Quark spectral functions from spectra of mesons and vice versa

Abstract

We extract the spectral function of quarks using the QCD functional formalism.The reliability of approximations is controlled by the masses and decays of pseudoscalar mesons. For light quarks, we select the pion; for charm quarks, we choose the ground and excited states of the $\eta_c$ meson. To this end, we solved the ladder-rainbow approximation of the spectral Dyson-Schwinger equations for quarks coupled to the Bethe-Salpeter equation for the pion and pseudoscalar charmonia. The obtained dynamical charm mass function varies from 1 to 1.5 GeV in the timelike domain, which is significant for narrow charmonium states. This yields a notable response in the bound state spectrum. We obtained purely continuous spectral functions and discussed their connection with confinement.