AI 中文总结
研究通过引入特定模型研究费米子预热时的螺旋不对称性，利用赝标量汤川机制，采用WKB方法计算博戈留波夫系数跃迁关系，发现赝质量改变高斯分布，实部提高螺旋态数密度，结论获数值结果验证。
AI 中文摘要
在本研究中，我们通过引入一个模型来研究预热期间的费米子螺旋不对称性。在该模型中，狄拉克场ψ通过由项\(- g\frac{\phi}{f} m_\psi \bar{\psi}\mathrm{i}\gamma^5 \psi\)描述的赝标量汤川机制直接与标量暴胀子φ耦合。暴胀之后，随着暴胀子在其势能最小值附近振荡，狄拉克场的有效频率非绝热地变化，导致粒子产生。这些振荡还表明赝质量\(m_5 = g \phi m_\psi/f\)改变符号，从而导致螺旋不对称费米子的产生。我们采用WKB方法解析地计算博戈留波夫系数的跃迁关系，该方法对任意数量的产生都是有效的，并且与无不对称情况相比显示出显著差异。在膨胀宇宙中，赝质量\(m_5\)的存在改变了每个螺旋态的高斯分布，因为泡利阻塞和参量共振的综合效应在某些频率范围内产生了相干增强和相干抑制。这种偏离源于一阶绝热复相位的虚部，记为\(\Theta^{(r)}_{1}\)。\(\Theta^{(r)}_{1}\)的实部在暴胀子八次振荡后由于相干叠加显著提高了每个螺旋态的数密度。这些结论也得到了数值结果的验证。
英文摘要
In this study, we investigate the fermionic helical asymmetry during preheating by introducing a model in which the Dirac field $ψ$ couples to the scalar inflaton $ϕ$ directly through the pseudoscalar Yukawa mechanism described by the term $- g\fracϕ{f} m_ψ\barψ\mathrm{i}γ^5 ψ$. 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 $m_5 = g ϕm_ψ/f$ 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 $Θ^{(r)}_{1}$. The real part of $Θ^{(r)}_{1}$ 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.
