# Hadronic Correlation Functions in the Random Instanton-dyon Ensemble

## TL;DR

This paper investigates hadronic correlation functions within the instanton-dyon ensemble, showing compatibility with phenomenological and lattice data at low temperatures when certain dyon types are strongly correlated.

## Contribution

It is the first study of a broad set of hadronic correlation functions in the instanton-dyon framework, highlighting the importance of dyon correlations.

## Key findings

- Correlation functions align with phenomenological data at low temperatures.
- Strong correlations between L and M dyons are necessary for compatibility.
- The approach extends understanding of gauge topology effects on hadronic physics.

## Abstract

It is known since 1980's that the instanton-induced 't Hooft effective Lagrangian not only can solve the so called $U(1)a$ problem, by making the $\eta'$ meson heavy etc, but it can also lead to chiral symmetry breaking. In 1990's 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 {\em instanton-dyons}, the constituents of the instantons. Some of them, called $L$-dyons, possess the anti-periodic 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.