Determination of the CKM angle γ and | V ub / V cb | from inclusive direct CP asymmetries and branching ratios in charmless B decays 1

We have calculated inclusive direct CP-asymmetries for charmless B–decays. After summing large logarithms to all orders the CP-asymmetries in ∆S = 0 and ∆S = 1 decays are found as aCP (∆S = 0) = ( 2.0 +1.2 −1.0 ) %, aCP (∆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 aCP (∆S = 0) is proportional to sin γ · |Vcb/Vub|. The constraints on the apex (ρ, η) of the unitarity triangle obtained from these two CP-asymmetries define circles in the (ρ, η)-plane. We have likewise analyzed the information on the unitarity triangle obtainable from a measurement of the average non-leptonic branching ratios Br(∆S = 0), Br(∆S = 1) and their sum BrNL(B → no charm). These CP-conserving quantities define circles centered on the ρ-axis of the (ρ, η)-plane. We expect a determination of |Vub/Vcb| from BrNL(B → no charm) to be promising. Our results contain some new QCD corrections enhancing Br(∆S = 1), which now exceeds Br(∆S = 0) by roughly a factor of two. 1Work supported by BMBF under contract no. 06-TM-874. 2e-mail:[email protected] 3e-mail:[email protected] 4e-mail:[email protected]