Final state interaction effects on the \(B^+\rightarrow J/\psi\rho^+\) decay (Q1949880)

Summary: The exclusive decay of \(B^+\rightarrow J/\psi\rho^+\) is studied in the framework of the QCD factorization (QCDF) method and final state interaction (FSI). A direct \(B^+\rightarrow J/\psi\rho^+\) decay is only occurred via a tree and a penguin based on the quark diagram analysis. The result that is found by using the QCDF method is less than the experimental result, so, the role of FSI is considered. The intermediate states \(D^+\bar{D}^0\), \(D^{+*}\bar{D}^{0*}\), \(D^{+*}\bar{D}^0\), and \(D^+\bar{D}^{0*}\) via the exchange of \(D^-\) and \(D^{-*}\) are contributed to the \(B^+\rightarrow J/\psi\rho^+\) decay. The above intermediate states is calculated by using the QCDF method. In the FSI effects the results of our calculations depend on ``\(\eta \)'' as the phenomenological parameter. The range of this parameter are selected from 1 to 2. For the exchanged particles \(D^-\) and \(D^{-*}\), it is found that if \(\eta = 1.58\sim 1.83\) is selected the numbers of the branching ratio are placed in the experimental range. The experimental branching ratio of \(B^+\rightarrow J/\psi\rho^+\) decay is \((5\pm 0.8)\times 10^{-5}\), and our prediction number is \((1.42\pm 0.36)\times 10^{-5}\) in the absence of FSI effects, and it becomes \((4.2\sim 5.8)\times 10^{-5}\) when FSI contributions are taken into account.