We review heavy quark flavor and spin symmetries, their exploitation in heavy meson effective theories and the flavored couplings of charmed and light mesons in the definition of their effective Lagrangians. We point out how nonperturbative continuum
QCD approaches based on Dyson-Schwinger and Bethe-Salpeter equations can be used to calculate strong and leptonic decays of open-charm mesons and heavy quarkonia. The strong decay $D^*to Dpi$ serves as a benchmark, as it is the only physical open-charm observable that can be related to the effective Lagrangians couplings. Nonetheless, a quantitative comparison of $D^*Dpi$, $rho DD$, $rho D^*D$ and $rho D^* D^*$ couplings for a range of off-shell momenta of the $rho$-meson invalidates SU(4)$_F$ symmetry relations between these couplings. Thus, besides the breaking of flavor symmetry by mass terms in the Lagrangians, the flavor-symmetry breaching in couplings and their dependence on the $rho$-meson virtuality cannot be ignored. We also take the opportunity to present new results for the effective $J/psi DD$ and $J/psi D^*D$ couplings. We conclude this contribution with a discussion on how the description of pseudoscalar and vector $D$, $D_s$, $B$ and $B_s$ meson properties can be drastically improved with a modest modification of the flavor-dependence in the Bethe-Salpeter equation.
In this work we use the framework of the Dyson-Schwinger and Bethe-Salpeter equations to compute Light-Cone Distribution Amplitudes of heavy-light mesons and quarkonia. In studying the meson properties, we introduce a flavor dependence in the heavy-q
uark sector of the Bethe-Salpeter ladder kernel which yields improved numerical results for masses and leptonic decay constants of the pseudoscalar $D$, $D_s$, $B$ and $B_s$ mesons. Finally, the corresponding heavy-light Bethe-Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full theory.
We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in
QCD. To this end, we consider transverse Slavnov-Taylor identities that constrain the transverse quark-gluon vertex and derive its eight associated scalar form factors. The complete vertex can be expressed in terms of the quarks mass and wave-renormalization functions, the ghost-dressing function, the quark-ghost scattering amplitude and a set of eight form factors. The latter parametrize the hitherto unknown nonlocal tensor structure in the transverse Slavnov-Taylor identity which arises from the Fourier transform of a four-point function involving a Wilson line in coordinate space. We determine the functional form of these eight form factors with the constraints provided by the Bashir-Bermudez vertex and study the effects of this novel vertex on the quark in the Dyson-Schwinger equation using lattice QCD input for the gluon and ghost propagators. We observe significant dynamical chiral symmetry breaking and a mass gap that leads to a constituent mass of the order of 500 MeV for the light quarks. The flavor dependence of the mass and wave-renormalization functions as well as their analytic behavior on the complex momentum plane is studied and as an application we calculate the quark condensate and the pions weak decay constant in the chiral limit. Both are in very good agreement with their reference values.
Based on the Generalized Quantum Electrodynamics expression for the Podolsky propagator, which preserves gauge invariance for massive photons, we propose a model for the massive gluon propagator that reproduces well-known features of established stro
ng-interaction models in the framework of the Dyson-Schwinger equation. By adjusting the Podolsky mass and the coupling strength we thus construct a model with simple analytical properties known from perturbative theory, yet well suited to describe a confining interaction. We obtain solutions of the Dyson-Schwinger equation for the quark at space-like momenta on the real axis as well as on the complex plane and solving the bound-state problem with the Bethe-Salpeter equation yields masses and weak decay constants of the $pi, K$ and $eta_c$ in excellent agreement with experimental values, while the $D$ and $D_s$ are reasonably well described. The analytical simplicity of this effective interaction has the potential to be useful for phenomenological applications and may facilitate calculations in Minkowski space.
We briefly review common features and overlapping issues in hadron and flavor physics focussing on continuum QCD approaches to heavy bound states, their mass spectrum and weak decay constants in different strong interaction models.
A continuum approach to the three valence-quark bound-state problem in quantum field theory is used to perform a comparative study of the four lightest $(I=1/2,J^P = 1/2^pm)$ baryon isospin-doublets in order to elucidate their structural similarities
and differences. Such analyses predict the presence of nonpointlike, electromagnetically-active quark-quark (diquark) correlations within all baryons; and in these doublets, isoscalar-scalar, isovector-pseudovector, isoscalar-pseudoscalar, and vector diquarks can all play a role. In the two lightest $(1/2,1/2^+)$ doublets, however, scalar and pseudovector diquarks are overwhelmingly dominant. The associated rest-frame wave functions are largely $S$-wave in nature; and the first excited state in this $1/2^+$ channel has the appearance of a radial excitation of the ground state. The two lightest $(1/2,1/2^-)$ doublets fit a different picture: accurate estimates of their masses are obtained by retaining only pseudovector diquarks; in their rest frames, the amplitudes describing their dressed-quark cores contain roughly equal fractions of even- and odd-parity diquarks; and the associated wave functions are predominantly $P$-wave in nature, but possess measurable $S$-wave components. Moreover, the first excited state in each negative-parity channel has little of the appearance of a radial excitation. In quantum field theory, all differences between positive- and negative-parity channels must owe to chiral symmetry breaking, which is overwhelmingly dynamical in the light-quark sector. Consequently, experiments that can validate the contrasts drawn herein between the structure of the four lightest $(1/2,1/2^pm)$ doublets will prove valuable in testing links between emergent mass generation and observable phenomena and, plausibly, thereby revealing dynamical features of confinement.
A symmetry-preserving treatment of a vector-vector contact interaction is used to study charmed heavy-light mesons. The contact interaction is a representation of nonperturbative kernels used in Dyson-Schwinger and Bethe-Salpeter equations of QCD. Th
e Dyson-Schwinger equation is solved for the $u,,d,,s$ and $c$ quark propagators and the bound-state Bethe-Salpeter amplitudes respecting spacetime-translation invariance and the Ward-Green-Takahashi identities associated with global symmetries of QCD are obtained to calculate masses and electroweak decay constants of the pseudoscalar $pi,,K$, $D$ and $D_s$ and vector $rho$, $K^*$, $D^*$, and $D^*_s$ mesons. The predictions of the model are in good agreement with available experimental and lattice QCD data.
We compute couplings between the $rho$-meson and $D$- and $D^ast$-mesons - $D^{(ast)}rho D^{(ast)}$ - that are relevant to phenomenological meson-exchange models used to analyse nucleon-$D$-meson scattering and explore the possibility of exotic charm
ed nuclei. Our framework is built from elements constrained by Dyson-Schwinger equation studies in QCD, and therefore expresses a consistent, simultaneous description of light- and heavy-quarks and the states they constitute, We find that all interactions, including the three independent $D^{ast} rho ,D^{ast}$ couplings, differ markedly amongst themselves in strength and also in range, as measured by their evolution with $rho$-meson virtuality. As a consequence, it appears that no single coupling strength or parametrization can realistically be employed in the study of interactions between $D^{(ast)}$-mesons and matter.
We highlight Hermiticity issues in bound-state equations whose kernels are subject to a highly asymmetric mass and momentum distribution and whose eigenvalue spectrum becomes complex for radially excited states. We trace back the presence of imaginar
y components in the eigenvalues and wave functions to truncation artifacts and suggest how they can be eliminated in the case of charmed mesons. The solutions of the gap equation in the complex plane, which play a crucial role in the analytic structure of the Bethe-Salpeter kernel, are discussed for several interaction models and qualitatively and quantitatively compared to analytic continuations by means of complex-conjugate pole models fitted to real solutions.
Amongst the bound states produced by the strong interaction, radially excited meson and nucleon states offer an important phenomenological window into the long-range behavior of the coupling constant in Quantum Chromodynamics. We here report on some
technical details related to the computation of the bound states eigenvalue spectrum in the framework of Bethe-Salpeter and Faddeev equations.
