Analytic Quest for Confining Interaction Kernels in Instantaneous Bethe-Salpeter Equations

The Salpeter equation, a standard tool in hadron physics, constitutes a well-defined three-dimensional approximation to the Bethe-Salpeter formalism for the description of bound states within quantum field theories. However, if confinement is implemented in a too careless manner, the Salpeter equation might predict unstable states where only truly bound states are expected. A systematic spectral analysis of the Salpeter equation might serve to single out those Bethe-Salpeter interaction kernels which indeed yield stable bound states, with associated energy eigenvalues belonging to a real discrete spectrum bounded from below.Comment: contributed to Quark Confinement and the Hadron Spectrum IX - QCHS IX (30 August - 3 September 2010, Madrid, Spain), to appear in the proceeding

Instantaneous Bethe-Salpeter Approach to Pseudoscalar Mesons

Light pseudoscalar mesons are Janus-type particles: Within quantum chromodynamics, they must be described as bound states of its fundamental degrees of freedom and as the (pseudo-) Goldstone bosons of its spontaneously broken chiral symmetry. This janiform nature of pions and kaons may be easily accommodated by the Bethe-Salpeter formalism in its instantaneous limit: Starting from the general behaviour of the Bethe-Salpeter solutions for light pseudoscalar mesons at large Euclidean momenta, we provide the exact relationship between the solutions of our bound-state equation and the underlying interactions, boiled down to a configuration-space potential depending on the interquark distance: the potential exhibits a logarithmically softened Coulomb singularity at the origin and, at large interquark distances, rises beyond bounds for massless quarks but approaches a non-positive finite limit for too heavy quarks.Comment: 2 pages, 2 figures, contributed to the European Physical Society Conference on High Energy Physics - EPS-HEP2013, 18-24 July 2013, Stockholm, Swede

Simplified Bethe-Salpeter Description of Basic Pseudoscalar-Meson Features

We assess a description of pseudoscalar mesons as pseudo-Goldstone bosons by its compatibility with some Gell-Mann-Oakes-Renner-type relation.Comment: 5 pages, 1 figure, contributed to "QCD@Work 2018 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (25 - 28 June 2018, Matera, Italy

Goldstone-Type Pseudoscalar Mesons: Instantaneous Bethe-Salpeter Models

A nontrivial instantaneous variant of the Bethe-Salpeter formalism allows us to discuss massless pseudoscalar mesons from a configuration-space-potential point of view.Comment: 6 pages, 5 figures, contributed to "Quark Confinement and the Hadron Spectrum XII" (28 August - 3 September 2016, Thessaloniki, Greece

Janus-Facedness of the Pion: Analytic Instantaneous Bethe-Salpeter Models

Inversion enables the construction of interaction potentials underlying - under fortunate circumstances even analytic - instantaneous Bethe-Salpeter descriptions of all lightest pseudoscalar mesons as quark-antiquark bound states of Goldstone-boson nature.Comment: 5 pages, 3 figures, contributed to "QCD@Work 2016 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (27 - 30 June 2016, Martina Franca, Italy

On properties of the exotic hadrons from QCD sum rules

We discuss the specific features of extracting properties of the exotic polyquark hadrons (tetraquarks, pentaquarks) compared to the usual hadrons by the QCD sum-rule approach. In the case of the ordinary hadrons, already the one-loop leading-order correlation functions provide the bulk of the hadron observables, e.g., of the form factor; inclusion of radiative corrections modifies already nonzero one-loop contributions. In the case of an exotic hadron, the situation is qualitatively different: discussing strong decays of an exotic tetraquark meson, which provide the main contribution to its width, we show that the disconnected leading-order diagrams are not related to the tetraquark properties. For a proper description of the tetraquark decay width, it is mandatory to calculate specific radiative corrections which generate the connected diagrams.Comment: 6 pages, 3 figures, talk presented at "QCD@Work 2016 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (27 - 30 June 2016, Martina Franca, Italy

Resolving the Puzzle of the Pion-Photon Transition Form Factor

We investigate the form factors for pseudoscalar-meson-photon transitions by means of dispersive QCD sum rules and demonstrate that most of the measurements done so far (in particular, those by BaBar for $\eta,$ $\eta',$ and $\eta_c$ and those by Belle for $\pi^0$) are, on the one hand, compatible with each other and with the saturation required by factorization theorems obtained from perturbative QCD and, on the other hand, give a hint that saturation is effective already at relatively low momentum transfers $Q^2;$ this hypothesis is supported by experimental data for the charged-pion elastic form factor available in the range Q^2\approx2-4\;\{GeV}^2. The only exception are the BaBar results for the $\pi^0\gamma$ transition form factor, which do not fit into such picture. We point out that results expected from SHMS at JLab on the pion elastic form factor in the region Q^2\approx5-8\;\{GeV}^2 will provide the ultimate test of saturation and factorization and strongly impact our general view of the form factors up to infinitely large $Q^2.$Comment: 7 pages, 4 figures, talk presented at the European Physical Society Conference on High Energy Physics - EPS-HEP2013, 18-24 July 2013, Stockholm, Swede