Vector mesons as dynamical resonances in the Bethe-Salpeter framework

TL;DR

This paper models the rho meson as a resonance within the Dyson-Schwinger/Bethe-Salpeter framework, incorporating two-pion exchange to calculate its mass and width, and compares results with lattice QCD data.

Contribution

It introduces a dynamical calculation of the rho meson as a resonance including explicit two-pion exchange in the Bethe-Salpeter framework, extending previous rainbow-ladder approaches.

Findings

Resonant mass of 640 MeV and width of 100 MeV for the rho meson.

Coupling constant g_{ρππ} = 5.7 derived from the model.

Dependence of rho meson parameters on pion mass compared with lattice QCD results.

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.