Final state interaction in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ with $K\pi$ I=1/2 and 3/2 channels

Abstract

The final state interaction contribution to $D^{+}$ decays is computed for the $K^{-}{\pi }^{+}{\pi }^{+}$ channel within a light-front relativistic three-body model for the final state interaction. The rescattering process between the kaon and two pions in the decay channel is considered. The off-shell decay amplitude is a solution of a four-dimensional Bethe-Salpeter equation, which is decomposed in a Faddeev form. The projection onto the light-front of the coupled set of integral equations is performed via a quasi-potential approach. The S-wave $K\pi$ interaction is introduced in the resonant isospin $1/2$ and the non-resonant isospin $3/2$ channels. The numerical solution of the light-front tridimensional inhomogeneous integral equations for the Faddeev components of the decay amplitude is performed perturbatively. The loop-expansion converges fast, and the three-loop contribution can be neglected in respect to the two-loop results for the practical application. The dependence on the model parameters in respect to the input amplitude at the partonic level is exploited and the phase found in the experimental analysis, is fitted with an appropriate choice of the real weights of the isospin components of the partonic amplitude. The data suggests a small mixture of total isospin $5/2$ to the dominant $3/2$ one. The modulus of the unsymmetrized decay amplitude, which presents a deep valley and a following increase for $K\pi$ masses above $1.5$ GeV, is fairly reproduced. This suggests the assignment of the quantum numbers $0^{+}$ to the isospin 1/2 $K^{\ast }(1630)$ resonance.

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Cited by in corpus (14)

• Dispersion-theoretical analysis of the D^+ --> K^- pi^+ pi^+ Dalitz plot
• CP violation: Dalitz interference, CPT and FSI
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• Consistent Dalitz plot analysis of Cabibbo-favored $D^{+}\to \bar{K}\pi {\pi }^{+}$ decays
• Direct CP violation in beauty and charm hadron decays
• Coupled-channel analysis of $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ decay
• Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit
• Suppressed $B\to PV$ CP asymmetry: CPT constraint
• Three-boson bound states in Minkowski space with contact interactions
• Proton image and momentum distributions from light-front dynamics
• $B^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$: three-body final state interactions and $K\pi$ isospin states
• The $D_s^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ reaction and the scalar $f_0(500)$, $f_0(980)$ and $K_0^{\ast }(700)$ resonances
• 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
• Hadronic rescattering to solve helicity puzzle in $B^{+}\to p\bar{p}{\pi }^{+}(K^{+})$ decays