Rho-meson, Bethe-Salpeter equation, and the far infrared

Martina Blank, A. Krassnigg, Axel Maas

Published 2010-07-22, updated 2011-02-09Version 2

The Bethe-Salpeter equation in QCD connects the gauge-dependent gluon and quark degrees of freedom with the gauge-invariant properties of mesons. We study the rho meson mass and decay constant for various versions of the gauge-dependent input functions discussed in the literature, which start to differ generically below the hadronic scale, and show qualitative different infrared behavior. We find that, once the gauge-dependent quark-gluon vertex is permitted to vary as well, the rho mass and decay constant is reproduced equally well for all forms investigated. A possible conclusion from this is that these $\rho$-meson properties are only sensitive to changes in the input at scales above a few hundred MeV.