Modular classes of Poisson-Nijenhuis Lie algebroids

The modular vector field of a Poisson-Nijenhuis Lie algebroid $A$ is defined and we prove that, in case of non-degeneracy, this vector field defines a hierarchy of bi-Hamiltonian $A$-vector fields. This hierarchy covers an integrable hierarchy on the base manifold, which may not have a Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic

A supergeometric approach to Poisson reduction

This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a generalization of the classical Poisson reduction by distributions (Marsden-Ratiu reduction). Further it allows one to construct actions of strict Lie 2-groups and to describe the corresponding reductions.Comment: 40 pages. Final version accepted for publicatio

Role of Scalar Meson Resonances in $K_{L}^{0} \rightarrow \pi^{0} \gamma \gamma Decay

Corrections to $K_{L}^{0}\rightarrow \pi^{0} \gamma \gamma$ decay induced by scalar meson exchange are studied within chiral perturbation theory. In spite of bad knowledge of scalar-mesons parameters, the calculated branching ratio can be changed by a few percent.Comment: 18 pages of text, 2 figures (available upon request); preprint IJS-TP-16-94 , TUM-T31-63-94

Insight into the Scalar Mesons from a Lattice Calculation

We study the possibility that the light scalar mesons are (qbar qbar q q) states rather than (qbar q). We perform a lattice QCD calculation of pseudoscalar meson scattering amplitudes, ignoring quark loops and quark annihilation, and find indications that for sufficiently heavy quarks there is a stable four-quark bound state with J^{PC}=0^{++} and non-exotic flavor quantum numbers.Comment: 16 pages, revtex, with eps figure

Kaon-Nucleon Scattering Amplitudes and Z∗^*-Enhancements from Quark Born Diagrams

We derive closed form kaon-nucleon scattering amplitudes using the ``quark Born diagram" formalism, which describes the scattering as a single interaction (here the OGE spin-spin term) followed by quark line rearrangement. The low energy I=0 and I=1 S-wave KN phase shifts are in reasonably good agreement with experiment given conventional quark model parameters. For $k_{lab}> 0.7$ Gev however the I=1 elastic phase shift is larger than predicted by Gaussian wavefunctions, and we suggest possible reasons for this discrepancy. Equivalent low energy KN potentials for S-wave scattering are also derived. Finally we consider OGE forces in the related channels K$\Delta$, K$^*$N and K$^*\Delta$, and determine which have attractive interactions and might therefore exhibit strong threshold enhancements or ``Z$^*$-molecule" meson-baryon bound states. We find that the minimum-spin, minimum-isospin channels and two additional K$^*\Delta$ channels are most conducive to the formation of bound states. Related interesting topics for future experimental and theoretical studies of KN interactions are also discussed.Comment: 34 pages, figures available from the authors, revte

Radiative Scalar Meson Decays in the Light-Front Quark Model

We construct a relativistic $^3P_0$ wavefunction for scalar mesons within the framework of light-front quark model(LFQM). This scalar wavefunction is used to perform relativistic calculations of absolute widths for the radiative decay processes$(0^{++})\to\gamma\gamma,(0^{++})\to\phi\gamma$, and $(0^{++})\to\rho\gamma$ which incorporate the effects of glueball-$q\bar{q}$ mixing. The mixed physical states are assumed to be $f_0(1370),f_0(1500)$,and $f_0(1710)$ for which the flavor-glue content is taken from the mixing calculations of other works. Since experimental data for these processes are poor, our results are compared with those of a recent non-relativistic model calculation. We find that while the relativistic corrections introduced by the LFQM reduce the magnitudes of the decay widths by 50-70%, the relative strengths between different decay processes are fairly well preserved. We also calculate decay widths for the processes $\phi\to(0^{++})\gamma$ and (0^{++})\to\gamma\gamm involving the light scalars $f_0(980)$ and $a_0(980)$ to test the simple $q\bar{q}$ model of these mesons. Our results of $q\bar{q}$ model for these processes are not quite consistent with well-established data, further supporting the idea that $f_0(980)$ and $a_0(980)$ are not conventional $q\bar{q}$ states.Comment: 10 pages, 4 figure

Glueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states I: Derivation of the relativistic equation

A rigorous three-dimensional relativistic equation satisfied by two-gluon bound states is derived from the QCD with massive gluons. With the gluon fields and the quark fields being expanded in terms of the gluon multipole fields and the spherical Dirac spinors respectively, the equation is well established in the angular momentum representation and hence is much convenient for solving the problem of two-gluon glueball spectra. In particular, the interaction kernel in the equation is exactly derived and given a closed expression which includes all the interactions taking place in the two-gluon glueballs. The kernel contains only a few types of Green's functions and commutators. Therefore, it is not only easily calculated by the perturbation method, but also provides a suitable basis for nonperturbative investigations

Glueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states II: calculation of the glueball spectrum

In the preceding paper, a rigorous three-dimensional relativistic equation for two-gluon bound states was derived from the QCD with massive gluons and represented in the angular momentum representation. In order to apply this equation to calculate the glueball spectrum, in this paper, the equation is recast in an equivalent three-dimensional relativistic equation satisfied by the two-gluon positive energy state amplitude. The interaction Hamiltonian in the equation is exactly derived and expressed as a perturbative series. The first term in the series describes the one-gluon exchange interaction which includes fully the retardation effect in it. This term plus the linear confining potential are chosen to be the interaction Hamiltonian and employed in the practical calculation. With the integrals containing three and four spherical Bessel functions in the QCD vertices being analytically calculated, the interaction Hamiltonian is given an explicit expression in the angular momentum representation. Numerically solving the relativistic equation with taking the contributions arising from the retardation effect and the longitudinal mode of gluon fields into account, a set of masses for the $0^{++},0^{-+},1^{++},1^{-+},2^{++}$ and $2^{-+\text{}}$ glueball states are obtained and are in fairly good agreement with the predictions given by the lattice simulatio

THE INTERPLAY OF THE K+K- ATOM AND THE f_0(975) RESONANCE

We predict that production of the K+K- atom in pd-3^HeX and similar reactions exhibits a drastic missing mass spectrum due to the interplay with f_0(975) resonance. We point out that high precision studies of the K+K- atom may shed a new light on the nature of f_0(975).Comment: 13 page

Evidence for two-quark content of f0(980)f_{0}(980) in exclusive b→cb\to c decays

Inspired by a large decay branching ratio (BR) of $B^{+}\to f_{0}(980)K^{+}$ measured by Belle recently, we propose that a significant evidence of the component of $n\bar{n}=(u\bar{u}+d\bar{d})/\sqrt{2}$ in $f_{0}(980)$ could be demonstrated in exclusive $b\to c$ decays by the observation of $f_{0}(980)$ in the final states $\bar{B}\to D^{0(*)} \pi^{+} \pi^{-}(KK)$ and $\bar{B}\to J/\Psi \pi^{+} \pi^{-}(KK)$. We predict the BRs of $\bar{B}\to D^{0(*)} (J/\Psi) f_{0}(980)$ to be ${\cal {O}}(10^{-4})$ (${\cal {O}}(10^{-5})$) while the unknown wave functions of $D^{(*)0}$ ($J/\Psi$) are chosen to fit the observed decays of $\bar{B}\to D^{(*)0} \pi^{0} (J/\Psi K^{0(*)})$.Comment: 4 pages, 2 figures, Revtex4, version to appear in PR