Corrections to sin(2 beta) from CP asymmetries in B^0 -> (pi^0,rho^0,eta,eta^',omega,phi) K_S decays

Neglecting smaller amplitudes the time-dependent CP asymmetry in penguin-dominated b -> s q \bar q transitions (such as B -> phi K_S) is expected to equal sin(2 beta), an expectation not borne out by the present average experimental data. I compute and discuss the correction due to the smaller amplitudes in the framework of QCD factorization.Comment: 11 pages, 2 figues, LaTe

Interpreting the time-dependent CP asymmetry in B0→π0KSB^0 \to \pi^0 K_S

Flavor SU(3) is used for studying the time-dependent CP asymmetry in $B^0 \to \pi^0 K_S$ by relating this process to $B^0\to \pi^0\pi^0$ and $B^0 \to K^+K^-$. We calculate correlated bounds on $S_{\pi K} - \sin 2\beta$ and $C_{\pi K}$, with maximal magnitudes of 0.2 and 0.3, where $S_{\pi K}$ and $C_{\pi K}$ are coefficients of $\sin\Delta mt$ and $\cos\Delta mt$ in the asymmetry. Stronger upper limits on $B^0 \to K^+K^-$ are expected to reduce these bounds and to imply nonzero lower limits on these observables. The asymmetry is studied as a function of a strong phase and the weak phase $\gamma$.Comment: 11 pages, 2 figures, to be published in Phys. Lett. B. Some equations corrected leading to small changes in figure

Precision Tests of Flavor and CP violation in B Decays

Isospin and flavor SU(3) set stringent bounds on penguin pollution in $B^0(t)\to \rho^+\rho^-$, providing a theoretically precise determination of $\alpha\equiv \phi_2$, $\alpha = (91\pm 7_{\rm exp}\pm 3_{\rm th})^\circ$. Isospin breaking in a sum rule for $B\to K\pi$ rates is shown to be suppressed. A similar sum rule holds for CP asymmetries in $B\to K\pi$. Violation of these sum rules would be evidence for an anomalous $\Delta I=1$ piece in ${\cal H}_{\rm eff}$.Comment: Reference added; Invited talk presented at the First Workshop on Theory, Phenomenology and Experiments in Heavy Flavor Physics, Anacapri, Italy, 29-31 200

A precise determination of α\alpha using B0→ρ+ρ−B^0\to\rho^+\rho^- and B+→K∗0ρ+B^+\to K^{*0}\rho^+

The effect of the penguin amplitude on extracting $\alpha$ from CP asymmetries in $B^0\to \rho^+\rho^-$ decays is studied using information on the SU(3)-related penguin amplitude in $B^+\to K^{*0}\rho^+$. Conservative bounds on non-factorizable SU(3) breaking, small amplitudes, and the strong phase difference between tree and penguin amplitudes, are shown to reduce the error in $\alpha$ in comparison with the one obtained using isospin symmetry in $B\to\rho\rho$. Current measurements imply $\alpha = [90 \pm 7 f{\rm exp})^{+2}_{-5} ({\rm th})]^\circ$.Comment: 12 pages. 2 figures, to be published in Physics Letters B; v2: Added "Note added in proof" to account for latest experimental result

Implications for CP asymmetries of improved data on B→K0π0B \to K^0 \pi^0

The decay $B^0 \to K^0 \pi^0$, dominated by a $b \to s$ penguin amplitude, holds the potential for exhibiting new physics in this amplitude. In the pure QCD penguin limit one expects \ckp = 0 and \skp = \sin 2 \beta for the coefficients of $\cos \Delta m t$ and $\sin \Delta m t$ in the time-dependent CP asymmetry. Small non-penguin contributions lead to corrections to these expressions which are calculated in terms of isospin-related $B\to K\pi$ rates and asymmetries, using information about strong phases from experiment. We study the prospects for incisive tests of the Standard Model through examination of these corrections. We update a prediction \ckp=0.15\pm 0.04, pointing out the sensitivity of a prediction \skp\approx 1 to the measured branching ratio for $B^0\to K^0\pi^0$ and to other observables.Comment: Note added, to be published in Physics Letters

The Role of Bs→KπB_s \to K \pi in Determining the Weak Phase γ\gamma

The decay rates for $B^0 \to K^+ \pi^-$, $B^+ \to K^0 \pi^+$, and the charge-conjugate processes were found to provide information on the weak phase $\gamma \equiv {\rm Arg}(V_{ub}^*)$ when the ratio $r$ of weak tree and penguin amplitudes was taken from data on $B \to \pi \pi$ or semileptonic $B \to \pi$ decays. We show here that the rates for $B_s \to K^- \pi^+$ and $\bar B_s \to K^+ \pi^-$ can provide the necessary information on $r$, and estimate the statistical accuracy of forthcoming measurements at the Fermilab Tevatron.Comment: 8 pages, LaTeX, no figures, submitted to Physics Letters B, corrections to discussion of SU(3) breaking adde

Weak phases from topological-amplitude parametrization

We propose a parametrization for two-body nonleptonic $B$ meson decays, in which the various topologies of amplitudes are counted in terms of powers of the Wolfenstein parameter $\lambda\sim 0.22$. The weak phases and the amplitudes are determined by comparing this parametrization with available measurements. It is possible to obtain the phase $\phi_3$ from the $B\to K\pi$ data up to theoretical uncertainty of $O(\lambda^3)\sim 1$. The recently measured $B_d^0\to\pi^0\pi^0$ branching ratio implies a large color-suppressed or penguin amplitude, and that the extraction of the phase $\phi_2$ from the $B\to\pi\pi$ data may suffer theoretical uncertainty more than the expected one of $O(\lambda^2)\sim 5$.Comment: 11 pages, 4 figure

CP Violation in B -> pi+ pi- and the Unitarity Triangle

We analyze the extraction of weak phases from CP violation in $B\to\pi^+\pi^-$ decays. We propose to determine the unitarity triangle $(\bar\rho,\bar\eta)$ by combining the information on mixing induced CP violation in $B\to\pi^+\pi^-$, $S$, with the precision observable $\sin 2\beta$ obtained from the CP asymmetry in $B\to\psi K_S$. It is then possible to write down exact analytical expressions for $\bar\rho$ and $\bar\eta$ as simple functions of the observables $S$ and $\sin 2\beta$, and of the penguin parameters $r$ and $\phi$. As an application clean lower bounds on $\bar\eta$ and $1-\bar\rho$ can be derived as functions of $S$ and $\sin 2\beta$, essentially without hadronic uncertainty. Computing $r$ and $\phi$ within QCD factorization yields precise determinations of $\bar\rho$ and $\bar\eta$ since the dependence on $r$ and $\phi$ is rather weak. It is emphasized that the sensitivity to the phase $\phi$ enters only at second order and is extremely small for moderate values of this phase, predicted in the heavy-quark limit. Transparent analytical formulas are further given and discussed for the parameter $C$ of direct CP violation in $B\to\pi^+\pi^-$. We also discuss alternative ways to analyze $S$ and $C$ that can be useful if new physics affects $B_d$--$\bar B_d$ mixing. Predictions and uncertainties for $r$ and $\phi$ in QCD factorization are examined in detail. It is pointed out that a simultaneous expansion in $1/m_b$ and 1/N leads to interesting simplifications. At first order infrared divergences are absent, while the most important effects are retained. Independent experimental tests of the factorization framework are briefly discussed.Comment: 26 pages, 7 figure

CP violation in B meson decays

Recent CP asymmetry measurements in tree-dominated processes, $B^0\to \pi^+\pi^-, \rho^+\rho^-, \rho^{\pm}\pi^{\mp}, B^+\to DK^+$, and in penguin-dominated decays, $B \to \pi^0 K_S, \eta' K_S, \phi K_S$, are interpreted in the framework of the Kobayashi-Maskawa (KM) mechanism of CP violation. The KM phase emerges as the dominant source of CP violation in tree-dominated decays, which are beginning to constrain the unitarity triangle beyond other constraints. Improving precision of CP asymmetry measurements in penguin-dominated decays may indicate the need for new physics.Comment: Talk presented at the Sixth International Conference on Hyperons, Charm and Beauty Hadrons, IIT, Chicago, June 27--July 3 200

Implications of CP Asymmetries in B→π+π−B \to \pi^+ \pi^-

CP asymmetries in $B^0(t)\to \pi^+ \pi^-$ are studied by relating this process in broken flavor SU(3) with $B^+\to K^0\pi^+$ and $B^0\to K^+\pi^-$. Using two different scenarios for SU(3) breaking, we show that the range of values of the weak phase $\alpha$ permitted by the measured asymmetries overlaps with that obtained from other CKM constraints, supporting the KM origin of the asymmetries. We evaluate the potential precision of this method to improve the determination of $\alpha$.Comment: 10 pages, 2 figures. To be submitted to Phys. Lett. B. Minor addition