Can instantons saturate the large mass of the $\eta'$ meson in the chiral limit?

Abstract

Using the trace anomaly and low energy relations, as well as Witten-Veneziano formula for the mass of the $\eta'$ meson, the chiral topology of the QCD nonperturbative instanton vacuum has been numerically evaluated. Our formalism makes it possible to express the topological susceptibility and the mass of the $\eta'$ meson as a functions of the instanton number density in the chiral limit. We have explicitly shown that the topological susceptibility in this case is approximately one fours and one half of its phenomenological value at instanton number densities in the chiral limit, 0.5 fm^{-4} and 1.0 fm^{-4}, respectively. Thus the instanton contributions substantially underestimate the mass of the $\eta'$ meson which still remains large in the chiral limit. With the help of the above-mentioned Witten-Veneziano formula, we derived an absolute lower bounds for the pion decay constant and the mass of the $\eta'$ meson in the chiral limit.