Testing the molecular nature of $D_{s0}^{*}(2317)$ and $D_0^{*}(2400)$ in semileptonic $B_s$ and $B$ decays

We study the semileptonic $B_s$ and $B$ decays into the $D_{s0}^{*}(2317)$ and $D_0^{*}(2400)$ resonances, respectively. With the help of a chiral unitarity model in coupled channels we compute the ratio of the decay widths of both processes. Using current values of the width for the ${\overline{B}}^0\to D_0^{*}(2400{)}^{+}{\overline{\nu }}_l{l}^{-}$ we make predictions for the rate of the ${\overline{B}}_s^0\to D_{s0}^{*}(2317{)}^{+}{\overline{\nu }}_l{l}^{-}$ decay and for the $DK$ invariant mass distribution in the ${\overline{B}}_s^0\to DK{\overline{\nu }}_l{l}^{-}$ decay.

Figure 1

Semileptonic decay of ${\overline{B}}_s^0$ into ${\overline{\nu }}_l{l}^{-}$ and a primary $c\overline{s}$ pair.

Figure 2

Semileptonic decay of ${\overline{B}}^0$ into ${\overline{\nu }}_l{l}^{-}$ and a primary $c\overline{d}$ pair.

Figure 3

Semileptonic decay of $B^{-}$ into ${\overline{\nu }}_l{l}^{-}$ and a primary $c\overline{u}$ pair.

Figure 4

Schematic representation of the hadronization $c\overline{q}\to c\overline{q}(\overline{u}u+\overline{d}d+\overline{s}s+\overline{c}c)$.

Figure 5

Diagrammatic representation of $D_{s0}^{*+}(2317)$ production via meson coalescence after rescattering.

Figure 6

Diagrammatic representation of $DK$ production: directly (on the left) and via rescattering (on the right) in ${\overline{B}}_s^0$ decays.

Figure 7

Differential decay width $d{\mathrm{\Gamma }}_i/d{M}_{\mathrm{inv}}^{(i)}$ for the two pseudoscalars channel $i$ in the isospin basis. Here we consider the semileptonic decays ${\overline{B}}_s^0\to (DK{)}^{+}{\overline{\nu }}_l{l}^{-}$, $(D_s{\pi }^0{)}^{+}{\overline{\nu }}_l{l}^{-}$ and ${\overline{B}}^0\to (D\pi {)}^{+}{\overline{\nu }}_l{l}^{-}$. The $DK$ and $D_s{\pi }^0$ channels couple to the $D_{s0}^{*}(2317{)}^{+}$ resonance, and $D\pi$ to the $D_0^{*}(2400)$ resonance. The peak height for the $D_s{\pi }^0$ channel is $d{\mathrm{\Gamma }}_{D_s{\pi }^0}/d{M}_{\mathrm{inv}}^{(D_s{\pi }^0)}\sim 1.5\times {10}^{-13}$.

Figure 8

Integrand of Eq. (45) as a function of the invariant mass of the lepton pair, $M_{\mathrm{inv}}^{(\nu l)}$ (factor outside the integral excluded). Here we consider the semileptonic decays ${\overline{B}}_s^0\to (DK{)}^{+}{\overline{\nu }}_l{l}^{-}$, $(D_s{\pi }^0{)}^{+}{\overline{\nu }}_l{l}^{-}$ and ${\overline{B}}^0\to (D\pi {)}^{+}{\overline{\nu }}_l{l}^{-}$. The invariant mass of the two pseudoscalar meson is fixed as $M_{\mathrm{inv}}^{(i)}=2.4\mathrm{GeV}$ in all decay modes.