Abstract
We show that the coherent axion field spontaneously decays by emitting axion particles via quantum tunneling if axion potential has more than one minimum. By employing the $\hbar$-expansion and mean field approximation, we develop a formalism to trace the real-time dynamics of the axion particle production including its backreaction to the coherent axion field. We also present numerical results for the time evolution of various physical quantities including the strength of the coherent axion field, phase-space density of produced axion particles, energy density, and pressure. Phenomenological implications of our results are also discussed.
Highlights
The Peccei-Quinn mechanism is one of the most compelling resolutions to the strong CP problem [1,2]
We show that dynamical axion particles are spontaneously produced from the coherent axion field φ ≠ 0 if the axion potential has more than one minimum
We show that axion particles are spontaneously produced from the coherent axion field if the axion potential has more than one minimum by explicitly computing the in-vacuum expectation value of the number operator
Summary
The Peccei-Quinn mechanism is one of the most compelling resolutions to the strong CP problem (where CP stands for charge-conjugate parity symmetry) [1,2]. As the QCD vacuum has 2π periodicity in terms of the θ angle, the axion potential would have infinitely degenerate minima in terms of the field φ This implies that if one considers quantum fluctuations on top of the coherent field, φ ≡ φ − hφi, the coherent field initially peaked at some value hφi ≠ 0 would be delocalized because of quantum tunneling between different minima and the quantum fluctuation hjφj2i grows. The product between the phase-space density f and the coupling constant g determines whether the scattering effects beyond the mean field approximation are important. This is intuitively because scattering takes place more frequently if there are more particles. We adopt the natural units, and ħ is not written explicitly in the following as long as it is not confusing
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