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}
}
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… 
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