Abstract
The $\textit{BABAR}$ Collaboration data of the $D^0 \to K^0_S K^+ K^-$ process are analyzed within a quasi two-body factorization framework. In earlier studies, assuming $D^0$ transitions to two kaons and the transitions between one kaon and two kaons to proceed through the dominant intermediate resonances, we approximated them as being proportional to the kaon form factors. To obtain good fits, one has to multiply the scalar-kaon form factors, derived from unitary relativistic coupled-channel models or in a dispersion relation approach, by phenomenological energy-dependent functions. The final state kaon-kaon interactions in the $S$-, $P$- and $D$- waves are taken into account. All $S$-wave channels are treated in a unitary way. The $K^+K^-$ and $\bar K^0 K^+$ $S$-wave effective mass squared distributions, corrected for phase space, are shown, in a model-independent manner, to be significantly different. Then the $f_0(980)$ resonance must be included at variance with the BABAR analysis. The best fit has 19 free parameters and indicates i) the dominance of annihilation amplitudes, ii) a large dominance of the $f_0(980)$ meson in the near threshold $K^+K^-$ invariant mass distribution and iii) a sizable branching fraction to the $K_S^0 \ [\rho(770)^+ + \rho(1450)^+ + \rho(1700)^+] $ final states. An appendix provides an update of the determination of the isoscalar-scalar meson-meson amplitudes based on an enlarged set of data. A second appendix proposes two alternative fits based on scalar-kaon form factors calculated from the Muskhelishvili-Omn\`es dispersion relation approach. These fits have $\chi^2$ quite close to that of the best fit but they show important contributions from both the $f_0$ and $a_0^0$ mesons and a weaker role of the $\rho^+$ mesons.
Highlights
Measurements of the D0 -D0 mixing parameters, throughDalitz-plot time dependent amplitude analyses of the weak process D0 → K 0S K þ K −, have been performed by theBelle [1] and BABAR collaborations [2]
In the following, starting from the expressions given in Eqs. (6) for the Cabibbo favored (CF) amplitudes and in (10) for the doubly Cabibbo suppressed (DCS) ones, we will express the different three-body matrix elements entering in the amplitudes in terms of vertex functions noted
The differential branching fraction or the Dalitz plot density distribution is defined as d2 Branching fractions (Br) jMj2
Summary
Dalitz-plot time dependent amplitude analyses of the weak process D0 → K 0S K þ K − , have been performed by the. This model has basically two fitted parameters for each part of the decay amplitude In this approach one can take into account many existing resonances coupled to the interacting pairs of mesons. K þ K − K decays [19,20] These S-wave form factors are derived using a unitary relativistic three coupled-channel model including ππ, K K, and effective ð2πÞð2πÞ interactions together with chiral symmetry constraints. They include the contributions of the f 0 ð980Þ and f 0 ð1400Þ resonances and require the knowledge of the isoscalarscalar meson-meson amplitudes from the two kaon threshold to energies above the D0 mass. 493.677 MeV denote the D0 , K 0 and charged kaon masses (Ref. [26])
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