Charmed scalar meson production in $B$ decays

Charmed scalar meson spectroscopy has become a hot topic on both experimental and theoretical sides. The $B_{(s)}$ decays provide an ideal place to study their properties. We employ the $B$-meson light-cone sum rules to calculate the ${\overline{B}}_s^0\to D_{s0}^{*+}(2317)$ and $B^{-}\to D_0^{*0}(2400)$ transition form factors at the large recoil region assuming $D_{s0}^{*+}(2317)$ and $D_0^{*0}(2400)$ are scalar quark-antiquark states. The results are extrapolated to the whole momentum region in heavy quark effective theory. We also estimate the $DK$ continuum state contribution to ${\overline{B}}_s^0\to D_{s0}^{*+}(2317)$ form factors with a phenomenological method. Compared with the resonance contribution, it is less than 15% for $f_{B{D}_{s0}^{*}}^{+}$ and about 60% for $f_{B{D}_{s0}^{*}}^{-}$. After including the theoretical uncertainties, our results can be consistent with the previous studies. The branching ratios of semileptonic decays ${\overline{B}}_s^0\to D_{s0}^{*+}(2317)l{\overline{\nu }}_l$ and $B^{-}\to D_0^{*0}(2400)l{\overline{\nu }}_l$ are then evaluated. For the light lepton final state, $\mathrm{Br}({\overline{B}}_s^0\to D_{s0}^{*+}(2317)l{\overline{\nu }}_l)$ is around $6.0\times {10}^{-3}$, which is decreased to about $0.8\times {10}^{-3}$ for the tau final state due to the phase space effect. The predicted branching ratio of $B^{-}\to D_0^{*0}(2400)l{\overline{\nu }}_l$ is slightly larger than that of ${\overline{B}}_s^0\to D_{s0}^{*+}(2317)l{\overline{\nu }}_l$.

Figure 1

Diagrams corresponding to the contributions of (a) two-particle and (b) three-particle $B$-meson DA’s to the correlation function in Eq. (2).

Figure 2

The dependence of form factors $f_{D_{s0}^{*+}(2317)}^{+}(0)$ (left) and $f_{D_{s0}^{*+}(2317)}^{-}(0)$ (right) on the Borel mass $M^2$, the contribution from 2-particle $B$-meson DA is denoted by the dashed line, and the dash-dotted line represents the 3-particle DA contribution. The solid line gives the total results.

Figure 3

The dependence form factor $f_{D_{s0}^{*+}(2317)}^{+}(0)$ (left) and $f_{D_{s0}^{*+}(2317)}^{-}(0)$ (right) on the Borel mass $M^2$, the contribution of higher exited states and the continuum states in the whole sum rules is shown by the dashed line.

Figure 4

The dependence of form factor $f_{D_{s0}^{*+}(2317)}^{+}$ on $q^2$.

Figure 5

The dependence of form factor $f_{D_{s0}^{*+}(2317)}^{+}$ on the renormalization scale.

Figure 6

Dependence of the $DK$ continuum state contribution to form factor $f_{D_{s0}^{*+}(2317)}^{+}$ (the dashed line) and $f_{D_{s0}^{*+}(2317)}^{-}$ (the solid line) on the Borel parameter ($q^2=0$).

Figure 7

Dependence of the $DK$ continuum state contribution to form factor $f_{D_{s0}^{*+}(2317))}^{+}$ and $f_{D_{s0}^{*+}(2317)}^{-}$ on $q^2$, the Borel parameter is fixed to be 4.0 GeV.

Figure 8

The $q^2$ dependence of differential decay width $\frac{d}{d{q}^2}\mathrm{\Gamma }({\overline{B}}_s^0\to D_{s0}^{*+}(2317)l^{-}{\overline{\nu }}_l)$ for the final states with $l=e,\mu$ (left) and $l=\tau$ (right). The dash-dotted line stands for the result without $DK$ continuum state, while the region between the solid and dashed line includes the contribution of $DK$ continuum states to $f_{D_{s0}^{*+}(2317)}^{+}$.

Figure 9

The $q^2$ dependence of differential decay width $\frac{d}{d{q}^2}\mathrm{\Gamma }({\overline{B}}_s^0\to D_{s0}^{*+}(2317)l^{-}{\overline{\nu }}_l)$ for the final states with $l=e,\mu$ (left) and $l=\tau$ (right). The meaning of each line is the same with Fig. 8 except that the $DK$ continuum states contribute to $f_{D_{s0}^{*+}(2317)}^{-}$.