The strong decay amplitudes and radiative partial widths of orbital and radially excited states of B and B s mesons are presented. These results are obtained with a nonrelativistic potential quark model, the nonrelativistic reduction of the electromagnetic transition operator, and the " 3 P 0 " model of strong decays. The predictions are compared to experiment where possible and assignments for the recently discovered states, B 1 (5721), B * 2 (5747), B J (5840), B J (5970), B s1 (5830), and B * s2 (5840), are made.

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The quark potential model for mesons and its extension for hybrid mesons are used to study the effects of radial excitations on the masses, sizes and radial wave functions at the origin for conventional and hybrid charmonium mesons. These results can help in experimentally recognizing hybrid mesons. The properties of conventional and hybrid charmonium mesons are calculated for the ground and radially excited states using the shooting method to numerically solve the required Schrödinger equation for the radial wave functions. We compare our results with the experimentally observed masses and theoretically predicted results of the other models. Our results have implications for scalar form factors, energy shifts, and polarizabilities of conventional and hybrid mesons. The comparison of masses of conventional and hybrid charmonium meson with the masses of recent discovered XYZ-particles is also discussed.

Using our extension of the quark potential model to hybrid mesons that fits well to the available lattice results, we now calculate the masses, radii, wave functions at origin, leptonic and two photon decay widths, E1 and M 1 radiative transitions for a significant number of bottomonium mesons. These mesons include both conventional and hybrid ones with radial and angular excitations. Our numerical solutions of the Schrödinger equation are related to QCD through the Born-Oppenheimer approach. Relativistic corrections in masses and decay widths are also calculated by applying the leading order perturbation theory. The calculated results are compared with available experimental data and the theoretical results by other groups. We also identify the states of Υ(10860), Υ(11020), and Y b (10890) mesons by comparing their experimental masses and decay widths with our results.

We propose some extensions of the quark potential model to hybrids, fit them to the lattice data and use them for the purpose of calculating the masses, root mean square radii and wave functions at the origin of the conventional and hybrid charmonium mesons. We treat the ground and excited gluonic field between a quark and an antiquark as in the Born-Oppenheimer expansion, and use the shooting method to numerically solve the required Schrödinger equation for the radial wave functions; from these wave functions we calculate the mesonic properties. For masses we also check through a Crank Nichelson discretization. For hybrid charmonium mesons, we consider the exotic quantum number states with J P C = 0 +− , 1 −+ and 2 +− . We also compare our results with the experimentally observed masses and theoretically predicted results of the other models. Our results have implications for scalar form factors, energy shifts, magnetic polarizabilities, decay constants, decay widths and differential cross sections of conventional and hybrid mesons.

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Here is presented a four-body potential model for q 2 q2 systems which includes both the spin and flavour degrees of freedom, extending the formalism presented already in the spin independent situation. This allows an application to a realistic situation, which is chosen to be K K scattering. It is seen that because of the gluonic effects in this multi-quark system, the K K attraction resulting from the quark-exchange mechanism gets appreciably decreased compared to that emerging through the naive two-body potential approach.

Energies of four-quark systems calculated by the static quenched SU(2) lattice Monte Carlo method are analyzed in 2 × 2 bases for square, rectangle, tilted rectangle, linear and quadrilateral geometry configurations and in 3 × 3 bases for a non-planar geometry configuration. For small interquark distances, a lattice effect is taken into account by considering perimeter dependent terms which are characterized by the cubic symmetry. It is then found that a parameter f -that can be identified as a gluon field overlap factor -is rather well described by the form, where A and P are the area and perimeter mainly defined by the positions of the four quarks, b s is the string constant in the 2-quark potentials and E, F are constants. 0 1. Fit eigen-energies of all the (r, d) sets directly.