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

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.

23 pages; revised version

References in corpus (1)

• $X$ Meson aka ${\eta }^{\prime }$ and Kobayashi-Maskawa-'t Hooft Six-quark Vertex -- $U(1{)}_A$ Anomaly and Generalized Nambu-Jona-Lasinio Model --

Cited by in corpus (2)

• QCD axion and topological susceptibility in chiral effective Lagrangian models at finite temperature
• Study of some local and global $U(1)$ axial condensates in QCD at finite temperature