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.

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 study chiral symmetry breaking for fundamental charged fermions coupled electromagnetically to photons with the inclusion of four-fermion contact self-interaction term, characterized by coupling strengths α and λ, respectively. We employ multiplicatively renormalizable models for the photon dressing function and the electron-photon vertex which minimally ensures mass anomalous dimension γm = 1. Vacuum polarization screens the interaction strength. Consequently, the pattern of dynamical mass generation for fermions is characterized by a critical number of massless fermion flavors N f = N c f above which chiral symmetry is restored. This effect is in diametrical opposition to the existence of criticality for the minimum interaction strengths, αc and λc, necessary to break chiral symmetry dynamically. The presence of virtual fermions dictates the nature of phase transition. Miransky scaling laws for the electromagnetic interaction strength α and the four-fermion coupling λ, observed for quenched QED, are replaced by a mean-field power law behavior corresponding to a second order phase transition. These results are derived analytically by employing the bifurcation analysis, and are later confirmed numerically by solving the original non-linearized gap equation. A three dimensional critical surface is drawn in the phase space of (α, λ, N f ) to clearly depict the interplay of their relative strengths to separate the two phases. We also compute the β-functions (βα and β λ ), and observe that αc and λc are their respective ultraviolet fixed points. The power law part of the momentum dependence, describing the mass function, implies γm = 1 + s, which reproduces the quenched limit trivially. We also comment on the continuum limit and the triviality of QED. 11.30.Rd, 11.15.Tk Since the works of Maskawa and Nakajima as well as the Kiev group [1], it is well known that quenched quantum electrodynamics (QED) exhibits vacuum rearrangement, which triggers chiral symmetry breaking when the interaction strength α = e 2 /(4π) exceeds a critical value α c ∼ 1. α c was argued to be an ultraviolet stable fixed point defining the continuum limit in supercritical QED. Although these works were carried out for the bare vertex in the Landau gauge, principle qualitative conclusions were later shown to be robust even for the most general and sophisticated ansätze put forward henceforth for an arbitrary value of the covariant gauge parameter, see e.g., [2][3][4][5]. Bardeen, Leung and Love [6] demonstrated that the composite operatorψψ acquires large anomalous dimensions at α = α c . In fact, the mass anomalous dimension was shown to be γ m = 1, leading to the fact that the four-fermion interaction operator (ψψ) 2 acquires the scaling dimension of d = 2(3 − γ m ) = 4 instead of 6, and becomes renormalizable. This is an example of when an interaction which is irrelevant in a certain region of phase space (perturbative) might become relevant in another (non perturbative). Consequently, the four-fermion contact interaction becomes mar...

Using our analytical expressions that well model the lattice simulations of the gluonic excitations, we use the extended quark potential model to study the effects of orbital and radial excitations on the masses and sizes of conventional and hybrid B c mesons. A non relativistic formalism is used to numerically calculate the wave functions using the shooting method; this allows us also calculating the E1, M 1 radiative partial widths for conventional meson to meson and hybrid to hybrid transitions. We incorporate spin mixing and compare our calculated spectrum and decay widths with the available experimental B c masses and the theoretically predicted spectra and the decay widths by other groups. Our results can help consider both conventional and hybrid quantum numbers to B c mesons as experimental results become available.