Dalitz plot studies of $D^0 \to K^0_S K^+ K^-$ decays in a factorization approach

The BABAR Collaboration data of the D0 → KS0K+K- process are analyzed within a quasi-two-body factorization framework. Starting from the weak effective Hamiltonian, one has to evaluate matrix elements of D0 transitions to two kaons for the tree amplitudes and the transitions between one kaon and two kaons for the annihilation ones ( W -exchange). In earlier studies, assuming these transitions to proceed through the dominant intermediate resonances, we approximated them as being proportional to the kaon form factors. Here, to obtain a good fit, 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. In other respects, it is shown in a model-independent manner that the K+K- and K ¯ 0K+ S -wave effective mass squared distributions, corrected for phase space, are significantly different. At variance with the BABAR analysis, it means that the f0 ( 980 ) resonance must be included in the phenomenological analysis of the D0 → KS0K+K- data. The best fit described in the main text has 19 free parameters and indicates (i) the dominance of annihilation amplitudes, (ii) a large dominance of the f0 ( 980 ) meson in the near threshold K+K- invariant mass distribution, and (iii) a sizable branching fraction to the [ ρ ( 770 ) ++ρ ( 1450 ) ++ρ ( 1700 ) + ] KS0 final states. A first Appendix provides an update of the determination of the isoscalar-scalar meson-meson amplitudes based on an enlarged set of data embodying new precise low energy ππ data. A second Appendix proposes two alternative fits using the scalar-kaon form factors calculated from the Muskhelishvili-Omnès dispersion relation approach. These fits have χ2 quite close to that of the best fit but they show important contributions from both the f0 and a00 mesons and a weaker role of the ρ+ mesons.