CLEO measurement of $B\to {\pi }^{+}{\pi }^{-}$ and determination of weak phase $\alpha$

Abstract

The CLEO collaboration has recently reported a (first) measurement of $BR(B\to {\pi }^{+}{\pi }^{-})=(4.7_{-1.5}^{+1.8}\pm 0.6)\times 10^{-6}$. We study, using recent results on QCD improved factorization, the implications of this measurement for the determination of the CKM phase $\alpha$ and also for the rate for $B\to {\pi }^0{\pi }^0$. If the $B\to {\pi }^{-}$ form factor is large $(\stackrel{>}{\sim }0.3)$, then we find that the CLEO measurement favors small $|V_{ub}/V_{cb}|$ so that the expected error (due to neglecting the QCD penguin amplitude) in the measurement of $\alpha$ using {\em only} the time-dependent analysis of the decay $B\to {\pi }^{+}{\pi }^{-}$ is large $\sim 15^{\circ }$. However, if $|V_{ub}/V_{cb}|$ is known, then it is possible to determine the correct value of $\sin 2\alpha$.

Comments: LaTeX file, 14 pages including 5 eps figures. Revised version with a slightly modified title. In the new version, we use QCD improved factorization. For the value of form factor used earlier, the conclusion that small Vub/Vcb is preferred leading to large error in alpha is unchanged. We have added results for a smaller value of the form factor. We also show that if Vub/Vcb is known, then it is possible to determine the correct value of sin 2 alpha. Typos corrected