New effect in wave-packet scattering of quantum fields

Abstract

We report calculations of a wave-packet amplitude of the two-body scattering $\varphi \varphi \to \Phi \to \varphi \varphi$, which leads to the measured probability in realistic experiments. We elucidate the decay amplitude of $\Phi \to \varphi \varphi$ from this. In such an amplitude of wave packets, there are in and out time boundaries for the initial $\Phi$ and final $\varphi \varphi$ configurations, respectively. In this paper, we prove that the effect of the in time boundary of $\Phi \to \varphi \varphi$ emerges from $\varphi \varphi \to \Phi \to \varphi \varphi$ without assuming any time boundary \emph{a priori}. This effect has been overlooked in the standard plane-wave formulation and can exhibit distinct phenomena in wide areas of science. We confirm the result in different integration orders. The result is also interpreted as a Stokes phenomenon in the Lefschetz-thimble decomposition.

arXiv comment32 pages with 6 figures; version accepted for publication in Physical Review D; Supplemental Materials in the previous version integrated into the main text

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