We present an analysis of the semi-inclusive decays $B_s to D_s^- X ell^+ u$ and $B_s to D_s^{*-} X ell^+ u$, where $X$ denotes a final state that may consist of additional hadrons or photons and $ell$ is an electron or muon. The studied $B_s$ deca
ys are contained in the $121.4~{rm fb}^{-1}$ $Upsilon(5S)$ data sample collected by the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. The branching fractions of the decays are measured to be $mathcal{B}(B_s to D_s^- X ell^+ u) = [8.2 pm 0.2 (text{stat}) pm 0.6 (text{syst}) pm 1.4 (text{ext})]%$ and $mathcal{B}(B_s to D_s^{*-} X ell^+ u) = [5.4 pm 0.4 (text{stat}) pm 0.4 (text{syst}) pm 0.9 (text{ext})]%$, where the first two uncertainties are statistical and systematic and the last is due to external parameters. The measurement also provides an estimate of the $B_s^{(*)}bar{B}_s^{(*)}$ production cross-section, $sigma(e^+e^- to B_s^{(*)}bar{B}_s^{(*)}) = (53.8 pm 1.4 (text{stat}) pm 4.0 (text{syst}) pm 3.4 (text{ext})),{rm pb}$, at the center-of-mass energy $sqrt{s} = 10.86,{rm GeV}$.
We report the measurement of the direct $CP$ asymmetry in the radiative $bar{B}rightarrow X_{s+d}gamma$ decay using a data sample of $(772 pm 11)times 10^6$ $Bbar{B}$ pairs collected at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB
asymmetric-energy $e^+e^-$ collider. The $CP$ asymmetry is measured as a function of the photon energy threshold. For $E^{rm{*}}_{gamma} geq 2.1~{rm{GeV}}$, where $E^{rm{*}}_{gamma}$ is the photon energy in the center-of-mass frame, we obtain $mathcal{A}_{CP}(bar{B}rightarrow X_{s+d}gamma)= (2.2 pm 3.9 pm 0.9) %$, consistent with the Standard Model prediction.
We report a measurement of the inclusive semileptonic $B_s^0$ branching fraction in a $121~fb^{-1}$ data sample collected near the $Upsilon(5S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^+ e^-$ collider. Events containing $B_
s^0$ pairs are selected by reconstructing a tag side $D_s^+$ and identifying a signal side lepton $ell^+$ ($ell = e, mu$) that is required to have the same-sign charge to ensure that both originate from different $B_s^0$ mesons. The $B_s^0 rightarrow X^- ell^+ u_ell$ branching fraction is extracted from the ratio of the measured yields of $D_s^+$ mesons and $D_s^+ ell^+$ pairs and the known production and branching fractions. The inclusive semileptonic branching fraction is measured to be $[9.6 pm 0.4text{(stat)} pm 0.7text{(syst)}]~%$.
