Calculation of Infrared-Divergent Feynman Diagrams with Zero Mass Threshold

Two-loop vertex Feynman diagrams with infrared and collinear divergences are investigated by two independent methods. On the one hand, a method of calculating Feynman diagrams from their small momentum expansion extended to diagrams with zero mass thresholds is applied. On the other hand, a numerical method based on a two-fold integral representation is used. The application of the latter method is possible by using lightcone coordinates in the parallel space. The numerical data obtained with the two methods are in impressive agreement.Comment: 20 pages, Latex with epsf-figures, References updated, to appear in Z.Phys.

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.

Relativistic description of electron scattering on the deuteron

Within a quasipotential framework a relativistic analysis is presented of the deuteron current. Assuming that the singularities from the nucleon propagators are important, a so-called equal time approximation of the current is constructed. This is applied to both elastic and inelastic electron scattering. As dynamical model the relativistic one boson exchange model is used. Reasonable agreement is found with a previous relativistic calculation of the elastic electromagnetic form factors of the deuteron. For the unpolarized inelastic electron scattering effects of final state interactions and relativistic corrections to the structure functions are considered in the impulse approximation. Two specific kinematic situations are studied as examples.Comment: (19 pages in revtex + 15 figures not included, available upon request.) report THU-93-10

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.

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.

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

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

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

Taming the Penguin in the B0(t) -> Pi+Pi- CP-asymmetry: Observables and Minimal Theoretical Input

Penguin contributions, being not negligible in general, can hide the information on the CKM angle alpha coming from the measurement of the time-dependent B0(t) -> pi+pi- CP-asymmetry. Nevertheless, we show that this information can be summarized in a set of simple equations, expressing alpha as a multi-valued function of a single theoretically unknown parameter, which conveniently can be chosen as a well-defined ratio of penguin to tree amplitudes. Using these exact analytic expressions, free of any assumption besides the Standard Model, and some reasonable hypotheses to constrain the modulus of the penguin amplitude, we derive several new upper bounds on the penguin-induced shift |2alpha-2alpha_eff|, generalizing the recent result of Grossman and Quinn. These bounds depend on the averaged branching ratios of some decays (pi0pi0, K0K0bar, K+-pi-+) particularly sensitive to the penguin. On the other hand, with further and less conservative approximations, we show that the knowledge of the B+- -> Kpi+- branching ratio alone gives sufficient information to extract the free parameter without the need of other measurements, and without knowing |V_td| or |V_ub|. More generally, knowing the modulus of the penguin amplitude with an accuracy of ~30% might result in an extraction of alpha competitive with the experimentally more difficult isospin analysis. We also show that our framework allows to recover most of the previous approaches in a transparent and simple way, and in some cases to improve them. In addition we discuss in detail the problem of the various kinds of discrete ambiguities.Comment: LaTeX2e, 44 pages, 9 figures (from 18 postscript files) included with epsf. Minor changes, references updated. New CLEO results from ICHEP'98 are taken into account. To appear in Phys. Rev.