Accounting for the analytical properties of the quark propagator from Dyson-Schwinger equation

Abstract

An approach based on combined solutions of the Bethe-Salpeter (BS) and Dyson-Schwinger (DS) equations within the ladder-rainbow approximation in the presence of singularities is proposed to describe the meson spectrum as quark antiquark bound states. We consistently implement into the BS equation the quark propagator functions from the DS equation, with and without pole-like singularities, and show that, by knowing the precise positions of the poles and their residues, one is able to develop reliable methods of obtaining finite interaction BS kernels and to solve the BS equation numerically. We show that, for bound states with masses $M<1$ GeV, there are no singularities in the propagator functions when employing the infrared part of the Maris-Tandy kernel in truncated BS-DS equations. For $M>1$ GeV, however, the propagator functions reveal pole-like structures. Consequently, for each type of mesons (unflavored, strange and charmed) we analyze the relevant intervals of $M$ where the pole-like singularities of the corresponding quark propagator influence the solution of the BS equation and develop a framework within which they can be consistently accounted for. The BS equation is solved for pseudo-scalar and vector mesons. Results are in a good agreement with experimental data. Our analysis is directly related to the future physics programme at FAIR with respect to open charm degrees of freedom.

28 pages, 4 figures, 3 tables. arXiv admin note: text overlap with arXiv:1312.2721

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• Hadron Properties and Dyson-Schwinger Equations
• Vector meson form factors and their quark-mass dependence
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Cited by in corpus (3)

• Masses of J^PC =1^-+ exotic quarkonia in a Bethe-Salpeter-equation approach
• Mass spectrum of pseudo-scalar glueballs from a Bethe-Salpeter approach with the rainbow-ladder truncation
• The analytic structure of the Landau gauge quark propagator from Padé analysis