Study of the theta dependence of the vacuum energy density in chiral effective Lagrangian models at zero temperature

TL;DR

This paper investigates how a small non-zero theta parameter affects the vacuum energy density in QCD using effective models, deriving expressions for topological susceptibility and cumulants, and comparing results with lattice data.

Contribution

It provides a systematic analysis of theta dependence in effective Lagrangian models, including derivations and numerical comparisons with lattice results.

Findings

Derived expressions for topological susceptibility and cumulants in various models.

Numerical results show consistency with lattice data.

Compared model predictions with Chiral Effective Lagrangian and lattice results.

Abstract

We perform a systematic study of the modifications to the QCD vacuum energy density $\epsilon_{vac}$ in the zero-temperature case ($T=0$) caused by a small, but non-zero, value of the parameter $\theta$, using different effective Lagrangian models which include the flavour-singlet meson field and implement the $U(1)$ axial anomaly of the fundamental theory. In particular, we derive 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 various models that we have considered. Moreover, we evaluate numerically our results, so as to compare them with each other, with the predictions of the Chiral Effective Lagrangian, and, finally, also with the available lattice data.