We compute an s-channel 2 → 2 scalar scattering φφ → Φ → φφ 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 Φ, persist even when we do not take into account the time boundary effect for 2 → 2 proposed earlier. An interpretation of the result is that a heavy scalar 1 → 2 decay Φ → φφ, taking into account the production of Φ, does not exhibit the in-state time boundary effect unless we further take into account in-boundary effects for the 2 → 2 scattering. We also show various plane-wave limits. © The Author(s) 2020. Published by Oxford University Press on behalf of the Physical Society of Japan.