Ratios of B and D Meson Decay Constants in Improved Mock Meson Model

We calculate the ratio fBs/fBd by following the Oakes’ method which is based on chiral symmetry breaking, but we improve his calculation by performing the calculation of the factor < 0|b̄γ5s|Bs >/< 0|b̄γ5d|Bd > in the mock meson model. In this calculation we improved the mock meson model by using the value of the parameter β which is obtained by the variational method in the relativistic quark model. We also calculate fDs/fDd, and then (fBs/fBd) / (fDs/fDd). In this method we also obtain the ratio fBs/fDs and fBd/fDd which are important for the knowledge of CP violation and B-B̄ mixing. 1: e-mail: [email protected] 2: e-mail: [email protected] Oakes [1] calculated the ratio fBs/fBd based on the usual assumption that chiral symmetry is broken by quark mass terms H1(x) = ∑ miq̄i(x)qi(x). Using the local relation ∂Aμ(x) = −i[Q5, H1(x)], he obtained fBs fBd = (MBd MBs )2(mb +ms mb +md < 0|b̄γ5s|Bs > < 0|b̄γ5d|Bd > , (1) where the decay constants are defined by < 0|b̄γγ5s|Bs(K) >= ifBsK, < 0|b̄γγ5d|Bd(K) >= ifBdKμ. (2) Through the symmetry consideration, he took the value of < 0|b̄γ5s|Bs >/< 0|b̄γ5d|Bd > as 1, and then obtained the results fBs/fBd = 0.989, fDs/fDd = 0.985, (fBs/fBd) / (fDs/fDd) = 1.004. (3) Because of the light quark SU(3) flavor symmetry the factor < 0|b̄γ5s|Bs >/< 0|b̄γ5d|Bd > is almost 1. However, since we are interested in the ratios in (3) which are by themselves very close to 1, the deviation of the above factor from 1 is still important even though it is very small. Therefore it would be nice if we could calculate the small correction of the symmetry consideration. In this Letter we calculate this factor in the mock meson model of Capstick, Godfrey, and Isgur [2, 3, 4], and improve the Oakes’ results in (3). We also apply this approach to the calculations of fBs/fDs and fBd/fDd, where the calculations of the above factor are essential since we can not apply the light quark flavor symmetry in these cases. The knowledge of these ratios are important since they allow us to get the values of fBs and fBd from the experimentally obtained value of fDs. The information of fBs and fBd is very important, since it is crucial for the magnitude of CP violation and the size of B-B̄ mixing. The mock meson state is represented by [2, 3, 4] |M(K) >= ∫ dpΦ(p)χss̄ φcc̄ |q( mq m K+ p, s) Q̄( mQ̄ m K − p, s̄) >, (4)