The First Estimates of Kinematically Forbidden D Meson Decays

The weak hadronic decay D^+ -> K^0\bar a_1^+ is kinematically forbidden at the peak mass values of the particles involved. However, occurrence of this decay has been reported with branching fraction (9.1 \plusminus 1.8) \cross 10^{-3} in the analysis of D^+ -> K^\bar0 4 \pi decay data. This is due to smearing effects on this decay caused mainly by the large width of a_1-resonance, which extends the phase space and allows this decay. Using a factorization model to evaluate decay amplitudes for external and internal W-emission diagrams, and incorporating Breit-Wigner smearing using the total a_1 width of 400 MeV, we obtain the first estimate for branching fraction of this decay to be 3.3 \cross 10^{-3} and 7.0 \cross 10^{-3}, for |V_1^{Da1} (0)|=0.40 and 1.50 respectively corresponding to different theoretical models, where |V_1^{Da1} (q^2)| is the vector form factor appearing in the D -> a_1 s-wave transition. The estimates are of the desired order of magnitude. We also predict branching fractions of its counterpart decays D^0 -> K^-\bar a_1^+ and D^0 -> K^0\bar a_1^0.