CLEO measurement of $B \to π^+ π^-$ and determination of weak phase $α$

Abstract

The CLEO collaboration has recently reported a (first) measurement of $BR (B \to π^+ π^-) = (4.7^{+1.8}_{-1.5} \pm 0.6) \times 10^{-6}$. We study, using recent results on QCD improved factorization, the implications of this measurement for the determination of the CKM phase $α$ and also for the rate for $B \to π^0 π^0$. If the $B \to π^-$ 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 $α$ using {\em only} the time-dependent analysis of the decay $B \to π^+ π^-$ is large $\sim 15^{\circ}$. However, if $|V_{ub}/V_{cb}|$ is known, then it is possible to determine the correct value of $\sin 2 α$.