Exploring the quark-gluon content of hadrons: from mesons to nuclear matters

Abstract

Even though Quantum Chromodynamics (QCD) was formulated over three decades ago, it poses enormous challenges for describing the properties of hadrons from the underlying quark-gluon degrees of freedom. Moreover, the problem of describing the nuclear force from its quark-gluon origin is still open. While a direct solution of QCD to describe the hadrons and nuclear force is not possible at this time, we explore a variety of developed approaches ranging from phenomenology to first principle calculations at one or other level of approximation in linking the nuclear force to QCD. The Dyson Schwinger formulation (DSE) of coupled integral equations for the QCD Green’s functions allows a non-perturbative approach to describe hadronic properties, starting from the level of QCD n-point functions. A significant approx- imation in this method is the employment of a finite truncation of the system of DSEs, that might distort the physical picture. In this work we explore the effects of including a more complete truncation of the quark-gluon vertex function on the resulting solutions for the quark 2-point functions as well as the pseudoscalar and vector meson masses. The exploration showed strong indications of possibly large contributions from the explicit inclusion of the gluon 3- and 4-point functions that are omitted in this and previous analyses. We then explore the possibility of ex- trapolating state of the art lattice QCD calculations of nucleon form factors to the physical regime using phenomenological models of nucleon structure. Finally, we further developed the Quark Meson Coupling model for describing atomic nuclei and nuclear matter, where the quark-gluon structure of nucleons is modeled by the MIT bag model and the nucleon many body interaction is mediated by the exchange of scalar and vector mesons. This approach allows us to formulate a fully relativistic theory, which can be expanded in the nonrelativistic limit to repro- duce the well known phenomenological Skyrme-type interaction density functional, thus providing a direct link to well modeled nuclear forces. Moreover, it allows for a derivation of the equation of state for cold uniform dense nuclear matter for application to calculations of the properties of neutron stars.