Determination of the CKM angle gamma and |V_{ub}/V_{cb}| from inclusive direct CP asymmetries and branching ratios in charmless B decays

Abstract

We have calculated inclusive direct CP-asymmetries for charmless B^{+/-} -decays. After summing large logarithms to all orders the CP-asymmetries in Delta S=0 and Delta S=1 decays are found as a_{CP} (Delta S=0) = (2.0 +1.2/-1.0)% and a_{CP} (Delta S=1) = ( -1.0 +/- 0.5)%. These results are much larger than previous estimates based on a work without summation of large logarithms. We further show that the dominant contribution to a_{CP} (\Delta S=0 ) is proportional to (sin gamma) times |V_{cb}/V_{ub}|. The constraints on the apex (rho-bar,eta-bar) of the unitarity triangle obtained from these two CP-asymmetries define circles in the (rho-bar,eta-bar)-plane. We have likewise analyzed the information on the unitarity triangle obtainable from a measurement of the average non-leptonic branching ratios Br(Delta S=0), Br(Delta S=1) and their sum Br_{NL} (B --> no charm). These CP-conserving quantities define circles centered on the rho-bar--axis of the (rho-bar,eta-bar)-plane. We expect a determination of |V_{ub}/V_{cb}| from Br_{NL} (B --> no charm) to be promising. Our results contain some new QCD corrections enhancing Br(Delta S=1), which now exceeds Br(Delta S=0) by roughly a factor of two.