Decay rate ratios of Y( 5S)→ B ¯ B reactions

We calculate the decay rate ratios for OZI allowed decays of Y( 5S) to two B mesons by using the decay am- plitudes which incorporate the wave function of the Y( 5S) state. We obtain the result that the branching ratio of the Y( 5S) decay to B ∗ s ¯ B ∗ s is much larger than the branching ratio to Bs ¯ B ∗ s or ¯ BsB ∗ s , in good agreement with the recent experimental results of CLEO and BELLE. This agreement with the experimental results is made possible since the nodes of the Y( 5S)radial wave function induce the nodes of the decay amplitude. We find that the results for the Y( 5S) decays to B (∗) u ¯ B (∗) u or B (∗) d ¯ B (∗) d pairs are sensitive to the pa- rameter values used for the potential between heavy quarks. s ¯ B ∗ ) is much smaller than the value which is expected from the spin countings. These results imply that there exists a delicate mechanism in the decays of Y( 5S)→ B ¯ B. The unitarized quark model (3-5) could predict similar results for the above ratios. These ratios were also calcu- lated in Ref. (6) by using the decay amplitudes which take into account the bound state effect through the wave func- tion of the Y( 5S) state. Even though these theoretical calcu- lations showed the nature of the above experimental results, they were performed before the masses of the B mesons, es- pecially Bs and B ∗ , are measured. Therefore, it is desirable to perform a theoretical calculation by using the experimen- tally established mass values of all B mesons in order to obtain the results which are more reliable quantitatively. It is the purpose of this paper. We use the same method for the calculation as that used in Ref. (6) with the experimentally measured values of B meson masses. We perform the nu- merical calculations for two sets of the parameter values for the potential between heavy quarks, in order to check how much the results are sensitive to the parameter values. We find that the positions of higher nodes of the decay ampli- tude are sensitive to the parameter values. Therefore, the re- sults for the Y( 5S) decays to the B (∗) s ¯ B (∗) s pairs are reliable,