A short look at epsilon'/epsilon

We analyze the theoretical implications of the new KTeV measurement of direct CP-violation in K->pi pi decays. The result is found consistent with the Standard Model for low values of the strange quark mass m_s. If the hadronic parameters B_6^{(1/2)} and B_8^{(3/2)} satisfy 2 B_6^{(1/2)} - B_8^{(3/2)} < 2, as suggested by lattice and 1/N_c calculations, we find an upper bound of 110 MeV for m_s (2 GeV)$. We parametrize potential new physics contributions to \epsilon'/\epsilon and illustrate their correlation with upper bounds on m_s. Finally we discuss a non-perturbative mechanism, which is not contained in the existing calculations of B_6^{(1/2)}. This mechanism enhances B_6^{(1/2)} and thereby leads to a better understanding of the Delta I=1/2 rule and the high measured value of Re (\epsilon^\prime/\epsilon)Comment: typo in eq. (5) corrected, 2 refs. added, some clarifications in text, keywords/PACS-no. adde

Fat penguins and imaginary penguins in perturbative QCD

We evaluate $B\to K\pi$ decay amplitudes in perturbative QCD picture. It is found that penguin contributions are dynamically enhanced by nearly 50% compared to those assumed in the factorization approximation. It is also shown that annihilation diagrams are not negligible, and give large strong phases. Our results for branching ratios of $B\to K\pi$ decays for a representative parameter set are consistent with data. We evaluate $B\to K\pi$ decay amplitudes in perturbative QCD picture. It is found that penguin contributions are dynamically enhanced by nearly 50% compared to those assumed in the factorization approximation. It is also shown that annihilation diagrams are not negligible, and give large strong phases. Our results for branching ratios of $B\to K\pi$ decays for a representative parameter set are consistent with data.Comment: 11 pages, Latex2e, 3 figures, corrected some typos and reduced no. of figures. Changed the abstract, Submit at PL

CP--Violating Invariants in Supersymmetry

I study the weak basis CP-violating invariants in supersymmetric models, in particular those which cannot be expressed in terms of the Jarlskog--type invariants, and find basis--independent conditions for CP conservation. With an example of the K-anti-K mixing, I clarify what are the combinations of supersymmetric parameters which are constrained by experiment.Comment: matches the PRD versio

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

Implications of the CP asymmetry in semileptonic B decay

Recent experimental searches for $A_{SL}$, the CP asymmetry in semileptonic B decay, have reached an accuracy of order one percent. Consequently, they give meaningful constraints on new physics. We find that cancellations between the Standard Model (SM) and new physics contributions to $B^0 - \bar B^0$ mixing cannot be as strong as was allowed prior to these measurements. The predictions for this asymmetry within the SM and within models of minimal flavor violation (MFV) are below the reach of present and near future measurements. Including order $m_c^2/m_b^2$ and $\Lambda_{QCD}/m_b$ corrections we obtain the SM prediction: $-1.3 \times 10^{-3} < A_{SL} < -0.5 \times 10^{-3}$. Future measurements can exclude not only the SM, but MFV as well, if the sign of the asymmetry is opposite to the SM or if it is same-sign but much enhanced. We also comment on the CP asymmetry in semileptonic $B_s$ decay, and update the range of the angle $\beta_s$ in the SM: $0.026 < \sin2\beta_s < 0.048$.Comment: 16 pages, a sign typo in eq.(11) fixed, to appear in Phys. Rev.

Analysis of Supersymmetric Effects on B -> phi K Decays in the PQCD Approach

We study the effects of the MSSM contribution on B -> phi K decays using the perturbative QCD approach. In this approach, strong phases can be calculated, so that we can predict the values of CP asymmetries with the MSSM contribution. We predict a large relative strong phase between the penguin amplitude and the chromomagnetic penguin amplitude. If there is a new CP violating phase in the chromomagnetic penguin amplitude, then the CP asymmetries may change significantly from the SM prediction. We parametrize the new physics contributions that appear in the Wilson coefficients. We maximize the new physics parameters up to the point where it is limited by experimental constraints. In the case of the LR insertion, we find that the direct CP asymmetries can reach about 85% and the indirect CP asymmetry can reach about -30%.Comment: 18 pages, 9 figures, REVTeX, Minor changes, Version to appear in Phys. Rev.

Aspects of Soft and Spontaneous CP Violation

We study four different models for CP violation: the standard (KM) model, the aspon model of spontaneous breaking and two models of soft breaking. In all except the standard model, the strong CP problem is addressed and solved. Testable predictions for the area of the unitarity triangle and for (epsilon'/epsilon)_K are emphasized. The issue of CP violation may well become the first place where the standard model of particle theory is shown definitively to be deficient. There are two reasons for expecting this to happen: (1) the strong CP problem is still not understood in the unadorned standard model and (2) the KM mechanism, although unquestionably present, may not provide the full explanation of epsilon_K and (epsilon'/epsilon)_K.Comment: 24 pages LaTeX including 4 figures. Minor modification to analysis of lower bound for d_n, summarized in new Table I

B -> K eta(') decay in perturbative QCD

We compute B->K eta' branching ratio using perturbative QCD approach. We show that a triangular relation among amplitudes for B^0->K^0 pi^0, B^0->K^0 eta, B^0->K^0 eta' receives large corrections from SU(3) breaking effects. If experimental value will come closer to the lower limit of the present BELLE data there will be a possibility to understand the large branching ratio of B^0->K^0 eta'. Otherwise, we perhaps need to modify our understanding of eta' meson, for example, inclusion of a possible admixture of gluonium state.Comment: 15 pages, LaTex, axodraw style fil

Branching ratios of B+→D(∗)+K(∗)0B^+ \to D^{(*)+}K^{(*)0} decays in perturbative QCD approach

We study the rare decays $B^+ \to D^{(*)+}K^{(*)0}$, which can occur only via annihilation type diagrams in the standard model. We calculate all of the four modes, $B \to PP, VP, PV, VV$, in the framework of perturbative QCD approach and give the branching ratios of the order about $10^{-6}$.Comment: 18 pages, 1 figure, Revte

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.