Decay constants and semileptonic decays of heavy mesons in the relativistic quark model

We investigate the B and D mesons in the relativistic quark model by applying the variational method with the Gaussian wave function. We calculate the Fermi momentum parameter pF, and obtain pF=0.50-0.54 GeV, which is almost independent of the input parameters α_s, m_b, m_c, and m_sp. We then calculate the ratio fB/fD, and obtain a result which is larger, by a factor of about 1.3, than √M^D/m^B given by the naive nonrelativistic analogy. This result is in a good agreement with the recent lattice calculations. We also calculate the ratio (M_B*-M_B)/(M_D*-M_D). In these calculations the wave function at the origin ψ(0) is essential. We also determine pF by comparing the theoretical prediction of the ACCMM model with the lepton energy spectrum of B→eνX from the recent ARGUS analysis, and find that (formula presented) GeV, when we use (formula presented)=1.5 GeV. However, this experimentally determined value of pF is strongly dependent on the value of the input parameter m_c.