Semileptonic $B_q\to D_q^{*}l\nu$ $(q=s,d,u)$ decays in QCD sum rules

The form factors relevant to $B_q\to D_q^{*}(J^P=1^{-})\ell \nu$ ($q=s$, $d$, $u$) decays are calculated in the framework of the three point QCD sum rules approach. The heavy quark effective theory prediction of the form factors as well as $1/m_b$ corrections to those form factors are obtained. A comparison of the results for the ratio of form factors at zero recoil limit and other values of $q^2$ with the predictions of the subleading Isgur-Wise form factor application for $B\to D^{*}\ell \nu$ is presented. The total decay width and branching ratio for these decays are also evaluated using the $q^2$ dependencies of these form factors. The results are in good agreement with the constituent quark meson model and existing experimental data. The $q=s$ case can also be detected at LHC in the near future.

Figure 1

Feynman diagrams for $B_q\to D_q^{*}l\nu$ ($q=s,d,u$) transitions.

Figure 2

The dependence of $f_V$ on $q^2$ at $M_1^2=19{\mathrm{GeV}}^2$, $M_2^2=5{\mathrm{GeV}}^2$, $s_0=35{\mathrm{GeV}}^2$, and $s_0^{\prime }=6{\mathrm{GeV}}^2$.

Figure 3

The dependence of $f_0$ on $q^2$ at $M_1^2=19{\mathrm{GeV}}^2$, $M_2^2=5{\mathrm{GeV}}^2$, $s_0=35{\mathrm{GeV}}^2$, and $s_0^{\prime }=6{\mathrm{GeV}}^2$.

Figure 4

The dependence of $f_{+}$ on $q^2$ at $M_1^2=19{\mathrm{GeV}}^2$, $M_2^2=5{\mathrm{GeV}}^2$, $s_0=35{\mathrm{GeV}}^2$, and $s_0^{\prime }=6{\mathrm{GeV}}^2$.

Figure 5

The dependence of $f_{-}$ on $q^2$ at $M_1^2=19{\mathrm{GeV}}^2$, $M_2^2=5{\mathrm{GeV}}^2$, $s_0=35{\mathrm{GeV}}^2$, and $s_0^{\prime }=6{\mathrm{GeV}}^2$.

Figure 6

Comparison of fit functions (i) and (ii) for form factor $f_V$ for $q=s$.