By comparing successful quark-gluon vertex interaction models with the corresponding interaction extracted from lattice-QCD data on the quarks propagator, we identify common qualitative features which could be important to tune future interaction mod
els beyond the rainbow ladder approximation. Clearly, a quantitative comparison is conceptually not simple, but qualitatively the results suggest that a realistic interaction should be relatively broad with a strong support at about $0.4-0.6$~GeV and infrared-finite.
We study ground and radial excitations of flavor singlet and flavored pseudoscalar mesons within the framework of the rainbow-ladder truncation using an infrared massive and finite interaction in agreement with recent results for the gluon-dressing f
unction from lattice QCD and Dyson-Schwinger equations. Whereas the ground-state masses and decay constants of the light mesons as well as charmonia are well described, we confirm previous observations that this truncation is inadequate to provide realistic predictions for the spectrum of excited and exotic states. Moreover, we find a complex conjugate pair of eigenvalues for the excited $D_{(s)}$ mesons, which indicates a non-Hermiticity of the interaction kernel in the case of heavy-light systems and the present truncation. Nevertheless, limiting ourselves to the leading contributions of the Bethe-Salpeter amplitudes, we find a reasonable description of the charmed ground states and their respective decay constants.
The elastic and $gamma to pi$ transition form factors of the pion along with its usual static observables are calculated within a light-front field approach to the constituent quark model. The focus of this exercise in a simple model is on a unified
description of all observables with one singly parametrized light-front wave function to detect possible discrepancies in experimental data, in particular the contentious large momentum-squared data on the transition factor as reported by BaBar and Belle. We also discuss the relation of a small to vanishing pion charge radius with an almost constant pion distribution amplitude and compare our results with those obtained in a holographic light-front model.
We give a snapshot of recent progress in solving the Dyson-Schwinger equation with a beyond rainbow-ladder ansatz for the dressed quark-gluon vertex which includes ghost contributions. We discuss the motivations for this approach with regard to heavy
-flavored bound states and form factors and briefly describe future steps to be taken.
We investigate the dressed quark-gluon vertex combining two established non-perturbative approaches to QCD: the Dyson-Schwinger equation (DSE) for the quark propagator and lattice-regularized simulations for the quark, gluon and ghost propagators. Th
e vertex is modeled using a generalized Ball-Chiu ansatz parameterized by a single form factor $tilde X_0$ which effectively represents the quark-ghost scattering kernel. The solution space of the DSE inversion for $tilde X_0$ is highly degenerate, which can be dealt with by a numerical regularization scheme. We consider two possibilities: (i) linear regularization and (ii) the Maximum Entropy Method. These two numerical approaches yield compatible $tilde X_0$ functions for the range of momenta where lattice data is available and feature a strong enhancement of the generalized Ball-Chiu vertex for momenta below 1 GeV. Our ansatz for the quark-gluon vertex is then used to solve the quark DSE which yields a mass function in good agreement with lattice simulations and thus provides adequate dynamical chiral symmetry breaking.
We study consistently the pions static observables and the elastic and gamma*gamma -> pi^0 transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adju
sted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the gamma*gamma -> pi^0 form factor at large q^2, yet the BaBar data on this transition form factor resists a sensible comparison. We relax the initial constraint on the bound-state wave function and show the BaBar data can partially be accommodated. This, however, comes at the cost of a hard elastic form factor not in agreement with experiment. Moreover, the pion charge radius is about 40% smaller than its experimentally determined value. It is argued that a decreasing charge radius produces an ever harder form factor with a bound-state amplitude difficultly reconcilable with soft QCD. We also discuss why vector dominance type models for the photon-quark vertex, based on analyticity and crossing symmetry, are unlikely to reproduce the litigious transition form factor data.
After a brief review of B_s^0 - bar B_s^0 oscillations, we discuss the weak decays B_s^0 -> J/psiphi and B_s^0 -> J/psi f_0(980) and the ratio R_{f_0/phi} of their decay rates in the light of recent measurements by the LHCb, D0 and CDF Collaborations
. We point out that the experimental values for R_{f_0/phi} impose tight limits on new physics contributions to both decay channels.
We report on an updated Paris nucleon-antinucleon optical potential. The long- and intermediate-range real parts are obtained by G-parity transformation of the Paris nucleon-nucleon potential based on a theoretical dispersion-relation treatment of th
e correlated and uncorrelated two-pion exchange. The short-range imaginary potential parametrization results from the calculation of the nucleon-antinucleon annihilation box diagram into two mesons with a nucleon-antinucleon intermediate state in the crossed channel. The parametrized real and imaginary short range parts are determined by fitting not only the existing experimental data included in the 1999 version of the Paris nucleon-antinucleon potential, but also the recent antiprotonic-hydrogen data and antineutron-proton total cross sections. The description of these new observables is improved. Only this readjusted potential generates an isospin zero 1S0, 52 MeV broad quasibound state at 4.8 MeV below the threshold. Recent BES data on J/psi decays could support the existence of such a state.
A phenomenological analysis of the scalar meson f0(980) is performed that relies on the quasi-two body decays D and Ds -> f0(980)P, with P=pi, K. The two-body branching ratios are deduced from experimental data on D or Ds -> pi pi pi, K Kbar pi and f
rom the f0(980) -> pi+ pi- and f0(980) -> K+ K- branching fractions. Within a covariant quark model, the scalar form factors F0(q2) for the transitions D and Ds -> f0(980) are computed. The weak D decay amplitudes, in which these form factors enter, are obtained in the naive factorization approach assuming a quark-antiquark state for the scalar and pseudoscalar mesons. They allow to extract information on the f0(980) wave function in terms of u-ubar, d-dbar and s-sbar pairs as well as on the mixing angle between the strange and non-strange components. The weak transition form factors are modeled by the one-loop triangular diagram using two different relativistic approaches: covariant light-front dynamics and dispersion relations. We use the information found on the f0(980) structure to evaluate the scalar and vector form factors in the transitions D and Ds -> f0(980), as well as to make predictions for B and Bs -> f0(980), for the entire kinematically allowed momentum range of q2.
We propose a model for $D^+ to pi^+ pi^- pi^+$ decays following experimental results which indicate that the two-pion interaction in the $S$-wave is dominated by the scalar resonances $f_0(600)/sigma$ and $f_0(980)$. The weak decay amplitude for $D^+
to R pi^+$, where $R$ is a resonance that subsequently decays into $pi^+pi^-$, is constructed in a factorization approach. In the $S$-wave, we implement the strong decay $Rto pi^-pi^+$ by means of a scalar form factor. This provides a unitary description of the pion-pion interaction in the entire kinematically allowed mass range $m_{pipi}^2$ from threshold to about 3 GeV$^2$. In order to reproduce the experimental Dalitz plot for $Dppp$, we include contributions beyond the $S$-wave. For the $P$-wave, dominated by the $rho(770)^0$, we use a Breit-Wigner description. Higher waves are accounted for by using the usual isobar prescription for the $f_2(1270)$ and $rho(1450)^0$. The major achievement is a good reproduction of the experimental $m_{pipi}^2$ distribution, and of the partial as well as the total $Dppp$ branching ratios. Our values are generally smaller than the experimental ones. We discuss this shortcoming and, as a byproduct, we predict a value for the poorly known $Dto sigma$ transition form factor at $q^2=m_pi^2$.
