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Based upon a combined formalism of Schwinger-Dyson and Bethe-Salpeter equations in quantum chromodynamics (QCD), we propose a QCD kindred algebraic model for the dressed quark propagator, for the Bethe-Salpeter amplitude of the pion and the electromagnetic quark-photon interaction vertex. We then compute the $\gamma^{*}\pi^0\gamma$ transition form factor $G^{\gamma^{*}\pi^0\gamma}(Q^2)$ for a wide range of photon momentum transfer squared $Q^2$. The quark propagator is expanded out in its perturbative functional form but with dynamically generated dressed quark mass. It has complex conjugate pole singularities in the complex-momentum plane which is motivated by the solution of the quark gap equation with rainbow-ladder truncation of the infinite set of Schwinger-Dyson equations. This complex pole singularity structure of the quark propagator can be associated with a signal of confinement which prevents quarks to become stable asymptotic states. The Bethe-Salpeter amplitude is expressed without a spectral density function, which encapsulate its low and large momentum behaviour. The QCD evolution of the distribution amplitude is also incorporated into our model through the direct implementation of Efremov-Radyushkin-Brodsky-Lepage evolution equations. We include the effects of the quark anomalous magnetic moment in the description of the quark-photon vertex whose infrared enhancement is known to dictate hadronic properties. Once the QCD kindred model is constructed, we calculate the form factor $G^{\gamma^{*}\pi^0\gamma}(Q^2)$ and find it consistent with direct QCD-based studies as well as most available experimental data. It slightly exceeds the conformal limit for large $Q^2$ which might be attributed to the scaling violations in QCD. The associated interaction radius and neutral pion decay width turn out to be compatible with experimental data., Comment: 11 pages, 4 figures

The $\mathcal{V}\to\mathcal{P}\gamma$ and $\eta(\eta^\prime) \to \gamma\gamma$ decays are evaluated within a Dyson-Schwinger and Bethe-Salpeter equations framework (here $\mathcal{V}=\{\rho^{\pm},K^{\star\pm},\phi\}$ and $\mathcal{P}=\{\pi^{\pm},K^{\pm},\eta,\eta^{\prime}\}$). The so-called impulse approximation (IA) is employed in the computation of the decay constants involved and decay widths, and so in the estimation of the associated charge and interaction radii. For their part, the required propagators and vertices stem from a contact interaction model, embedded within a beyond rainbow-ladder (RL) truncation that accounts for the typical ladder exchanges, quark anomalous magnetic moment, as well as the non-Abelian anomaly. While the examined transitions produce decay widths plainly compatible with the available experimental data, those processes involving the $\eta-\eta'$ mesons highlight the incompleteness of the IA when considering beyond RL effects in the interaction kernels., Comment: 9 pages

Given the unique role played by the gravitational form factors (GFFs) in unraveling the internal mechanics of hadrons, we examine the GFFs of ground state pseudoscalar mesons $\pi$, $\eta_c$, $\eta_b$ and the hypothetical {\em strangeonium} $\eta_s(s\bar{s})$. We adopt the coupled framework of Dyson-Schwinger and Bethe-Salpeter equations within a contact interaction, and employ a novel approach to the dressed amputated meson-meson scattering amplitude which makes connection with the energy-momentum tensor and with the GFFs. The resulting GFFs fulfill the anticipated symmetry constraints. The corresponding charge and mass radii and the $D-$term are also computed. We show that the $D-$term for the pseudoscalar mesons is bounded within the $(-1, -1/3)$ range; these bounds correspond to the massless (chiral limit) and infinitely massive cases, respectively. Considering the current interest in the GFFs, understanding the \textit{D}-term of pseudoscalar mesons and their GFFs can provide an important first step for future endeavors in the field., Comment: 10 pages, 5 figures

In this work, the $\gamma\to3\pi$ form factor is calculated within the Dyson-Schwinger equations framework using a contact interaction model within the so-called modified rainbow ladder truncation. The present calculation takes into account the pseudovector component in the pion Bethe-Salpeter amplitude (BSA) and $\pi-\pi$ scattering effects, producing a $\gamma\to3\pi$ anomaly which is $1+6\mathcal{R}_\pi^2$ larger than the low energy prediction. Here $\mathcal{R_\pi}$ is the relative ratio of the pseudovector and pseudoscalar components in the pion BSA; with our parameters input, this correction raises the $\gamma\to3\pi$ anomaly by around $10\%$. The main outcome of this work is the unveiling of the origin of such correction, which could be a possible explanation of the discrepancy between the existing experimental data and the low energy prediction. Moreover, it is highlighted how the magnitude of the anomaly is affected in effective theories that require an irremovable ultraviolet cutoff. We find that for both the anomalous processes $\pi\to2\gamma$ and $\gamma\to 3\pi$, the missing contribution to the anomaly can be compensated by the additional structures related with the quark anomalous magnetic moment., Comment: 10 pages, 3 figures, references added

In the presence of a momentum cutoff, effective theories seem unable to faithfully reproduce the so called chiral anomaly in the Standard Model. A novel prospect to overcome this related issue is discussed herein via the calculation of the $\gamma^{*}\pi^0\gamma$ transition form factor, $G^{\gamma^* \pi^0 \gamma}(Q^2)$, whose normalization is intimately connected with the chiral anomaly and dynamical chiral symmetry breaking (DCSB). To compute such transition, we employ contact interaction model of Quantum Chromodynamics (QCD) under a modified rainbow ladder truncation, which automatically generates a quark anomalous magnetic moment term, weighted by a strenght parameter $\xi$. This term, whose origin is also connected with DCSB, is interpreted as an additional interaction that mimics the complex dynamics beyond the cutoff. By fixing $\xi$ to produce the value of $G^{\gamma^* \pi^0 \gamma}(0)$ dictated by the chiral anomaly, the computed transition form factor, as well as the interaction radius and neutral pion decay width, turn out to be comparable with QCD-based studies and experimental data., Comment: 9 pages, 2 figures

We calculate the spectrum of $B_c$ mesons using a non-relativistic quark potential model. Using the calculated wave functions, we compute the radiative widths of $B_c$ excited states. The strong decay widths are calculated in a modified $^3P_0$ model, assuming harmonic oscillator wave functions. The hadronic transition rates of $B_c$ mesons are calculated using the Kuang-Yan approach. These results are used to determine branching ratios of possible decay channels of several $B_c$ excited states. Calculated branching ratios are then combined with production cross section of $B_c$ states at the LHC to suggest strategies to find missing excited states of $B_c$ mesons., Comment: 31 pages, 2 figures

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 $E1$, $M1$ 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., Comment: 15 pages, 11 Tables

In this work, we investigate how the details of the quark-gluon interaction vertex affect the quantitative description of chiral symmetry breaking through the gap equation for quarks. We start from two gluon propagator models widely used in literature and constructed in direct connection with our gradually improved understanding of infrared quantum chromodynamics coupled with its exact one-loop limit. The gap equation is then solved by employing a variety of vertex \emph{Ans\"atze}, which have been constructed in order to implement some of the key aspects of quantum chromodynamics, namely, multiplicative renormalizability of the quark propagator, gauge invariance, matching with perturbation theory in the weak coupling regime, independence from unphysical kinematic singularities as well as manifestly correct transformation properties under charge conjugation and parity operations. On general grounds, all truncation schemes exhibit the same qualitative and quantitative pattern of chiral symmetry breaking, ensuring the overall robustness of this approach and its potentially reliable description of the hadron spectrum and properties., Comment: 14 pages. Text matching the published version in Physical Review D

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 "$^3P_0$" 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., Comment: 36 pages, 3 figures

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 M1 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 Schrodinger 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 $\Upsilon(10860)$, $\Upsilon(11020)$, and $Y_b(10890)$ mesons by comparing their experimental masses and decay widths with our results., Comment: 20 pages,1 figures

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 Schrodinger 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., Comment: 22 pages, 4 figures