M ar 1 99 7 Decay Constant Ratios f η c / f J / ψ and f η b / f Υ

We calculate the decay constant ratios fηc/fJ/ψ and fηb/fΥ. In the calculation we take into account the mock meson structures of the mesons, as well as the difference of the wave functions at origin of the vector and pseudoscalar mesons studied by Ahmady and Mendel. We find that the different spin structures of the mesons much affect the ratios. We incorporate our results in the prediction of the branching ratios of B → K ηc. e-mail: [email protected] e-mail: [email protected] The decay constants fJ/ψ and fΥ of the vector mesons are given experimentally from the decay rates to ee, but fηc and fηb of the pseudoscalar mesons are lack of experimental results. So it is necessary to calculate theoretically the ratios fηc/fJ/ψ and fηb/fΥ for various applications, for example, for the prediction of B(B + → K ηc) from the experimental result B(B + → K J/ψ) = [1.02 ± 0.14] × 10 [1, 2]. It has been widely assumed that the decay constants of the vector and pseudoscalar mesons are almost the same by considering their wave functions at origin to be the same and using the Van Royen-Weisskopf formula. However, Ahmady and Mendel [3] calculated the ratio of the wave functions at origin by considering the perturbation caused by the hyperfine splitting Hamiltonian, and found that the ratio is significantly different from unity. Then fηc and fηb become very different from fJ/ψ and fΥ. In this paper we will further take into account the influence of the mock meson structure [4, 5] of the mesons on the calculation of the decay constants. We will consider its effects on fηc , fηb , and fJ/ψ, fΥ, which are originated from the different mock meson spin structures of the pseudoscalar and vector mesons. We find that the effects are very important contrary to the expectation that they are not important for the mesons composed of two heavy quarks. As a result, fηc and fηb become very close to fJ/ψ and fΥ again, as we will show in this paper. The decay constants of pseudoscalar and vector mesons are defined by < 0| Q̄γγ5Q |MP (K) >= fPK, < 0| Q̄γQ |MV (K, ε) >= fVmV ε. (1) The Van Royen-Weisskopf formula [4] for the decay constants is given by fM =