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

Understand

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.