Hadronic correlation functions in the random instanton-dyon ensemble

Abstract

It is known since the 1980s that the instanton-induced 't Hooft effective Lagrangian not only can solve the so-called $U(1)a$ problem, by making the ${\ensuremath{\eta}}^{\ensuremath{'}}$ meson heavy etc., but it can also lead to chiral symmetry breaking. In the 1990s it was demonstrated that, taken to higher orders, this Lagrangian correctly reproduces effective forces in a large set of hadronic channels, mesonic and baryonic ones. Recent progress in understanding gauge topology at finite temperatures is related with the so-called instanton-dyons, the constituents of the instantons. Some of them, called $L$-dyons, possess the antiperiodic fermionic zero modes, and thus form a new version of the 't Hooft effective Lagrangian. This paper is our first study of a wide set of hadronic correlation function. We found that, at the lowest temperatures at which this approach is expected to be applicable, those may be well compatible with what is known about them based on phenomenological and lattice studies, provided $L$ and $M$ type dyons are strongly correlated.