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

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

1999-09-08

arxiv.org/abs/hep-ph/9909298v5

Phys.Rev.D61:071301,2000

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX file, 14 pages including 5 eps figures. Revised version with a slightly modified title. In the new version, we use QCD i

Scientific paper

10.1103/PhysRevD.61.071301

The CLEO collaboration has recently reported a (first) measurement of $BR (B \to \pi^+ \pi^-) = (4.7^{+1.8}_{-1.5} \pm 0.6) \times 10^{-6}$. We study, using recent results on QCD improved factorization, the implications of this measurement for the determination of the CKM phase $\alpha$ 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 $\sin 2 \alpha$.

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