Pseudoscalar Yukawa Coupling Induced Helical Asymmetry in Fermionic Preheating

Abstract

In this study, we investigate the fermionic helical asymmetry during preheating by introducing a model in which the Dirac field $\psi$ couples to the scalar inflaton $\phi$ directly through the pseudoscalar Yukawa mechanism described by the term $- g\frac{\phi}{f} m_\psi \bar{\psi}\mathrm{i}\gamma^5 \psi$. Following inflation, as the inflaton oscillates around the minimum of its potential, the effective frequency of Dirac field changes non-adiabatically, resulting in particle production. These oscillations also indicate that the pseudo-mass $m_5 = g \phi m_\psi/f$ changes the sign, leading to the production of helical-asymmetric fermions. We employ the WKB method to analytically calculate the transition relations of the Bogoliubov coefficients, which is valid for an arbitrary number of productions and demonstrates a significant difference compared to the case without asymmetry. In the expanding universe, the presence of pseudo-mass $m_5$ alters the Gaussian distributions for each helical state, since the combined effects of Pauli blocking and parametric resonance produce coherent enhancement and coherent suppression in certain frequency ranges. This departure arises from the imaginary component of the first-order adiabatic complex phase, denoted as $\Theta^{(r)}_{1}$. The real part of $\Theta^{(r)}_{1}$ significantly enhances the number density of each helical state after eight oscillations of the inflaton since the coherent superposition. These conclusions have also been validated by the numerical results.