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

References in corpus (6)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Mass and width of the lowest resonance in QCD
• Experimental evidence for a light and broad scalar resonance in $D^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ decay
• Final State Interactions in Hadronic D decays
• The phase of the sigma -> pi-pi amplitude in J/Psi -> omega-pi-pi
• Three-body dispersion-relation N/D equations for the coupled decay channels ppbar (J^{PC}=0^{-+}) --> pi^0 pi^0 pi^0, eta pi^0 pi^0, eta eta pi^0, K Kbar pi^0

Cited by in corpus (8)

• Towards three-body unitarity in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$
• Final state interactions in the decays J/psi->VPP
• Mass and width of the sigma
• Scalar resonances: scattering and production amplitudes
• Dalitz Analyses: A Tool for Physics within and Beyond the Standard Model
• Unitarization and low-energy scattering data
• Phenomenological description of the ${\pi }^{-}{\pi }^{+}$ $S$-waves in $D^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ and $D_s^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ decays: The problem of phases
• Studies on ${\pi }^{+}{\pi }^{-}$ phase motion in the ${\Psi }^{\prime }\to J/\Psi {\pi }^{+}{\pi }^{-}$ process