New effect in wave-packet scattering of quantum fields

We report calculations of a wave-packet amplitude of the two-body scattering phi phi -> phi -> phi phi, which leads to the measured probability in realistic experiments. We elucidate the decay amplitude of phi -> 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 -> phi phi emerges from phi phi -> phi -> phi phi without assuming any time boundary 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.

Automated summary

In this paper, calculations of wave-packet amplitudes for the two-body scattering process phi phi -> phi -> phi phi are reported, along with the elucidation of the decay amplitude of phi -> phi phi. The time boundaries for the initial and final configurations are explored, and it is demonstrated that the effect of the in-time boundary of phi -> phi phi emerges from phi phi -> phi -> phi phi without any prior assumptions. This overlooked effect in the standard plane-wave formulation can have significant implications across various scientific areas, and its result is confirmed through different integration orders, also interpreted as a Stokes phenomenon in the Lefschetz-thimble decomposition.