Investigating the effects of the phenomenological parameters changes in the final state interaction

Abstract

In this research, the decay of is studied in two stages. 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 [0.9, 8.0]%, the result for QCDF approach becomes ) ** → = and the branching ratio in the experimental observation is obtained in the range of 2.57%–29.76% which is a large range. Therefore, it is decided to calculate the theoretical branch ratio by applying the effects of the final state interaction (FSI) through only possible cross section channel. In this process, before the meson decays into two final mesons, , first, it decays into two intermediate mesons (as ), then these two intermediate mesons are converted into two final mesons by the exchange of another meson, (such as K+ corresponding to ). The FSI effects are highly sensitive to the phenomenological parameters that appear in the form factor relationship, so that in most calculations, change the three units in the numeric value of this parameter changes the final result ten times. Therefore, the decision to use FSI is not unexpected. In this study, there are four intermediate states in the cross section channel in which the amplitude of each of them are calculated separately and included in the final amplitude. Considering , the numerical value of the is from (1.54 ± 0.20) × 10−3 to (2.89 ± 0.41) × 10−3 for which obtained by entering the QCDF approach and FSI effects (η = 0.5–1.5). It should be noted that by choosing the value of the η according to the mass of the exchange meson, as η = 1.5 for exchange meson of B* (or B) and η = 0.5 for exchange meson of K* (or K) the obtained result is , that is in very good agreement with the experimental result.