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 a pplying the variational method with the Gaussian wave function. We cal culate the Fermi momentum parameter p(F), and obtain p(F) = 0.50-0.54 GeV, which is almost independent of the input parameters alpha(s), m(b ), m(c), and m(sp). We then calculate the ratio f(B)/f(D), and obtain a result which is larger, by a factor of about 1.3, than root 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 fu nction at the origin psi(0) is essential. We also determine p(F) by co mparing the theoretical prediction of the ACCMM model with the lepton energy spectrum of B --> e nu X from the recent ARGUS analysis, and fi nd that p(F) = 0.27 +/- (+0.22)(-0.27) GeV, when we use m(c) = 1.5 GeV . However, this experimentally determined value of p(F) is strongly de pendent on the value of the input parameter m(c).