Scalar resonances in a unitary $\pi -\pi$ $S$-wave model for $D^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$

Abstract

We propose a model for $D^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$ decays following experimental results which indicate that the two-pion interaction in the $S$-wave is dominated by the scalar resonances $f_0(600)/\sigma$ and $f_0(980)$. The weak decay amplitude for $D^{+}\to R{\pi }^{+}$, where $R$ is a resonance that subsequently decays into ${\pi }^{+}{\pi }^{-}$, is constructed in a factorization approach. In the $S$-wave, we implement the strong decay $R\to {\pi }^{-}{\pi }^{+}$ by means of a scalar form factor. This provides a unitary description of the pion-pion interaction in the entire kinematically allowed mass range $m_{\pi \pi }^2$ from threshold to about 3 GeV${}^2$. In order to reproduce the experimental Dalitz plot for $\Dppp$, we include contributions beyond the $S$-wave. For the $P$-wave, dominated by the $\rho (770{)}^0$, we use a Breit-Wigner description. Higher waves are accounted for by using the usual isobar prescription for the $f_2(1270)$ and $\rho (1450{)}^0$. The major achievement is a good reproduction of the experimental $m_{\pi \pi }^2$ distribution, and of the partial as well as the total $\Dppp$ branching ratios. Our values are generally smaller than the experimental ones. We discuss this shortcoming and, as a byproduct, we predict a value for the poorly known $D\to \sigma$ transition form factor at $q^2=m_{\pi }^2$.

23 pages, 2 figures. Two new equations. The value for the strength of the contribution of the scalar form factor now agrees with other results in the literature. Main results unchanged. Version to appear in Phys. Rev. D

References in corpus (37)

• Heavy Quark Symmetry
• Soft-Collinear Factorization in Effective Field Theory
• QCD factorization for B->PP and B->PV decays
• 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
• Roy equation analysis of pi pi scattering
• Non-perturbative Approach to effective chiral Lagrangians and Meson Interactions
• Experimental evidence for a light and broad scalar resonance in $D^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ decay
• A low-lying scalar meson nonet in a unitarized meson model
• Dalitz Plot Analysis of the Decay D^+ --> K^- pi^+ pi^+ and Indication of a Low-Mass Scalar K pi Resonance
• Charmless hadronic B decays involving scalar mesons: Implications to the nature of light scalar mesons
• Effective Lagrangian for Heavy and Light Mesons: Semileptonic Decays
• J/Ψ\to ϕππ(K \bar{K}) decays, chiral dynamcis and OZI violation
• Charm Meson Decays
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• Hadronic D Decays Involving Scalar Mesons
• 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
• Final State Interactions in Hadronic D decays
• Rescattering and chiral dynamics in B\to ρπdecay
• Interference between f0(980) and rho(770) resonances in B --> pion-pion-kaon decays
• Long-distance effects and final state interactions in B to pion pion K and B to K anti-K K decays
• Dalitz plot analysis of D_s+ and D+ decay to pi+pi-pi+ using the K-matrix formalism
• Dalitz plot analysis of the D^+ -> K^-pi^+pi^+ decay
• Three channel model of meson-meson scattering and scalar meson spectroscopy
• Improved Analysis of J/psi Decays into a Vector Meson and Two Pseudoscalars
• B->rho pi decays, resonant and nonresonant contributions
• Dalitz Plot Analysis of the D+ --> pi- pi+ pi+ Decay
• Predicting D -> sigma pi
• On the Dalitz Plot Approach in Non-leptonic Charm Meson Decays
• Observing Direct CP Violation in Untagged B-Meson Decays
• Estimating sigma-meson couplings from D \to 3πdecays
• Scalar resonances: scattering and production amplitudes
• A Phenomenological Analysis of Non-resonant Charm Meson Decays
• Resonances and weak interactions in $D^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$ decays

Cited by in corpus (10)

• Collective perspective on advances in Dyson-Schwinger Equation QCD
• Hadronic D decays involving even-parity light mesons
• Parametrizations of three-body hadronic $B$- and $D$-decay amplitudes in terms of analytic and unitary meson-meson form factors
• Dalitz plot studies of D0 --> K0S pi+ pi- decays in a factorization approach
• Scalar resonance effects on the B_s - \bar B_s mixing angle
• Kpi form factors and final state interactions in D+ --> K- pi+ pi+ decays
• Hadronic three-body D decays mediated by scalar resonances
• Observation of $D^{+}\to K_S^0{a}_0(980{)}^{+}$ in the amplitude analysis of $D^{+}\to K_S^0{\pi }^{+}\eta$
• Analysis of $CP$ violation in $D^0\to K^{+}{K}^{-}{\pi }^0$
• The $D_s^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ reaction and the scalar $f_0(500)$, $f_0(980)$ and $K_0^{\ast }(700)$ resonances