Vector mesons as dynamical resonances in the Bethe-Salpeter framework

Understand

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.