Strong and Weak Phases from Time-Dependent Measurements of $B\to \pi \pi$

Abstract

Time-dependence in $B^0(t)\to {\pi }^{+}{\pi }^{-}$ and $\ob(t) \to π^+ π^-$ is utilized to obtain a maximal set of information on strong and weak phases. One can thereby check theoretical predictions of a small strong phase $\delta$ between penguin and tree amplitudes. A discrete ambiguity between $\delta \simeq 0$ and $\delta \simeq \pi$ may be resolved by comparing the observed charge-averaged branching ratio predicted for the tree amplitude alone, using measurements of $B\to \pi l\nu$ and factorization, or by direct comparison of parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix with those determined by other means. It is found that with 150 fb${}^{-1}$ from BaBar and Belle, this ambiguity will be resolvable if no direct CP violation is found. In the presence of direct CP violation, the discrete ambiguity between $\delta$ and $\pi -\delta$ becomes less important, vanishing altogether as $|\delta |\to \pi /2$. The role of measurements involving the lifetime difference between neutral $B$ eigenstates is mentioned briefly.

14 pages, LaTeX, 5 figures, to be published in Phys. Rev. D. Updated version with one reference changed

References in corpus (17)

• QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
• Observation of Large CP Violation in the Neutral B Meson System
• Observation of CP violation in the B^0 meson system
• A New Approach to a Global Fit of the CKM Matrix
• 2000 CKM-Triangle Analysis A Critical Review with Updated Experimental Inputs and Theoretical Parameters
• In Pursuit of New Physics with B_s Decays
• New Strategies to Extract $\beta$ and $\gamma$ from $B_d\to {\pi }^{+}{\pi }^{-}$ and $B_s\to K^{+}{K}^{-}$
• Constraining the CKM angle $\gamma$ and penguin contributions through combined $B\to \pi K$ branching ratios
• Nonleptonic charmless B decays: factorization vs perturbative QCD
• Measurement of the Lifetime Difference of $B_d$ Mesons: Possible and Worthwhile?
• Implications of CP Asymmetry Limits for $B\to K\pi$ and $B\to \pi \pi$
• New Information on B Decays to Charmless VP Final States
• Factorization in Color-Favored B Meson Decays to Charm
• Indications for Factorization and $Re{V}_{ub}<0$ from Rare B Decay Data
• How well can we predict CP asymmetry in $B\to \pi \pi$, $K\pi$ decays?
• Study of CP-violating asymmetries in B^0 --> pi^+pi^-, K^+pi^- decays
• Information on $B\to \pi \pi$ Provided by the Semileptonic Process $B\to \pi l\nu$

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