Decay Constant Ratios F C =f J= and F B =f

We calculate the decay constant ratios f c=fJ= and f b=f . In the calculation we take into account the mock meson structures of the mesons, as well as the di erence of the wave functions at origin of the vector and pseudoscalar mesons studied by Ahmady and Mendel. We nd that the di erent spin structures of the mesons much a ect the ratios. We incorporate our results in the prediction of the branching ratios of B ! K c. e-mail: [email protected] e-mail: [email protected] The decay constants fJ= and f of the vector mesons are given experimentally from the decay rates to ee , but f c and f b of the pseudoscalar mesons are lack of experimental results. So it is necessary to calculate theoretically the ratios f c=fJ= and f b=f for various applications, for example, for the prediction of B(B + ! K c) from the experimental result B(B + ! K J= ) = [1:02 0:14] 10 3 [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 hyper ne splitting Hamiltonian, and found that the ratio is signi cantly di erent from unity. Then f c and f b become very di erent from fJ= and f . In this paper we will further take into account the in uence of the mock meson structure [4, 5] of the mesons on the calculation of the decay constants. We will consider its e ects on f c , f b , and fJ= , f , which are originated from the di erent mock meson spin structures of the pseudoscalar and vector mesons. We nd that the e ects are very important contrary to the expectation that they are not important for the mesons composed of two heavy quarks. As a result, f c and f b become very close to fJ= and f again, as we will show in this paper. The decay constants of pseudoscalar and vector mesons are de ned by < 0j Q 5Q jMP (K) >= fPK ; < 0j Q Q jMV (K; ") >= fVmV " : (1) The Van Royen-Weisskopf formula [4] for the decay constants is given by fM = q 12=mM j M(0)j, where mM and M(0) are the mass and the wave function at origin of the meson respectively. The Van Royen-Weisskopf formula is widely used for the calculation of the meson decay constants. This formula is obtained in the limit that the spinors of the quarks inside meson are approximated to twocomponent Pauli spinors [4, 6]. In this paper we are interested in the J= and