We employ a Dyson-Schwinger equation model to effect a unified and uniformly accurate description of light- and heavy-meson observables, which we characterise by heavy-meson leptonic decays, semileptonic heavy-to-heavy and heavy-to-light transitions - B -> D*, D, rho, pi; D -> K*, K, pi, radiative and strong decays - B(s)* -> B(s) gamma; D(s)* -> D(s) gamma, D pi, and the rare B-> K* gamma flavour-changing neutral-current process. We elucidate the heavy-quark limit of these processes and, using a model-independent mass formula valid for all nonsinglet pseudoscalar mesons, demonstrate that their mass rises linearly with the mass of their heaviest constituent. In our numerical calculations we eschew a heavy-quark expansion and rely instead on the observation that the dressed c,b-quark mass functions are well approximated by a constant, interpreted as their constituent-mass: we find M_c=1.32 GeV and M_b=4.65 GeV. The calculated heavy-meson leptonic decay constants and transition form factors are a necessary element in the experimental determination of CKM matrix elements. The results also show that this framework, as employed hitherto, is well able to describe vector meson polarisation observables.Comment: 32 pages, 7 figures, REVTEX. Some quantitative modification of tables and figures: calculation of additional processes. To appear in Phys. Rev.

Phase transitions in hot and dense matter and the in-medium behavior of pseudoscalar mesons (π ± , π 0 , K ± , K 0 ,K 0 , η and η ′ ) are investigated, in the framework of the three flavor NambuJona-Lasinio model, including the 't Hooft interaction, which breaks the U A (1) symmetry. Three different scenarios are considered: zero density and finite temperature, zero temperature and finite density in quark matter with different degrees of strangeness, and finite temperature and density.At T = 0, the role of strange valence quarks in the medium is discussed, in connection with the phase transition and the mesonic behavior. It is found that the appearance of strange quarks, above certain densities, leads to meaningful changes in different observables, especially in matter with β -equilibrium. The behavior of mesons in the T − ρ plane is analyzed in connection with possible signatures of restoration of symmetries.

Deconfinement and chiral symmetry restoration are explored in a confining, renormalisable, Dyson-Schwinger equation model of two-flavour QCD. An order parameter for deconfinement is introduced and used to establish that, in the chiral limit, deconfinement and chiral symmetry restoration are coincident at T c ≈ 150 MeV. The transitions are second order and each has the same critical exponent: β ≈ 0.3. The deconfinement transition is found to exhibit sensitivity to the current-quark mass. f π and m π change by no more than 10% for T < 0.7 T c , however, as T → T c , thermal fluctuations cause the pion bound state contribution to the four-point quark-antiquark correlation function to disappear.

A simple confining separable interaction Ansatz for the rainbow-ladder truncated QCD Dyson-Schwinger equations is used to implement chiral restoration and quark deconfinement in a study ofqq meson states at finite temperature. The model is fixed at T = 0 by reproducing selected π and ρ properties. Deconfinement and chiral restoration are found to both occur at Tc = 146 MeV. In the pion sector, we investigate Mπ(T ) and fπ(T ) along with the exact QCD mass relation and the GMOR relation. For the vector mode, we investigate the 3-space transverse and longitudinal masses M T ρ (T ) and M L ρ (T ), along with the width for the decay ρ 0 → e + e − . The equation of state (EOS) for the model is investigated in the T − µ plane, a tri-critical point is identified and the relationship to a bag model is discussed. The deconfinement transition in rapidly rotating neutron stars is considered and a new signal from the pulsar timing in binary systems with mass accretion is suggested. The model is used to discuss the possibility of a superconducting quark matter phase.