Evaluation of the decay by the factorization approaches and applying the effects of the final state interaction

Abstract

In this paper the decay of meson which consists of two b and c heavy quarks, into the D0 and mesons is studied in two steps. In the first step, the QCD factorization (QCDF) approach is considered in the initial evaluation, the result of calculation is . While the available experimental result for this decay is , by applying the theoretical value of the that span the range of [0.4, 1.2]%, the result for QCDF approach becomes and the branching ratio in the experimental observation is obtained in the range of (3.72 ± 0.24) × 10−5 to (11.16 ± 0.72) × 10−5. Therefore, it is decided to calculate the theoretical branching ratio by applying the final state interaction (FSI) through the T and cross section channels. In this process, before the meson decays into two final state mesons of , it first decays into two intermediate mesons like , then these two mesons transform into two final mesons by exchanging another meson like D0. The FSI effects are very sensitive to the changes in the phenomenological parameter which appear in the form factor relation. In most calculations, changing two units in this parameter, makes the final result multiplied in the branching ratio, therefor the decision to use FSI is not unexpected. In this study there are nineteen intermediate states in which the contribution of each one is calculated and summed in the final amplitude. Considering , the numerical value of the is from (0.47 ± 0.08) × 10−7 to (13.98 ± 2.08) × 10−7 for which obtained by entering the FSI effects (η = 1 ∼ 3). It should be noted that by choosing the value of the η according to the mass of the exchange meson, as η = 3 for exchange meson of (or D) and η = 1 for exchange meson of (or K) the obtained result is , that is in very good agreement with the experimental result.