# Theta dependence of the vacuum energy density in chiral effective Lagrangian models at finite temperature, above $T_c$

## TL;DR

This paper investigates how the QCD vacuum energy density's dependence on the parameter theta changes at finite temperature above the chiral transition, using two effective models that incorporate the U(1) axial anomaly.

## Contribution

It extends previous zero-temperature studies by analyzing theta dependence of vacuum energy density above T_c with two effective Lagrangian models.

## Key findings

- Derived expressions for topological susceptibility and second cumulant.
- Compared theta dependence of vacuum energy in two models.
- Provided insights into the behavior of QCD vacuum at finite temperature.

## Abstract

In this work, extending a previous study at zero temperature ($T=0$), we perform a systematic study of the modifications to the QCD vacuum energy density $\epsilon_{vac}$ in the finite-temperature case, above the chiral transition at $T_c$, caused by a nonzero value of the parameter $\theta$, using two different effective Lagrangian models which implement the $U(1)$ axial anomaly of the fundamental theory and which are both well defined also above $T_c$. In particular, we derive (and critically compare) the expressions for the topological susceptibility $\chi$ and for the second cumulant $c_4$ starting from the $\theta$ dependence of $\epsilon_{vac}(\theta)$ in the two models.