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We find a new contribution in wave-packet scatterings, which has been overlooked in the standard formulation of S-matrix. As a concrete example, we consider a two-to-two scattering of light scalars ϕ by another intermediate heavy scalar Φ, in the Gaussian wave-packet formalism: ϕϕ→Φ→ϕϕ. This contribution can be interpreted as an “in-time-boundary effect” of Φ for the corresponding Φ→ϕϕ decay, proposed by Ishikawa et al., with a newly found modification that would cure the previously observed ultraviolet divergence. We show that such an effect can be understood as a Stokes phenomenon in an integral over complex energy plane: The number of relevant saddle points and Lefschetz thimbles (steepest descent paths) discretely changes depending on the configurations of initial and final states in the scattering.
By the way, this night, or tomorrow morning, for those for whom it is georaphically acceptable, there is a KEK seminar by one of the authors. https://researchseminars.org/seminar/KEKTheory https://kds.kek.jp/event/37860 I think it is a very important thing as it affects the very foundations of S-matrix approach to scattering.
Interesting, had not known of this claim (from the introduction):
Ishikawa et al. claim that indeed a wave-packet effect—more specifically the time-boundary effect due to localization of wave-packet overlap in time— is responsible for diverse phenomena in science such as the LSND neutrino anomaly [2, 3]; violation of selection rules [4]; the solar coronal heating problem [5]; anoma- lous Thomson scattering
Precisely that sentence from the intro made me more interested than the abstract.
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