Multi-Meson Model for the $D^{+}\to K^{+}{K}^{-}{K}^{+}$ decay amplitude

Abstract

We propose a novel approach to describe the $D^{+}\to K^{+}{K}^{-}{K}^{+}$ decay amplitude, based on chiral effective Lagrangians, which can be used to extract information about $K\bar{K}$ scattering. Our trial function is an alternative to the widely used isobar model and includes both nonresonant three-body interactions and two-body rescattering amplitudes, based on coupled channels and resonances, for S- and P-waves with isospin $0$ and $1$. The latter are unitarized in the $K$-matrix approximation and represent the only source of complex phases in the problem. Free parameters are just resonance masses and coupling constants, with transparent physical meanings. The nonresonant component, given by chiral symmetry as a real polynomium, is an important prediction of the model, which goes beyond the (2+1) approximation. Our approach allows one to disentangle the two-body scalar contributions with different isospins, associated with the $f_0(980)$ and $a_0(980)$ channels. We show how the $K\bar{K}$ amplitude can be obtained from the decay $D^{+}\to K^{+}{K}^{-}{K}^{+}$ and discuss extensions to other three-body final states.

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Cited by in corpus (11)

• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• Theoretical study of the $D^0\to K^{-}{\pi }^{+}\eta$ reaction
• Scalar resonances in the $D^{+}\to K^{-}{K}^{+}{K}^{+}$ decay
• Dalitz plot analysis of the $D^{+}\to K^{-}{K}^{+}{K}^{+}$ decay
• Combined theoretical study of the $D^{+}\to {\pi }^{+}\eta \eta$ and $D^{+}\to {\pi }^{+}{\pi }^0\eta$ reactions
• Cross sections for 2-to-1 meson-meson scattering
• Multibody decay analyses -- a new phenomenological model for meson-meson subamplitudes
• Amplitude analysis of the $D_s^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ decay
• The $D_s^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ reaction and the scalar $f_0(500)$, $f_0(980)$ and $K_0^{\ast }(700)$ resonances
• Cross sections for 2-to-3 meson-meson scattering
• CP violation in quasi-two-body $D\to VP$ decays and three-body $D$ decays mediated by vector resonances