Determination of the CKM angle γ and|Vub/Vcb|from inclusive directCPasymmetries and branching ratios in charmlessBdecays

We calculate inclusive direct CP asymmetries for charmless $B^{\pm }$ decays. After summing large logarithms to all orders the CP asymmetries in $\Delta S=0\mathrm{}$ and $\Delta S=1\mathrm{}$ decays are found as $a_{\mathrm{CP}}\left(\Delta {S=0)=(2.0\mathrm{}}_{-1.0}^{+1.2\mathrm{}}\right)\%,$ $a_{\mathrm{CP}}(\Delta S=1)=(-1.0\pm 0.5)\%.$ 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 $a_{\mathrm{CP}}(\Delta S=0)$ is proportional to $\sin \gamma |V_{\mathrm{cb}}{/V}_{\mathrm{ub}}|.$ The constraints on the apex $(\overline{\rho },\overline{\eta })$ of the unitarity triangle obtained from these two CP asymmetries define circles in the $(\overline{\rho },\overline{\eta })$ plane. We have likewise analyzed the information on the unitarity triangle obtainable from a measurement of the average nonleptonic branching ratios $\overline{\mathrm{Br}}(\Delta S=0),$ $\overline{\mathrm{Br}}(\Delta S=1)$ and their sum ${\overline{\mathrm{Br}}}_{\mathrm{NL}}\left(\overrightarrow{B}\mathrm{no}\mathrm{}\mathrm{charm}\right).\mathrm{}$ These CP-conserving quantities define circles centered on the $\overline{\rho }$ axis of the $(\overline{\rho },\overline{\eta })$ plane. We expect a determination of $|V_{\mathrm{ub}}{/V}_{\mathrm{cb}}|$ from ${\overline{\mathrm{Br}}}_{\mathrm{NL}}\left(\overrightarrow{B}\mathrm{no}\mathrm{}\mathrm{charm}\right)$ to be promising. Our results contain some new QCD corrections enhancing $\overline{\mathrm{Br}}(\Delta S=1),$ which now exceeds $\overline{\mathrm{Br}}(\Delta S=0)$ by roughly a factor of 2.