宇宙学和粒子物理学中的$t$通道奇异性
$t$-channel singularities in cosmology and particle physics
摘要：
当在$t$通道中交换的粒子在运动学上被允许在其质量壳层上时，即当该过程可以被视为两个物理子过程的序列时，二元$2 \to 2$散射过程的横截面的$t$通道奇异性发生：两体衰变$1\to 2$和逆衰变$2 \to 1$。我们推导出的奇异性是目前在一个二元过程的条件。本文用弱康普顿散射$Ze^{-}\to Ze^{-}$模拟了一类标准模型过程的发散截面。在对文献中提出的正则化方法进行批判性回顾之后，我们讨论了由处于热平衡的粒子组成的介质中的奇异过程。介质被示出自然地调节的奇异性作为粒子获得有限的宽度。通过计算简单标量模型中弹性散射的热平均截面，我们展示了一个可能的宇宙学应用。的横截面，这是在真空中发散，成为有限的过程中发生在一个热浴由于在Keldysh-Schwinger形式主义计算的$t$通道介质的虚自能。
英文摘要：
The $t$-channel singularity of a cross-section for a binary $2 \to 2$ scattering process occurs when a particle exchanged in the $t$ channel is kinematically allowed to be on its mass-shell, that is when the process can be viewed as a sequence of two physical subprocesses: a two-body decay $1\to 2$ and an inverse decay $2 \to 1$. We derive conditions for the singularity to be present in a binary process. A class of divergent cross sections for Standard Model processes has been determined and illustrated by the weak analog of the Compton scattering $Ze^{-}\to Ze^{-}$. After critically reviewing regularization methods proposed in literature, we discuss singular processes which occur in a medium composed of particles in thermal equilibrium. The medium is shown to regulate the singularities naturally as particles acquire a finite width. We demonstrate a possible cosmological application by calculating thermally averaged cross section for an elastic scattering within a simple scalar model. The cross section, which is divergent in vacuum, becomes finite when the process occurs in a thermal bath due to the imaginary self-energy of the $t$-channel mediator computed within the Keldysh-Schwinger formalism.
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