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

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.

36 pages, 2 figures; revised version, published in PRD

References in corpus (2)

• An Improved Experimental Limit on the Electric Dipole Moment of the Neutron
• $X$ 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 (7)

• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Topological susceptibility of $N_f=2+1$ QCD from staggered fermions spectral projectors at high temperatures
• QCD $\theta$-vacuum energy and axion properties
• Dispersive analysis of glueball masses
• Study of the interactions of the axion with mesons and photons using a chiral effective Lagrangian model
• QCD axion and topological susceptibility in chiral effective Lagrangian models at finite temperature
• Theta dependence of the vacuum energy density in chiral effective Lagrangian models at finite temperature, above $T_c$