A Simplified Approach to Determine $\alpha$ and the Penguin Amplitude in $B_d\to \pi \pi$

Abstract

The effect of inelastic final-state interactions (IFSI's) on the determination of the weak phase $\alpha$ from the isospin triangles of $B\to \pi \pi$ is qualitatively illustrated. Neglecting the electroweak penguins and IFSI's and assuming the dominance of the top-quark loop in strong penguin diagrams, we propose an experimentally accessible way to approximately determine $\alpha$ and the penguin amplitude in $B_d\to \pi \pi$. This approach relies on a simplified isospin consideration and the factorization approximation, and its feasibility is irrelevant to the time-dependent measurements of $B_d\to \pi \pi$.

This work has been accepted for publication in Phys. Lett. B. In the revised version, we add a new section to give a qualitative illustration of the effect of inelastic final-state interactions on the determination of the weak phase $\alpha$ from the isospin triangles of $B\to \pi \pi$ . 10 Latex pages (with 1 figure)

References in corpus (9)

• Decays of $B$ Mesons to Two Light Pseudoscalars
• Weak Coupling Phase from Decays of Charged B Mesons to $\pi K$ and $\pi \pi$
• Isospin Structure of Penguins And Their Consequences in $B$ Physics
• Nonfactorizable Amplitudes in Weak Nonleptonic Decays of Heavy Mesons
• Large Penguin effects in the CP Asymmetry of B0d ->pi+pi-
• On Test of CPT Symmetry in CP Violating B Decays
• Test of $CPT$ Symmetry in $CP$-violating $B$ Decays
• A Further Study of $CP$ Asymmetries in Pure Penguin-induced $B_u^{\pm }$ Decays
• On Measuring $CP$ Violation in Neutral $B$-meson Decays at the ${\rm Y}(4S)$ Resonance

Cited by in corpus (6)

• Penguin corrections and strong phases in a time-dependent analysis of $B_d^0\to {\pi }^{+}{\pi }^{-}$
• CP Violation in B Decays: The Standard Model and Beyond
• Final-state Rescattering Effects on B_d-->ππDecays and CP Violation
• Remarks on a Technique of Measuring CP phase $\alpha$
• Theory of CP Violation
• Direct CP Violation and Isospin Triangles of B->ππDecays