Dynamics of axion-neutral pseudoscalar mixing

Axions mix with neutral pions after the QCD phase transition through their common coupling to the radiation bath via a Chern-Simons term, as a consequence of the $U(1)$ anomaly. The nonequilibrium effective action that describes this mixing phenomenon is obtained to second order in the coupling of neutral pions and axions to photons. We show that a misaligned axion condensate induces a neutral pion condensate after the QCD phase transition. We argue that even a very small axion-photon coupling will “seed” the chiral phase transition. The dynamics of the pion condensate displays long and short timescales and decays on the longer timescale exhibiting a phenomenon akin to the “purification” in a kaon beam. On the intermediate timescales the macroscopic pion condensate is proportional to a condensate of the Abelian Chern-Simons term induced by the axion. We argue that the coupling to the common bath also induces kinetic mixing. We obtain the axion and pion populations, and these exhibit thermalization with the bath. The mutual coupling to the bath induces long-lived axion–neutral pion coherence independent of initial conditions. The framework of the effective action and many of the consequences are more broadly general and applicable to scalar or pseudoscalar particles mixing in a medium.

Figure 1

Contributions to the influence functional $\mathcal{I}[{\varphi }^{+},{\varphi }^{-}]$. The black circle denotes the correlation functions $G^{\lessgtr }$ to all orders in the couplings to degrees of freedom other than the fields ${\varphi }_{a,b}$.

Figure 2

Contributions to the influence functional for the pion-axion mixing case. The self-energy diagram corresponds to the processes ${\pi }^0\leftrightarrow 2{\gamma }^{*}\leftrightarrow a$ and the inverse process, with ${\gamma }^{*}$ a photon in the medium. These processes induce axion-pion mixing. The photon propagators can be dressed by loops of charged particles. The branch labels $\pm$ are suppressed for clarity.