Determination of the CKM unitarity triangle by B -> X_d l^+ l^- decay

We attempt to extract the angle $\gamma$ of the Cabibbo-Kobayashi-Maskawa matrix by the inclusive $B \to X_d \l^+ \l^- $ decay in the Standard Model. An independent information for the angle is coming out from the non-trivial contribution due to CP violation factor, which induces CP asymmetry in the channel. The decay rate and asymmetries are examined with including the long-distance contributions due to vector-mesons as well as the momentum dependences of the vector-mesons, that would reduce the long-distance backgrounds in the process. It is shown that in the low dilepton invariant mass region, the branching-ratio for any dilepton final states and the lepton polarization asymmetry for dimuon final state would be sensitive to the CP violation contribution in addition to the trivial CP asymmetry. On the other hand, in the high dilepton invariant mass region, the contribution is tiny that make it a good probe to confirm the measurement of $x_d$ in addition to the present data from $B_d^0-\bar{B}_d^0$ mixing.