Measurement of the Semileptonic Branching Ratio of $B_s^0$ to an Orbitally Excited $D_s^{**}$ State: $\mathrm{Br}\mathbf{(}{B}_s^0\to D_{s1}^{-}(2536){\mu }^{+}\nu X\mathbf{)}$

In a data sample of approximately $1.3{\mathrm{fb}}^{-1}$ collected with the D0 detector between 2002 and 2006, the orbitally excited charm state $D_{s1}^{\pm }(2536)$ has been observed with a measured mass of $2535.7\pm 0.6(\mathrm{stat})\pm 0.5(\mathrm{syst})\mathrm{MeV}/c^2$ via the decay mode $B_s^0\to D_{s1}^{-}(2536){\mu }^{+}{\nu }_{\mu }X$. A first measurement is made of the branching ratio product $\mathrm{Br}\mathbf{(}\overline{b}\to D_{s1}^{-}(2536){\mu }^{+}{\nu }_{\mu }X\mathbf{)}\times \mathrm{Br}(D_{s1}^{-}\to D^{*-}{K}_S^0)$. Assuming that $D_{s1}^{-}(2536)$ production in semileptonic decay is entirely from $B_s^0$, an extraction of the semileptonic branching ratio $\mathrm{Br}\mathbf{(}{B}_s^0\to D_{s1}^{-}(2536){\mu }^{+}{\nu }_{\mu }X\mathbf{)}$ is made.