Mass of the $η'$ meson in the chiral limit in the zero momentum modes enhancement quantum model of the QCD nonperturbative vacuum

Abstract

Using the trace anomaly and low energy relations, as well as the Witten-Veneziano formula for the mass of the $η'$ meson, we have developed a formalism which makes it possible to express the gluon condensate, the topological susceptibility and the mass of the $η'$ meson as a functions of the truly nonperturbative vacuum energy density which is one of the most important characteristics of the QCD true ground state. It was directly applied to the numerical evaluation of the chiral QCD vacuum topological structure within its quantum zero momentum modes enhancement model. A rather good agreement with phenomenological and experimental values of the above-mentioned quantities has been achieved. With the help of the Witten-Veneziano formula, we derived an absolute lower bounds for the pion decay constant and the mass of the $η'$ meson in the chiral limit. By introducing the most general parametrization of the gluon condensate, we also proposed how the correct $N_f$ (number of flavors) dependence of its phenomenologically extracted value could be restored.