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

Abstract

I examine a possibility to extract the angle $γ$ of the Cabibbo-Kobayashi-Maskawa unitarity triangle by the inclusive $B \to X_d ł^+ ł^- $ decay. An independent information for the angle is expected from the non-trivial contribution induced in $u \bar{u}$ and $c \bar{c}$ loops. The contributions induce CP asymmetry which has high sensitivity to the angle $γ$ 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 dimuon final state. In the high dilepton invariant mass region, the sensitivity is tiny in all measurements with the exception of the CP asymmetry, that make them to be good probes to confirm the measurement of ${V_{td}}^\ast V_{tb}$ in addition to the present data from $B_d^0-\bar{B}_d^0$ mixing. The decay rate and asymmetries are examined in the Standard Model with taking into account the long-distance contributions due to vector-mesons as well as its momentum dependences that would reduce the long-distance backgrounds in the channel.