Study of the leptonic decays of pseudoscalar $B,D$ and vector $B^{\ast },D^{\ast }$ mesons and of the semileptonic $B\to D$ and $B\to D^{\ast }$ decays

Abstract

We present results for different observables in weak decays of pseudoscalar and vector mesons with a heavy $c$ or $b$ quark. The calculations are done in a nonrelativistic constituent quark model improved at some instances by heavy quark effective theory constraints. We determine pseudoscalar and vector meson decay constants that within a few per cent satisfy $f_V{M}_V/f_P{M}_P=1$, a result expected in heavy quark symmetry when the heavy quark masses tend to infinity. We also analyze the semileptonic $B\to D$ and $B\to D^{\ast }$ decays for which we evaluate the different form factors. Here we impose heavy quark effective theory constraints among form factors that are not satisfied by a direct quark model calculation. The value of the form factors at zero recoil allows us to determine, by comparison with experimental data, the value of the $|V_{cb}|$ Cabbibo-Kobayashi-Maskawa matrix element. From the $B\to D$ semileptonic decay we get $|V_{cb}|=0.040\pm 0.006$ in perfect agreement with our previous determination based on the study of the semileptonic $\hat{I}{›}_b\to \hat{I}{›}_c$ decay and also in excellent agreement with a recent experimental determination by the DELPHI Collaboration. We further make use of the partial conservation of axial current hypothesis to determine the strong coupling constants $g_{B^{\ast }B\ddot{I}€}(0)=60.5\pm 1.1$ and $g_{D^{\ast }D\ddot{I}€}(0)=22.1\pm 0.4$. The ratio $R=(g_{B^{\ast }B\ddot{I}€}(0)f_{B^{\ast }}\sqrt{M_D})/(g_{D^{\ast }D\ddot{I}€}(0)f_{D^{\ast }}\sqrt{M_B})=1.105\pm 0.005$ agrees with the heavy quark symmetry prediction of 1.

19 Latex pages,6 figures, references added, corrected typos, content enlarged