Vector mesons as dynamical resonances in the Bethe-Salpeter framework

Abstract

We present the first dynamical calculation of the $\rho$-meson as a resonance in the Dyson-Schwinger/Bethe-Salpeter framework by including explicit two-pion exchange in addition to the t-channel one-gluon exchange of rainbow-ladder in the interaction kernel. The width is determined from the imaginary part of the resonance pole and is generated by the singularity structure of the integrand, treated by means of suitable path deformations. We find the resonant mass and width to be $640$ MeV and $100$ MeV respectively, corresponding to a coupling constant $g_{\rho\pi\pi}=5.7$; repulsive corrections beyond rainbow-ladder are known to bring these in alignment with experiment. Furthermore we present the dependence of these parameters on the pion mass and compare with results from lattice QCD.