Hadronic three-body D decays mediated by scalar resonances

We study the quasi-two-body D -> SP decays and the three-body D decays proceeding through intermediate scalar resonances, where S and P denote scalar and pseudoscalar mesons, respectively. Our main results are the following: (i) Certain external and internal W-emission diagrams with the emitted meson being a scalar meson are naively expected to vanish, but they actually receive contributions from vertex and hard spectator-scattering corrections beyond the factorization approximation. (ii) For light scalars with masses below or close to 1 GeV, it is more sensible to study three-body decays directly and compare with experiment as the two-body branching fractions are either unavailable or subject to large finite-width effects of the scalar meson. (iii) We consider the two-quark (scheme I) and four-quark (scheme II) descriptions of the light scalar mesons, and find the latter generally in better agreement with experiment. This is in line with recent BESIII measurements of semileptonic charm decays that prefer the tetraquark description of light scalars produced in charmed meson decays. (iv) The topological amplitude approach fails here as the D -> SP decay branching fractions cannot be reliably inferred from the measurements of three-body decays, mainly because the decay rates cannot be factorized into the topological amplitude squared and the phase space factor. (v) The predicted rates for D-0 -> f(0)P, a(0)P are generally smaller than experimental data by one order of magnitude, presumably implying the significance of W-exchange amplitudes. (vi) The W-annihilation amplitude is found to be very sizable in the SP sector with vertical bar A/T vertical bar(SP) similar to 1/2, contrary to its suppression in the PP sector with vertical bar A/T vertical bar(PP) similar to 0.18. (vii) Finite-width effects are very important for the very broad sigma/f(0)(500) and kappa/K-0*(700) mesons. The experimental branching fractions B(D+ -> sigma pi(+)) and B(D+ -> (kappa) over bar (0)pi(+)) are thus corrected to be (3.8 +/- 0.3) x 10(-3) and (6.7(-4.5)(+5.6))%, respectively.

Automated summary

In this study, we investigate the quasi-two-body and three-body decays and derive several important results, including the discovery that certain naïve expectation of vanishing emission diagrams actually receive correction contributions, the suggestion that studying three-body decays of light scalars is more sensible than two-body decays, the finding that the four-quark description of light scalars is generally in better agreement with experiment, the failure of the topological amplitude approach in inferring the branching fractions of D -> SP decays, the prediction of smaller branching fractions for D-0 -> f(0)P, a(0)P compared to experimental data, the significance of W-exchange amplitudes in the SP sector, and the importance of finite-width effects for broad sigma/f(0)(500) and kappa/K-0*(700) mesons.