# Scalar scattering amplitude in the Gaussian wave-packet formalism

@article{Ishikawa2020ScalarSA,
title={Scalar scattering amplitude in the Gaussian wave-packet formalism},
author={Kenzo Ishikawa and Kenji Nishiwaki and Kin-ya Oda},
journal={Progress of Theoretical and Experimental Physics},
year={2020},
volume={2020}
}
• Published 25 June 2020
• Physics
• Progress of Theoretical and Experimental Physics
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 width of the propagator of $\Phi$, persist even when we do not take into account the time-boundary effect for $2\to2$, proposed earlier. The result can be interpreted that a heavy scalar $1\to2$ decay $\Phi\to\phi\phi$, taking into account the production of $\Phi$, does not exhibit the in…
1 Citations

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## References

SHOWING 1-10 OF 12 REFERENCES
Particle decay in Gaussian wave-packet formalism revisited
• Physics
Progress of Theoretical and Experimental Physics
• 2018
We derive the Fermi's golden rule in the Gaussian wave-packet formalism of quantum field theory, proposed by Ishikawa, Shimomura, and Tobita, for the particle decay within a finite time interval. We
Search for the correction term to Fermi’s golden rule in positron annihilation
• Physics
Progress of Theoretical and Experimental Physics
• 2020
In the positron–electron annihilation process, finite deviations from the standard calculation based on Fermi’s golden rule are suggested in recent theoretical work. This paper describes an
The Theory of Positrons
The problem of the behavior of positrons and electrons in given external potentials, neglecting their mutual interaction, is analyzed by replacing the theory of holes by a reinterpretation of the
Generalized S-Matrix in Mixed Representation
• Physics
• 2005
We formulate a generalized scattering amplitude in which the momenta and positions of incoming particles and outgoing particles are specified. Ideal beams and ideal measuring instruments, for which
Finite-size corrections to Fermi's Golden rule II: Quasi-stationary composite states
• Physics
• 2016
Many-body states described by a Schr\"{o}dinger equation include states of overlapping waves of non-vanishing interaction energies. These peculiar states formed in many-body transitions remain in
On experimental confirmation of the corrections to Fermi’s golden rule
• Physics
Progress of Theoretical and Experimental Physics
• 2019
Standard calculations by Fermi's golden rule involve approximations. These approximations could lead to deviations from the predictions of the standard model, as discussed in another paper. In this