Kinetic approach to ${\eta }^{\prime }$ production from a CP-odd phase

The production of $(\eta ,{\eta }^{\prime })$ mesons during the decay of a CP-odd phase is studied within an evolution operator approach. We derive a quantum kinetic equation starting from the Witten–Di Vecchia–Veneziano Lagrangian for pseudoscalar mesons containing a ${\mathrm{U}}_A\mathrm{}\left(1\right)\mathrm{}$ symmetry breaking term. The nonlinear vacuum mean field for the flavor singlet pseudoscalar meson is treated as a classical, self-interacting background field with fluctuations assumed to be small. The numerical solution provides the time evolution of the momentum distribution function of the produced ${\eta }^{\prime }$ mesons after a quench at the deconfinement phase transition. We show that the time evolution of the momentum distribution of the produced mesons depends strongly on the shape of the effective potential at the end of the quench, exhibiting either parametric or tachyonic resonances. Quantum statistical effects are essential and lead to a pronounced Bose enhancement of the low-momentum states.