Parameter optimization for the latest quark-meson coupling energy-density functional

The quark-meson-coupling (QMC) model self-consistently relates the dynamics of the internal quark structure of a hadron to the relativistic mean fields arising in nuclear matter. It offers a natural explanation to some open questions in nuclear theory, including the origin of many-body nuclear forces and their saturation, the spin-orbit interaction, and properties of hadronic matter at a wide range of densities. The QMC energy density functionals QMC-I and $\mathrm{QMC}\ensuremath{\pi}$-I have been successfully applied to calculate ground state observables of finite nuclei in the Hartree-Fock $+$ BCS approximation, as well as to predict properties of dense nuclear matter and cold nonrotating neutron stars. Here we report the latest development of the model, $\mathrm{QMC}\ensuremath{\pi}$-II, which includes higher order terms in density in the expansion of the relativistic energy-density functional, as well as the self-interaction of the $\ensuremath{\sigma}$ meson. A derivative-free optimization algorithm has been employed to determine a new set of the model parameters and their statistics, including errors and correlations. $\mathrm{QMC}\ensuremath{\pi}$-II predictions for a wide range of properties of even-even nuclei across the nuclear chart, with fewer adjustable parameters, are comparable with other models. The nuclear incompressibility is significantly reduced in this version, leading to a description of giant monopole resonances which is consistent with experimental data.