Contribution of final state interaction to the branching ratio of $B\to J/ψD$

Xiang Liu, Zheng-Tao Wei, Xue-Qian Li

Published 2008-05-19, updated 2008-05-20Version 2

To testify the validity of the perturbative QCD (pQCD) and investigate its application range, one should look for a suitable process to do the job. $B\to J/\psi D$ is a promising candidate. The linear momentum of the products is relatively small, so that there may exist a region where exchanged gluons are soft and the perturbative treatment may fail, so that the non-perturbative effect would be significant. We attribute such non-perturbative QCD effects into the long-distance final state interaction (FSI) which is estimated in this work. We find that the contribution from the FSI to the branching ratio is indeed sizable and may span a rather wide range of $10^{-6}\sim 10^{-5}$, and cover a region where the pQCD prediction has the same order. A more accurate measurement on its branching ratio may provide important information about the application region of pQCD and help to clarify the picture of the inelastic rescattering (i.e. FSI) which is generally believed to play an important role in B decays.