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

TL;DR

This paper analyzes CLEO's measurement of B to pi+ pi- decay to assess its impact on determining the CKM phase alpha, highlighting the importance of form factors and CKM parameters for accurate phase extraction.

Contribution

It applies QCD improved factorization to interpret experimental data and explores how form factors and CKM ratios influence the measurement of the weak phase alpha.

Findings

Large B to pi- form factor favors small |V_ub/V_cb|

Neglecting QCD penguin amplitude causes ~15° error in alpha measurement

Knowing |V_ub/V_cb| allows accurate determination of sin 2 alpha

Abstract

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 $\sin 2 \alpha$.