Scalar resonances: scattering and production amplitudes

Abstract

Scattering and production amplitudes involving scalar resonances are known, according to Watson's theorem, to share the same phase $\delta (s)$. We show that, at low energies, the production amplitude is fully determined by the combination of $\delta (s)$ with another phase $\omega (s)$, which describes intermediate two-meson propagation and is theoretically unambiguous. Our main result is a simple and almost model independent expression, which generalizes the usual $K$-matrix unitarization procedure and is suited to be used in analyses of production data involving scalar resonances.

10 pages, 4 figures. Minor changes, references added, version to appear in Phys. Rev. D

References in corpus (15)

• ππscattering
• Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the σ, f_0(980), a_0(980) Scalar Mesons
• Chiral symmetry amplitudes in the s-wave isoscalar and isovector channels and the $\sigma ,f_0(980),a_0(980)$ scalar mesons
• 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
• J/Ψ\to ϕππ(K \bar{K}) decays, chiral dynamcis and OZI violation
• Unitarized pseudoscalar meson scattering amplitudes in three flavor linear sigma models
• The $\sigma$ pole in $J/\psi \to \omega {\pi }^{+}{\pi }^{-}$
• Model Independent Measurement of \swave $K^{-}{\pi }^{+}$ systems using $\Dp\to Kππ$ Decays from Fermilab E791
• Rescattering and chiral dynamics in B\to ρπdecay
• Long-distance effects and final state interactions in B to pion pion K and B to K anti-K K decays
• Amplitude Analysis of the decay D^0 --> K^- K^+ pi^0
• Dalitz Plot Analysis of the D+ --> pi- pi+ pi+ Decay
• Rescattering effects and the $\sigma$ pole in hadronic decays
• Phase Motion in the Scalar Low-Mass pi+pi- Amplitude in D+ -> pi-pi+pi+ Decay

Cited by in corpus (4)

• Towards three-body unitarity in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$
• Relating multichannel scattering and production amplitudes in a microscopic OZI-based model
• Scalar resonances in a unitary $\pi -\pi$ $S$-wave model for $D^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$
• Interpretation of K+K0bar pair production in pp collisions