Topological observables and $\theta$ dependence in high temperature QCD from lattice simulations

TL;DR

This study uses lattice QCD simulations with physical quark masses at high temperatures to analyze topological properties, the $ heta$ dependence, and the transition to dilute instanton gas behavior, providing new insights into QCD topology at finite temperature.

Contribution

First lattice QCD study to analyze topological observables and $ heta$ dependence at high temperatures with physical quark masses and multiple lattice spacings.

Findings

Topological susceptibility agrees across different definitions within errors.

Rapid crossover to dilute instanton gas behavior above 300 MeV.

First measurement of free energy as a function of $ heta$ at high T.

Abstract

We study topology in Quantum Chromodynamics at high temperatures by means of lattice calculations. Simulations are performed with $N_f=2+1+1$ Wilson twisted mass fermions at maximal twist with physical quark masses, and temperatures $T~\gtrsim~180$ MeV. The results obtained with three lattice spacings ranging between $0.057$ and $0.080$ fm are extrapolated to the continuum limit. We compare the results for the topological susceptibility obtained with the field-theoretic definition with those obtained from an observable constructed with the disconnected part of the chiral susceptibility, and we confirm their agreement -- within the largish errors -- on our range of temperatures. We also study the topological charge distribution, the next order cumulant $b_2$ and, for the first time, the Free Energy as a function of the $\theta$ angle. We find a rapid crossover to the Dilute Instanton Gas behaviour above $ T \simeq 300$ MeV for all the observables we have considered.