Weak Phase $\gamma$ and Strong Phase $\delta$ from CP Averaged $B\to \pi \pi$ and $\pi K$ Decays

Abstract

Assuming SU(3) symmetry for the strong phases in the four decay modes $B\rarrow π^-π^+, π^0 π^+, π^- K^+, π^- \bar{K}^0$ and ignoring the relative small electroweak penguin effects in those decays, the weak phase $\gamma$ and the strong phase $\delta$ can be determined in a model independent way by the CP-averaged branching ratios of the four decay modes. It appears that the current experimental data for $B\to \pi \pi$ and $\pi K$ decays prefer a negative value of $\cos \gamma \cos \delta$. By combining with the other constraints from $V_{ub}$, $B_{d,s}^0-{\bar{B}}_{d,s}^0$ mixings and indirect CP-violating parameter ${\epsilon }_K$ within the standard model, two favorable solutions for the phases $\gamma$ and $\delta$ are found to lie in the region: $35^{\circ}\altγ\alt 62^{\circ}$ and $106^{\circ}\alt δ\alt 180^{\circ}$ or $86^{\circ}\altγ\alt 151^{\circ}$ and $0^{\circ}\altδ\alt 75^{\circ} $ within 1$\sigma$ standard deviation. It is noted that if allowing the standard deviation of the data to be more than 1$\sigma$, the two solutions could approach to one solution with a much larger region for the phases $\gamma$ and $\delta$. Direct CP asymme try $a_{{\epsilon }^{\prime \prime }}^{({\pi }^{-}{K}^{+})}$ in $B\rarrow π^-K^+$ decay can be as large as the present experimental upper bound. Direct CP asymmetry $a_{{\epsilon }^{\prime \prime }}^{({\pi }^{+}{\pi }^{-})}$ in $B\rarrow π^-π^+$ decay can reach up to about 40% at 1$\sigma$ level.

14 Pages, ReVTeX, 5 figures, one figure (Fig.3) is corrected

References in corpus (5)

• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• Constraints on the phase $\gamma$ and new physics from $B\to K\pi$ Decays
• New Information on B Decays to Charmless VP Final States
• $F^0-{\bar{F}}^0$ Mixing and CP Violation in the General Two Higgs Doublet Model
• CLEO measurement of $B\to {\pi }^{+}{\pi }^{-}$ and determination of weak phase $\alpha$

Cited by in corpus (9)

• QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
• The CP violating phase $\gamma$ from global fit of rare charmless hadronic B decays
• Implications of Charmless B Decays with Large Direct CP Violation
• Charmless decays B->pipi, piK and KK in broken SU(3)symmetry
• Model independent sum rules for B-> pi K decays
• The interplay between Weak and Strong Phases and Direct CP Violation from the Charmless B-meson Decays
• Implications of new data in charmless B decays
• Determining weak phase gamma and probing new physics in b->s transitions from B->eta(eta')K
• Constraining Charming Penguins in Charmless B Decays