Evidence for $B^{\mathbf{-}}\to D_s^{\mathbf{+}}{K}^{\mathbf{-}}{\ell }^{\mathbf{-}}{\overline{\nu }}_{\ell }$ and search for $B^{\mathbf{-}}\to D_s^{*\mathbf{+}}{K}^{\mathbf{-}}{\ell }^{\mathbf{-}}{\overline{\nu }}_{\ell }$

We report measurements of the decays $B^{-}\to D_s^{(*)+}{K}^{-}{\ell }^{-}{\overline{\nu }}_{\ell }$ in a data sample containing $657\times {10}^{6}B\overline{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We observe a signal with a significance of $6\sigma$ for the combined $D_s$ and $D_s^{*}$ modes and find the first evidence of the $B^{-}\to D_s^{+}{K}^{-}{\ell }^{-}{\overline{\nu }}_{\ell }$ decay with a significance of $3.4\sigma$. We measure the following branching fractions: $\mathcal{B}(B^{-}\to D_s^{+}{K}^{-}{\ell }^{-}{\overline{\nu }}_{\ell })=(0.30\pm 0.09(\mathrm{stat}{)}_{-0.08}^{+0.11}(\mathrm{syst}))\times {10}^{-3}$ and $\mathcal{B}(B^{-}\to D_s^{(*)+}{K}^{-}{\ell }^{-}{\overline{\nu }}_{\ell })=(0.59\pm 0.12(\mathrm{stat})\pm 0.15(\mathrm{syst}))\times {10}^{-3}$ and set an upper limit $\mathcal{B}(B^{-}\to D_s^{*+}{K}^{-}{\ell }^{-}{\overline{\nu }}_{\ell })<0.56\times {10}^{-3}$ at the 90% confidence level. We also present the first measurement of the $D_s^{+}{K}^{-}$ invariant mass distribution in these decays, which is dominated by a prominent peak around $2.6\mathrm{GeV}/c^2$.

Figure 1

$M_{\mathrm{tag}}^c$ (left) and $X_{\mathrm{tag}}$ (right) distributions for signal (blue, solid) and background (red, dashed) MC.

Figure 2

Distributions (from left to right) in $X_{\mathrm{mis}}$ and $M_{D_s}$ in the $D_s$ sample (top), and $X_{\mathrm{mis}}$, $M_{D_s}$ and $M_{D_s^{*}}$ in the $D_s^{*}$ sample (bottom). Points with error bars are the data, and lines show the fit projections. Each variable is shown in the signal region of the other variable(s). For the $D_s$ sample the lines represent (from bottom to top) the fitted background components with fake (red dashed) and true $D_s$ (red solid), and the signal contributions from the $D_s^{*}$ (blue dashed) and $D_s$ (blue solid) modes. For the $D_s^{*}$ sample the lines (from bottom to top) represent the fitted background components with fake $D_s$ (red dashed), fake $D_s^{*}$ (red dotted), true $D_s^{*}$ (red solid), and the signal contributions from the $D_s$ mode (blue dashed), the $D_s^{*}$ mode with fake $D_s^{*}$ (blue dotted), and with true $D_s^{*}$ (blue solid). The fitted contributions are superimposed additively.

Figure 3

The invariant mass distribution of $D_s^{+}{K}^{-}$ for the combined $D_s$ and $D_s^{*}$ samples in the signal window (left) and in the $X_{\mathrm{mis}}$ sidebands (right). The full (blank) histograms show the expected background contribution from fake (true) $D_s$. The histograms are superimposed additively.