Nonrelativistic meson masses from the Curci-Ferrari model

Abstract: We study the mass spectrum of nonrelativistic mesons composed of charm and bottom quarks within the framework of the Curci-Ferrari model in the Landau gauge, focusing on the influence of the gluon mass on our results. We derive the Hamiltonian from the scattering amplitude of a single massive gluon exchange. By incorporating a confining Cornell potential we solve the Schr\"odinger equation for the dominant terms of the Hamiltonian, which include the kinetic energy and a Yukawa-type potential. Corrections to the energy are then introduced perturbatively. By studying the parameter space of the model we fit the experimental mass spectrum of charmonium, bottomonium and charm-bottom mesons. From the five parameters of our approach, we allow the gluon mass and the gauge coupling to run with the energy scale according to the ultraviolet one-loop renormalization flows, computed in [1]. Our results show very good agreement with the data, suggesting that a nonvanishing gluon mass provides a better description of the spectrum of heavy mesons than the massless case.