Exploring CP Violation through Correlations in B --> pi K, B_d --> pi^+pi^-, B_s --> K^+K^- Observable Space

We investigate allowed regions in observable space of B --> pi K, B_d --> pi^+pi^- and B_s --> K^+K^- decays, characterizing these modes in the Standard Model. After a discussion of a new kind of contour plots for the $B\to\pi K$ system, we focus on the mixing- induced and direct CP asymmetries of the decays B_d --> pi^+pi^- and B_s--> K^+K^-. Using experimental information on the CP-averaged B_d --> pi^{+/-}K^{+/-} and B_d --> pi^+pi^- branching ratios, the relevant hadronic penguin parameters can be constrained,implying certain allowed regions in observable space. In the case of B_d --> pi^+pi^-, an interesting situation arises now in view of the recent B-factory measurements of CP violation in this channel, allowing us to obtain new constraints on the CKM angle gamma as a function of the B^0_d--\bar{B^0_d} mixing phase phi_d=2beta, which is fixed through A_{CP}^{mix}(B_d --> J/psi K_S) up to a twofold ambiguity. If we assume that A_{CP}^{mix}(B_d --> pi^+pi^-) is positive, as indicated by recent Belle data, and that phi_d is in agreement with the ``indirect'' fits of the unitarity triangle, also the corresponding values for gamma around 60 degrees can be accommodated. On the other hand, for the second solution of phi_d, we obtain a gap around gamma ~ 60 degrees. The allowed region in the space of A_{CP}^{mix}(B_s --> K^+K^-) and A_{CP}^{dir}(B_s --> K^+K^-) is very constrained in the Standard Model, thereby providing a narrow target range for run II of the Tevatron and the experiments of the LHC era.Comment: 34 pages, LaTeX, 12 figures. More detailed introduction and a few Comments added, conclusions unchanged. To appear in Phys. Rev.

Weak Phase γ\gamma From Ratio of B→KπB \to K \pi Rates

The ratio of partial decay rates for charged and neutral $B$ mesons to $K \pi$ final states provides information on the weak phase $\gamma \equiv {\rm Arg} (V_{ub}^*)$ when augmented with information on the CP-violating asymmetry in the $K^\pm \pi^\mp$ mode. The requirements for a useful determination of $\gamma$ are examined in the light of present information about the decays $B^0 \to K^+ \pi^-$, $B^+ \to K^0 \pi^+$, and the corresponding charge-conjugate modes. The effects of electroweak penguins and rescattering corrections are noted, and proposals are made for estimating and measuring their importance.Comment: 16 pages, latex, 3 figures, revised version sent to Phys. Rev.

Exploring CP Violation with BcB_c Decays

We point out that the pure ``tree'' decays $B_c^\pm\to D^\pm_s D$ are particularly well suited to extract the CKM angle $\gamma$ through amplitude relations. In contrast to conceptually similar strategies using $B^\pm\to K^\pm D$ or $B_d\to K^{\ast0} D$ decays, the advantage of the $B_c$ approach is that the corresponding triangles have three sides of comparable length and do not involve small amplitudes. Decays of the type $B_c^\pm\to D^\pm D$ -- the $U$-spin counterparts of $B_c^\pm\to D^\pm_s D$ -- can be added to the analysis, as well as channels, where the $D^\pm_s$- and $D^\pm$-mesons are replaced by higher resonances.Comment: 9 pages, LaTeX, 3 figures, reference adde

A Possibility of large electro-weak penguin contribution in B -> K pi modes

We discuss about a possibility of large electro-weak penguin contribution in B -> K pi from recent experimental data. The several relations among the branching ratios which realize when the contributions from tree type and electro-weak penguin are small compared with the gluon penguin and can be treated as the expansion parameters do not satisfy the data. The difference comes from the r^2 terms which is the square of the ratio with the gluon penguin and the main contribution comes from electro-weak penguin. We find that the contribution from electro-weak penguin may be large to explain the experimental data. If the magnitude estimated from experiment is quite large compared with the theoretical estimation, then it may be including some new physics effects.Comment: 11 pages, 1 figure, Typos correcte

Rescattering Information from B→KKˉB \to K \bar K Decays

Rescattering effects can modify the dependence on the weak phase $\gamma = -{\rm Arg}(V^*_{ub}V_{ud}/V^*_{cb} V_{cd})$ of the ratio of rates for $B^{\pm} \to K \pi^\pm$ and $B \to K^\pm \pi^\mp$. A test for these effects based on the processes $B^\pm \to K^\pm K$ has been suggested. It is pointed out that the rates for the processes $B \to K^+ K^-$, which are expected to be {\it dominated} by rescattering and for which considerably better experimental bounds exist, are likely to provide a more stringent constraint on these effects.Comment: 22 pages, latex, 7 figures, to be published in Phys. Rev. D. Minor corrections and addition

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

Bs,d→ππ,πK,KKB_{s,d} \to \pi\pi,\pi K, KK: Status and Prospects

Several years ago, it was pointed out that the U-spin-related decays $B_d\to\pi^+\pi^-$, $B_s\to K^+K^-$ and $B_d\to\pi^\mp K^\pm$, $B_s\to \pi^\pm K^\mp$ offer interesting strategies for the extraction of the angle gamma of the unitarity triangle. Using the first results from the Tevatron on the $B_s$ decays and the B-factory data on $B_{u,d}$ modes, we compare the determinations of gamma from both strategies, study the sensitivity on U-spin-breaking effects, discuss the resolution of discrete ambiguities, predict observables that were not yet measured but will be accessible at LHCb, explore the extraction of the width difference $\Delta\Gamma_s$ from untagged $B_s\to K^+K^-$ rates, and address the impact of new physics. The data for the $B_d\to\pi^+\pi^-$, $B_s\to K^+K^-$ system favour the BaBar measurement of direct CP violation in $B_d\to\pi^+\pi^-$, which will be used in the numerical analysis, and result in a fortunate situation, yielding $\gamma=(66.6^{+4.3+4.0}_{-5.0-3.0})^\circ$, where the latter errors correspond to a generous estimate of U-spin-breaking effects. On the other hand, the $B_d\to\pi^\mp K^\pm$, $B_s\to \pi^\pm K^\mp$ analysis leaves us with $26^\circ\leq\gamma\leq70^\circ$, and points to a value of the $B_s\to \pi^\pm K^\mp$ branching ratio that is larger than the current Tevatron result. An important further step will be the measurement of mixing-induced CP violation in $B_s\to K^+K^-$, which will also allow us to extract the $B^0_s$--$\bar B^0_s$ mixing phase unambiguously with the help of $B_s\to J/\psi \phi$ at the LHC. Finally, the measurement of direct CP violation in $B_s\to K^+K^-$ will make the full exploitation of the physics potential of the $B_{s,d}\to \pi\pi, \pi K, KK$ modes possible.Comment: 28 pages, 10 figure

Vibration analysis of moving machine tool axes based on phase information in video data

Vibrations of machine tools limit quality and productivity and therefore need to be analyzed. Video based vibration analysis using spatial phase information could in principle reduce measuring effort significantly. However, feasibility of these approaches for moving machine tool axes and relative movement between camera and object is yet to be shown. This paper investigates an approach for stabilizing linear axis movement to analyze vibration. It is shown that shaker induced vibration on a linearly moving clamping tower can be derived for low frequencies. However, influences of actual cutting processes as well as compensation of unwanted camera vibration needs further investigation

A Critical Study of B Decays to Light Pseudoscalar

Motivated by the large branching ratios observed for the process $B\to\eta^{\prime}K$, we examine critically all the ingredients that go into estimates of B decays into two light pseudoscalars. Within factorization approximation, we examine several assumptions on the input parameters that could have a strong bearing on the predictions. Among these are (i) the QCD scale $\mu$ (ii) value of the form factors (iii) value of the light quark masses, and in particular $m_s$ (iv) the value $\xi=1/N_c$, (v) charm content of $\eta^{\prime}$. It is possible to account for all the data without invoking new physics, though future experiments will provide tighter constraints on the parameter space. We fin that CP violating asymmetries are in the observable range for some modes.Comment: 29 pages(Latex), 17 figures, a few changes have been made, version to appear in Phys.Rev.