Determining the Weak Phase $\gamma$ From Charged $B$ Decays

Abstract

A quadrangle relation is shown to be satisfied by the amplitudes for $B^{+}\to {\pi }^0{K}^{+},{\pi }^{+}{K}^0,\eta K^{+}$, and ${\eta }^{\prime }{K}^{+}$. By comparison with the corresponding relation satisfied by $B^{-}$ decay amplitudes, it is shown that the relative phases of all the amplitudes can be determined up to discrete ambiguities. Making use of an SU(3) relation between amplitudes contributing to the above decays and those contributing to $B^{\pm }\to {\pi }^{\pm }{\pi }^0$, it is then shown that one can determine the weak phase $\gamma \equiv \mathrm{Arg}(V_{ub}^{\ast }{V}_{cb}/V_{us}^{\ast }{V}_{cs})$, where $V$ is the Cabibbo-Kobayashi-Maskawa matrix describing the charge-changing weak interactions between the quarks $(u,c,t)$ and $(d,s,b)$.

16 pages, latex, 7 uuencoded figures

References in corpus (3)

• ELECTROWEAK PENGUINS AND TWO-BODY B DECAYS
• Broken SU(3) Symmetry in Two-Body B Decays
• A method for determining CP violating phase $\gamma$

Cited by in corpus (46)

• Charmless $B\to PP$ decays using flavor SU(3) symmetry
• Determination of the Weak Phase gamma from Rate Measurements in B^+- -> pi K, pi pi Decays
• Charmless Final States and S--D-wave mixing in the ${\psi }^{\prime \prime }$
• Low-Mass Baryon-Antibaryon Enhancements in B Decays
• eta - eta prime Mixing -From electromagnetic transitions to weak decays of charm and beauty hadrons
• Two-Body B Meson Decays to $\eta$ and ${\eta }^{{}^{\prime }}$ -- Observation of $B\to \eta${'}K$
• Weak Phase $\gamma$ From Ratio of $B\to K\pi$ Rates
• Annihilation, Rescattering, and CP Asymmetries in B Meson Decays
• B Decays Involving $\eta$ and ${\eta }^{\prime }$ in the Light of the $B\to K{\eta }^{\prime }$ Process
• Isospin-breaking effects on alpha extracted in B --> pi pi, rho rho, rho pi
• SU(3) Decomposition of Two-Body B Decay Amplitudes
• Two-Body Charmless B Decays Involving eta and eta'
• Final-State Phases in Charmed Meson Two-Body Nonleptonic Decays
• On Large Final-State Phases in Heavy Meson Decays
• Measurements of the branching fractions of exclusive charmless B meson decays with ${\eta }^{p}rime$ or $\omega$ mesons
• Improved method for CKM constraints in charmless three-body B and B_s decays
• B Decays to Charmless VP Final States
• Correlated bounds on CP asymmetries in $B^0\to {\eta }^{\prime }{K}_S$
• Rescattering Information from $B\to K\bar{K}$ Decays
• Charmless decays B->pipi, piK and KK in broken SU(3)symmetry
• The CP violating asymmetry in $B^{\pm }\to M\bar{M}{\pi }^{\pm }$ decays
• Weak Phases From B Decays to Kaons and Charged Pions
• The eta (eta') gamma transition form factor and the gluon-gluon distribution amplitude
• Penguin decays of B mesons
• Final-State Phases in $B\to D\pi ,D^{\ast }\pi$, and $D\rho$ Decays
• B meson decays to charmless meson pairs containing eta or eta' mesons
• Suppression of flavor symmetry breaking in B decay sum rules
• Exploring Final State Hadron Structure and SU(3) Flavor Symmetry Breaking Effects in D->PP and D->PV Decays
• Update analysis of two-body charmed $B$ meson decays
• Determining the Weak Phase $\gamma$ in the Presence of Rescattering
• $V_{td}$ from Hadronic Two-Body $B$ Decays
• The gluonic B and J/psi decays into the eta' meson
• CP Violation in B Decays: The Standard Model and Beyond
• Calculating Phases Between B => K* pi Amplitudes
• B Physics - A Theoretical Review
• CKM Matrix and Standard-Model CP Violation
• Determining weak phase gamma and probing new physics in b->s transitions from B->eta(eta')K
• Rescattering and electroweak penguin effects in determinations of the weak phase $\gamma$
• Zweig-rule-satisfying inelastic rescattering in B decays to pseudoscalar mesons
• Determining the Weak Phase $\gamma$ using the decays $B_d$, $B^{+}\to K\eta ({\eta }^{\prime })$ and $B_s\to \pi \eta ({\eta }^{\prime })$
• Elastic and inelastic SU(3)-breaking final-state interactions in B decays to pseudoscalar mesons
• B decays and models for CP violation
• Theoretical Review on CP Violation in Rare B decays
• Selected Theoretical Issues in B-meson Physics: CKM matrix and Semileptonic Decays
• Phenomenology of charmless hadronic B decays
• Lattice QCD and heavy quarks