Analytical properties of the quark propagator from truncated DysonSchwinger equation in complex Euclidean space
Analytical properties of the quark propagator from truncated DysonSchwinger equation in complex Euclidean space
Dorkin, S. M.; Kaptari, L. P.; Hilger, T.; Kämpfer, B.
In view of the mass spectrum of heavy mesons in vacuum the analytical properties of the solutions of the truncated DysonSchwinger equatio for the quark propagator within the rainbow approximation are analysed in some detail. In Euclidean space, the quark propagator is not an analytical function possessing, in general, an infinite number of singularities (poles) which hamper to solve the BetheSalpeter equation. However, for light mesons (with masses M_{q\bar q} <= 1 GeV) all singularities are located outside the region within which the BetheSalpeter equation is defined. With an increase of the considered meson masses this region enlarges and already at masses >= 1 GeV, the poles of propagators of u,d and s quarks fall within the integration domain of the BetheSalpeter equation. Nevertheless, it is established that for meson masses up to M_{q\bar q}~=3 GeV only the first, mutually complex conjugated, poles contribute to the solution. We argue that, by knowing the position of the poles and their residues, a reliable parametrisation of the quark propagators can be found and used in numerical procedures of solving the BetheSalpeter equation. Our analysis is directly related to the future physics programme at FAIR with respect to open charm degrees of freedom.

Contribution to WWW
http://arxiv.org/abs/1312.2721 
Physical Review C 89(2014), 034005
DOI: 10.1103/PhysRevC.89.034005
Cited 36 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ19538
Publ.Id: 19538