Studies of Three-Body B^+→D ̅^* 〖(2007)〗^0 K^+ K ̅^0 and B^0→D^* 〖(2010)〗^- K^+ K ̅^0 Decays

We analyze three-body decays of and . Under the factorization approach, there are tree level diagrams for these decay modes and the transition matrix element of decay is factorized into a form factor multiplied by decay constant and form factor multiplied into weak vertices form factor. The transition matrix element of decay is also factorized into a form factor multiplied into weak vertices form factor. We investigate these decays by using the Dalitz plot technique. First, we use the general form of this technique and calculate the branching ratios of the and decays and obtain the values of and , while the experimental results are less than and respectively. Then we assume that, in the decays, because the mass of the is too heavy against the K-mesons.So the momentum of the can have a small amount. Namely, the carries small momentum. In the probability summation of the amplitudes, the momentum of the , instead of starting from its maximum value, starts from a state in which two light mesons make an angle of degrees. Using our assumption, we calculate the branching ratios of and decays and obtain and respectively. In addition, we estimate the branching ratios for different angles between the two light mesons and get that when the angle between them is , in fact they decay back to back, and these values become and , which are the best answers close to the experimental values. The branching ratios obtained by applying our assumption are compatible with the experimental results.