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We present a unified Dyson-Schwinger equation treatment of static and electromagnetic properties of pseudoscalar and vector mesons, and scalar and axial-vector diquark correlations, based upon a vector-vector contact-interaction. A basic motivation for this study is the need to document a comparison between the electromagnetic form factors of mesons and those diquarks which play a material role in nucleon structure. This is an important step toward a unified description of meson and baryon form factors based on a single interaction. A notable result, therefore, is the large degree of similarity between related meson and diquark form factors. The simplicity of the interaction enables computation of the form factors at arbitrarily-large spacelike-Q^2, which enables us to expose a zero in the rho-meson electric form factor at z_Q^rho ~ Sqrt[6] m_rho. Notably, r_rho*z_Q^rho ~ r_D*z_Q^D, where r_rho, r_D are, respectively, the electric radii of the rho-meson and deuteron.
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The purpose of the present study was to explore the possibility of accommodating the $d^*(2380)$ and its flavor SU(3) partners in a diquark model. Proposing that $d^*(2380)$ is composed of three vector diquarks, its mass is calculated by use of an effective Hamiltonian approach and its decay width is estimated by considering the effects of quark tunneling from one diquark to the others and the decays of the subsequent two-baryon bound state. Both the obtained mass and decay width of $d^*(2380)$ are in agreement with the experimental data, with the unexpected narrow decay width being naturally explained by the large tunneling suppression of a quark between a pair of diquarks. The masses and decay widths of the flavor SU(3) partners of $d^*(2380)$ are also predicated within the same diquark scenario.
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. The 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 charmed 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 review the recent results of heavy meson diffusion in thermal hadronic matter. The interactions of D and B-bar mesons with other hadrons (light mesons and baryons) are extracted from effective field theories based on chiral and heavy-quark symmetries. When these guiding principles are combined with exact unitarity, physical values of the cross sections are obtained. These cross sections (which contain resonant contributions) are used to calculate the drag and diffusion coefficients of heavy mesons immersed in a thermal and dense medium. The transport coefficients are computed using a Fokker-Planck reduction of the Boltzmann equation.
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 imaginary 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.
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