Scalar scattering amplitude in the Gaussian wave-packet formalism

• Published in: Progress of theoretical and experimental physics Vol. 2020; no. 10
• Main Authors: Ishikawa, Kenzo, Nishiwaki, Kenji, Oda, Kin-ya
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.10.2020
• Subjects: Physics; B39; B30
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptaa127

Abstract We compute an $s$-channel $2\to2$ scalar scattering $\phi\phi\to\Phi\to\phi\phi$ in the Gaussian wave-packet formalism at the tree level. We find that wave-packet effects, including shifts of the pole and the width of the propagator of $\Phi$, persist even when we do not take into account the time boundary effect for $2\to2$ proposed earlier. An interpretation of the result is that a heavy scalar $1\to2$ decay $\Phi\to\phi\phi$, taking into account the production of $\Phi$, does not exhibit the in-state time boundary effect unless we further take into account in-boundary effects for the $2\to2$ scattering. We also show various plane-wave limits.