New effect in wave-packet scattering of quantum fields

TL;DR

This paper investigates a novel boundary effect in wave-packet scattering of quantum fields, revealing phenomena overlooked in traditional plane-wave approaches, with implications across various scientific fields.

Contribution

It demonstrates that the in time boundary effect in wave-packet scattering naturally emerges without prior assumptions, highlighting a new aspect of quantum field interactions.

Findings

The in time boundary effect arises from wave-packet scattering without explicit boundary assumptions.

The effect can be interpreted as a Stokes phenomenon in Lefschetz-thimble decomposition.

The results are confirmed through different integration order analyses.

Abstract

We report calculations of a wave-packet amplitude of the two-body scattering $\phi \phi \to \Phi \to \phi \phi$, which leads to the measured probability in realistic experiments. We elucidate the decay amplitude of $ \Phi \rightarrow \phi \phi$ from this. In such an amplitude of wave packets, there are in and out time boundaries for the initial $\Phi$ and final $\phi\phi$ configurations, respectively. In this paper, we prove that the effect of the in time boundary of $\Phi\to\phi\phi$ emerges from $\phi\phi\to\Phi\to\phi\phi$ 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.