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

Abstract

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 ${\mathit{p}}_{\mathit{F}}$, and obtain ${\mathit{p}}_{\mathit{F}}$=0.50-0.54 GeV, which is almost independent of the input parameters ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$, ${\mathit{m}}_{\mathit{b}}$, ${\mathit{m}}_{\mathit{c}}$, and ${\mathit{m}}_{\mathit{sp}}$. We then calculate the ratio ${\mathit{f}}_{\mathit{B}}$/${\mathit{f}}_{\mathit{D}}$, and obtain a result which is larger, by a factor of about 1.3, than \ensuremath{\surd}${\mathit{M}}_{\mathit{D}}$/${\mathit{M}}_{\mathit{B}}$ given by the naive nonrelativistic analogy. This result is in a good agreement with the recent lattice calculations. We also calculate the ratio (${\mathit{M}}_{{\mathit{B}}^{\mathrm{*}}}$-${\mathit{M}}_{\mathit{B}}$)/(${\mathit{M}}_{{\mathit{D}}^{\mathrm{*}}}$-${\mathit{M}}_{\mathit{D}}$). In these calculations the wave function at the origin \ensuremath{\psi}(0) is essential. We also determine ${\mathit{p}}_{\mathit{F}}$ by comparing the theoretical prediction of the ACCMM model with the lepton energy spectrum of B\ensuremath{\rightarrow}e\ensuremath{\nu}X from the recent ARGUS analysis, and find that ${\mathit{p}}_{\mathit{F}}$=0.27${\ifmmode\pm\else\textpm\fi{}}_{0.27}^{0.22}$ GeV, when we use ${\mathit{m}}_{\mathit{c}}$=1.5 GeV. However, this experimentally determined value of ${\mathit{p}}_{\mathit{F}}$ is strongly dependent on the value of the input parameter ${\mathit{m}}_{\mathit{c}}$. \textcopyright{} 1996 The American Physical Society.