Accounting for the analytical properties of the quark propagator from DysonSchwinger equation
Accounting for the analytical properties of the quark propagator from DysonSchwinger equation
Dorkin, S. M.; Kaptari, L. P.; Kämpfer, B.
An approach based on combined solutions of the BetheSalpeter (BS) and DysonSchwinger (DS) equations within the ladderrainbow approximation in the presence of singularities is proposed to describe the meson spectrum as quarkantiquark bound states. We consistently implement into the BS equation the quark propagator functions from the DS equation, with and without polelike 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 MarisTandy kernel in truncated BSDS equations. For M > 1 GeV, however, the propagator functions reveal polelike structures. Consequently, for each type of mesons (unflavored, strange and charmed) we analyze the relevant intervals of M where the polelike 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 pseudoscalar 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.

Contribution to WWW
arXiv:1412.3345 [hepph]: http://arxiv.org/abs/1412.3345 
Physical Review C 91(2015), 055201
DOI: 10.1103/PhysRevC.91.055201
Cited 23 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ21381
Publ.Id: 21381