SU(3) model due to the effects of the baryon Dirac sea. This is taken into account through the summation of baryonic tadpole diagrams in the relativistic Hartree approximation. The appreciable decrease of the in-medium vector meson masses is due to the vacuum polarisation effects from the nucleon sector and is not observed in the mean field approximation.
We consider a chiral baryon-meson model for nucleons and their parity partners in mirror assignment interacting with pions, sigma and omega mesons to describe the liquid-gas transition of nuclear matter together with chiral symmetry restoration in the high density phase. Within the mean-field approximation the model is known to provide a phenomenologically successful description of the nuclear-matter transition. Here, we go beyond this approximation and include mesonic fluctuations by means of the functional renormalization group. While these fluctuations do not lead to major qualitative changes in the phase diagram of the model, beyond mean-field, one is no-longer free to adjust the parameters so as to reproduce the binding energy per nucleon, the nuclear saturation density, and the nucleon sigma term all at the same time. However, the prediction of a clear first-order chiral transition at low temperatures inside the high baryon-density phase appears to be robust.
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