Hadronic resonances from the 4PI effective action of QCD

Abstract

We discuss the 4PI effective action as a tool to study resonances in QCD. To this end, we present the 4PI effective action of QCD in linear covariant gauges up to four loops and derive from it the kernels for two-body bound states, using mesons as an example. The emergence of resonances via decay channels is built into the formalism at the level of the four-point functions, and we employ an on-shell decomposition of its physical channels to arrive at a diagrammatic representation for physical two-body decays within the Bethe-Salpeter equation framework. We apply this formalism to the $\rho$, $K^*$ and $\phi$ mesons and extract their widths.