New effect in wave-packet scattering of quantum fields

Kenzo Ishikawa (Department of Physics, Hokkaido University, Hokkaido 060-0810, Japan; Research and Education Center for Natural Sciences, Keio University, Kanagawa 223-8521, Japan) ; Kenji Nishiwaki (Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar 201314, India) ; Kin-ya Oda (Department of Physics, Osaka University, Osaka 560-0043, Japan; Department of Mathematics, Tokyo Woman’s Christian University, Tokyo 167-8585, Japan)

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

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      "source": "APS", 
      "value": "We report calculations of a wave-packet amplitude of the two-body scattering <math><mi>\u03d5</mi><mi>\u03d5</mi><mo>\u2192</mo><mi>\u03a6</mi><mo>\u2192</mo><mi>\u03d5</mi><mi>\u03d5</mi></math>, which leads to the measured probability in realistic experiments. We elucidate the decay amplitude of <math><mi>\u03a6</mi><mo>\u2192</mo><mi>\u03d5</mi><mi>\u03d5</mi></math> from this. In such an amplitude of wave packets, there are in and out time boundaries for the initial <math><mi>\u03a6</mi></math> and final <math><mi>\u03d5</mi><mi>\u03d5</mi></math> configurations, respectively. In this paper, we prove that the effect of the in time boundary of <math><mi>\u03a6</mi><mo>\u2192</mo><mi>\u03d5</mi><mi>\u03d5</mi></math> emerges from <math><mi>\u03d5</mi><mi>\u03d5</mi><mo>\u2192</mo><mi>\u03a6</mi><mo>\u2192</mo><mi>\u03d5</mi><mi>\u03d5</mi></math> 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."
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Published on:
15 November 2023
Publisher:
APS
Published in:
Physical Review D , Volume 108 (2023)
Issue 9
DOI:
https://doi.org/10.1103/PhysRevD.108.096013
arXiv:
2102.12032
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

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