Rescattering effects and the $\sigma$ pole in hadronic decays

Abstract

The $\sigma$ resonance was observed as a conspicuous ${\pi }^{+}{\pi }^{-}$ peak in hadronic decays like $J/\psi \to {\pi }^{+}{\pi }^{-}\omega$ or $D^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$. The phase of the $\sigma \to {\pi }^{+}{\pi }^{-}$ amplitude, extracted from production data within the conventional isobar model, is assumed to coincide with that in $\pi \pi$ 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.

10 pages, minor text changes, version to appear in Phys.Lett.B

Cited by in corpus (3)

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