Unquenching the quark-antiquark Green's function

摘要

We propose a nonperturbative resummation scheme for the four-point connected quark-antiquark Green's function G(4) that shows how the Bethe-Salpeter equation may be "unquenched" with respect to quark-antiquark loops. This mechanism allows to dynamically account for hadronic meson decays and multiquark structures whilst respecting the underlying symmetries. An initial approximation to the four-point Schwinger-Dyson equation - suitable for phenomenological application - is examined numerically in a couple of aspects. It is demonstrated that this approximation explicitly maintains the correct asymptotic limits and contains the physical resonance structures in the near timelike region in the quark-antiquark channel.