Determination of the CKM unitarity triangle byB→Xdl+l−decay

I examine the possibility to extract the angle $\gamma$ of the Cabibbo-Kobayashi-Maskawa unitarity triangle by the inclusive $\overrightarrow{B}{X}_d{l}^{+}{l}^{-}$ decay. Independent information for the angle is expected from the nontrivial contribution induced in $uū$ and $c\overline{c}$ loops. The contributions induce $\mathrm{CP}$ asymmetry which has a high sensitivity to the angle $\gamma$ in the whole dilepton invariant mass region. Particularly, in the low dilepton invariant mass region, the sensitivity is also recognized in the branching ratio with any dilepton final states and the lepton polarization asymmetry with a dimuon final state. In the high dilepton invariant mass region, the sensitivity is tiny in all measurements with the exception of the $\mathrm{CP}$ asymmetry, which makes them good probes to confirm the measurement of $V_{\mathrm{td}}^{*}{V}_{\mathrm{tb}}$ in addition to the present data from $B_d^0$-$B_d^0$ mixing. The decay rate and asymmetries are examined in the standard model taking into account the long-distance contributions due to vector mesons as well as its momentum dependences which would reduce the long-distance backgrounds in the channel.