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arXiv · hep-ph/0603250

Rescattering effects and the $σ$ pole in hadronic decays

Irinel Caprini
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Abstract

The $σ$ resonance was observed as a conspicuous $π^+π^-$ peak in hadronic decays like $J/ψ\to π^+π^-ω$ or $D^+\toπ^+π^-π^+$. The phase of the $σ\toπ^+π^-$ amplitude, extracted from production data within the conventional isobar model, is assumed to coincide with that in $ππ$ elastic scattering. We check the validity of this assumption by using Lehmann-Symanzik-Zimmermann (LSZ) reduction and unitarity. The rescattering effects in the final three-particle states are shown to generate a correction to the phase given by a naive application of Watson theorem. We briefly discuss the implications of this result for the pole determination from production data.

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Irinel Caprini. 2006-06-19. Rescattering effects and the $σ$ pole in hadronic decays. https://doi.org/10.1016/j.physletb.2006.06.003

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