Hunting for the alpha: B→ρρB\to \rho\rho, B→ππB \to \pi\pi, B→πρB \to\pi\rho

The hypothesis of the smallness of penguin contribution to charmless strangeless $B_d (\bar B_d)$ decays allows to determine with high accuracy the value of angle $\alpha$ from the currently available $B \to \rho\rho$, $B \to \pi\pi$ and $B\to \rho\pi$ decay data.Comment: 9 page

A method for determining CP violating phase γ\gamma

A new way of determining the phases of weak amplitudes in charged $B$ decays based on SU(3) symmetry is proposed. The CP violating phase $\gamma$ can now be determined without the previous difficulty associated with electroweak penguins.Comment: 9 pages plus one figure, Revte

SU(3) Decomposition of Two-Body B Decay Amplitudes

We present the complete flavor SU(3) decomposition of decay amplitudes for decays of the triplet (B^+_u, B^0_d, B^0_s) of B mesons nonleptonically into two pseudoscalar mesons. This analysis holds for arbitrarily broken SU(3) and can be used to generate amplitude relations when physical arguments permit one to neglect or relate any of the reduced amplitudes.Comment: 31 pages, revtex, no figure

Weak Coupling Phase from Decays of Charged B Mesons to πK\pi K and ππ\pi\pi

The theory of $CP$ violation based on phases in weak couplings in the Cabibbo-Kobayashi-Maskawa (CKM) matrix requires the phase $\gamma \equiv {\rm Arg~} V^*_{ub}$ (in a standard convention) to be nonzero. A measurement of $\gamma$ is proposed based on charged $B$ meson decay rates to $\pi^+ K^0$, $\pi^0 K^+$, $\pi^+ \pi^0$, and the charge-conjugate states. The corresponding branching ratios are expected to be of the order of $10^{-5}$. (submitted to Physical Review Letters)Comment: LaTeX, 8 pages, 2 figures (not included, available upon request), TECHNION-PH-94-7, EFI-94-14, UdeM-LPN-TH-94-19

B-> rho pi, rho rho, pi pi: hunting for alpha

We determine the domains of the values of unitarity triangle angle alpha, allowed by the charmless strangeless B_d (\bar B_d) decays.Comment: 16 pages. Recent Belle results on CP asymmetries in B_d(\bar{B}_d)-->rho^+ rho^- decays are taken into account. Version to be published in Yad.Fi

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

Time-dependence in $B^0(t) \to \pi^+ \pi^-$ and \ob(t) \to \pi^+ \pi^- 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.Comment: 14 pages, LaTeX, 5 figures, to be published in Phys. Rev. D. Updated version with one reference change

Combining CP Asymmetries in B→KπB \to K \pi Decays

We prove an approximate relation, to leading order in dominant terms, between CP-violating rate differences in $B^0/\bar{B}^0 \to K^{\pm}\pi^{\mp}$ and $B^{\pm} \to K^{\pm}\pi^0$. We show how data from these two processes may be combined in order to enhance the significance of a nonzero result.Comment: 9 pages, latex, no figures, submitted to Phys. Rev. Letters, revise

Determination of CKM phases through rigid polygons of flavor SU(3) amplitudes

Some new methods for the extraction of CKM phases $\alpha$ and $\gamma$ using flavor SU(3) symmetry have been suggested through the construction of rigid polygons in the complex plane with sides equal to the decay amplitudes of B mesons into two mesons belonging to the light (charmless) pseudoscalar octet. These rigid polygons incorporate all the possible amplitude triangles and, being overdetermined, also serve as consistency checks and in estimating the rates of some decay modes. The same techniques also lead to numerous useful amplitude triangles when octet-singlet mixing has been taken into account and nearly physical $\eta,\eta'$ are used.Comment: A few detailed explanations added, some rearrangement of sections and a few minor changes in notation. 19 pages, 1 PostScript figure, uses psfig.st

Determining the Weak Phase γ\gamma From Charged BB Decays

A quadrangle relation is shown to be satisfied by the amplitudes for $B^+ \to \pi^0 K^+,~\pi^+ K^0,~\eta K^+$, and $\eta' K^+$. 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 $\gamma \equiv {\rm Arg} (V_{ub}^* V_{cb}/V_{us}^* V_{cs})$, where $V$ is the Cabibbo-Kobayashi-Maskawa matrix describing the charge-changing weak interactions between the quarks $(u,c,t)$ and $(d,s,b)$.Comment: 16 pages, latex, 7 uuencoded figure

Annihilation, Rescattering, and CP Asymmetries in B Meson Decays

A number of $B$ meson decays may proceed only through participation of the spectator quark, whether through amplitudes proportional to $f_B/m_B$ or via rescattering from other less-suppressed amplitudes. An expected hierarchy of amplitudes in the absence of rescattering will be violated by rescattering corrections. Such violations could point the way toward channels in which final-state interactions could be important. Cases in which final state phases can lead to large CP asymmetries are pointed out.Comment: 9 page