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arXiv 0705.0703hep-ph
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不育物种的产生:量子动力学

Production of a sterile species: quantum kinetics

D. Boyanovsky, C. M. Ho

摘要:

本文在一个有效的热平衡介质中活性-无菌中微子混合模型中研究了无菌粒子的产生。分布函数和相干度的量子动力学方程由两种独立的方法得到:有效作用量和量子主方程。主动-无菌振荡的退相干时间尺度是$τ_{dec} = 2/Γ_{aa}$,但分布函数的演化是由与介质中准粒子模式的阻尼率相关的两个不同的时间尺度决定的:$Γ_1=Γ_{aa}\cos^2\tm ; Γ_2=Γ_{aa}\sin^2\tm$其中$Γ_{aa}$是没有混合时活性物质的相互作用率,$\tm$是介质中的混合角。这两个时间尺度是非常不同的MSW共振,并排除了一个简单的速率方程的动力学描述的活性-无菌生产。我们给出了完整的一套量子动力学方程的活跃和不育人口和凝聚力,并详细讨论了各种近似。通过量子主方程给出了活跃-无菌跃迁概率\emph{in a medium}的推广。我们明确推导出通常的量子动力学方程的“极化矢量”,并显示其等价性的量子主方程和有效作用量。

英文摘要:

Production of a sterile species is studied within an effective model of active-sterile neutrino mixing in a medium in thermal equilibrium. The quantum kinetic equations for the distribution functions and coherences are obtained from two independent methods: the effective action and the quantum master equation. The decoherence time scale for active-sterile oscillations is $τ_{dec} = 2/Γ_{aa}$, but the evolution of the distribution functions is determined by the two different time scales associated with the damping rates of the quasiparticle modes in the medium: $Γ_1=Γ_{aa}\cos^2\tm ; Γ_2=Γ_{aa}\sin^2\tm$ where $Γ_{aa}$ is the interaction rate of the active species in absence of mixing and $\tm$ the mixing angle in the medium. These two time scales are widely different away from MSW resonances and preclude the kinetic description of active-sterile production in terms of a simple rate equation. We give the complete set of quantum kinetic equations for the active and sterile populations and coherences and discuss in detail the various approximations. A generalization of the active-sterile transition probability \emph{in a medium} is provided via the quantum master equation. We derive explicitly the usual quantum kinetic equations in terms of the ``polarization vector'' and show their equivalence to those obtained from the quantum master equation and effective action.

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