CP Violation in B and K Decays: 2003

These lectures give a brief description of CP violation in B and K meson decays with particular emphasize put on the determination of the CKM matrix. The following topics will be discussed: i) The CKM matrix, the unitarity triangle and general aspects of the theoretical framework, ii) Particle-antiparticle mixing and various types of CP violation, iii) Standard analysis of the unitarity triangle, iv) The ratio epsilon^prime/epsilon, v) The most important strategies for the determination of the angles $\alpha$, $\beta$ and $\gamma$ from B decays, vi) Rare decays $K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$ vii) Models with minimal flavour violation.Comment: Schladming lectures 2003, Main latex-file, 8 figures, 51 page

Sweeping the Space of Admissible Quark Mass Matrices

We propose a new and efficient method of reconstructing quark mass matrices from their eigenvalues and a complete set of mixing observables. By a combination of the principle of NNI (nearest neighbour interaction) bases which are known to cover the general case, and of the polar decomposition theorem that allows to convert arbitrary nonsingular matrices to triangular form, we achieve a parameterization where the remaining freedom is reduced to one complex parameter. While this parameter runs through the domain bounded by a circle with radius R determined by the up-quark masses around the origin in the complex plane one sweeps the space of all mass matrices compatible with the given set of data.Comment: 18 page

Anatomy of Prominent B and K Decays and Signatures of CP-Violating New Physics in the Electroweak Penguin Sector

The recent observation of B_d -> pi^0 pi^0 at the B factories with a surprisingly large branching ratio represents a challenge for theory, and complements the amazingly small B_d -> pi^+ pi^- rate. We point out that all puzzling B -> pi pi features can be accommodated in the Standard Model (SM) through non-factorizable hadronic interference effects, extract the relevant parameters, and predict the CP asymmetries of B_d -> pi^0 pi^0. Using then SU(3) flavour-symmetry and plausible dynamical assumptions, we fix the hadronic B -> pi K parameters through their B -> pi pi counterparts, and determine the CKM angle gamma, with a result in remarkable accordance with the usual fits for the unitarity triangle. We may then analyse the B -> pi K system in the SM, where we find agreement with the experimental picture, with the exception of those observables that are significantly affected by electroweak (EW) penguins, thereby suggesting new physics (NP) in this sector. Indeed, a moderate enhancement of these topologies and a large CP-violating NP phase allow us to describe any currently observed feature of the B -> pi K modes, and to predict the CP-violating B_d -> pi^0 K_S observables. If we then restrict ourselves to a specific scenario where NP enters only through Z^0 penguins, we obtain a link to rare K and B decays, where the most spectacular NP effects are an enhancement of the K_L -> pi^0 nu nu_bar rate by one order of magnitude with BR(K_L -> pi^0 nu nu_bar) ~ 4 BR(K^+ -> pi^+ nu nu_bar), BR(K_L -> pi^0 e^+ e^-) = O(10^-10), (sin 2beta)_{pi nu nu_bar} < 0, and a large forward-backward CP asymmetry in B_d -> K^* mu^+ mu^-. We address also epsilon'/epsilon and other prominent decays, including B -> phi K and B -> J/psi K modes.Comment: 78 pages, 12 figures, LaTe

Renormalization of the neutrino mass matrix

The renormalization group equations for the general 2 by 2, complex, neutrino mass matrix are shown to have exact, analytic solutions. Simple formulas are given for the physical mixing angle, complex phase and mass ratio in terms of their initial values and the energy scales. We also establish a (complex) renormalization invariant relating these parameters. The qualitative features of the physical parameters' renormalization are clearly illustrated in vector field plots. In both the SM and MSSM, maximal mixing is a saddle point.Comment: 16 pages, 5 figure

Testing the Higgs Sector of the Minimal Supersymmetric Standard Model at Large Hadron Colliders

We study the Higgs sector of the Minimal Supersymmetric Standard Model, in the context of proton-proton collisions at LHC and SSC energies. We assume a relatively heavy supersymmetric particle spectrum, and include recent results on one-loop radiative corrections to Higgs-boson masses and couplings. We begin by discussing present and future constraints from the LEP experiments. We then compute branching ratios and total widths for the neutral ($h,H,A$) and charged ($H^\pm$) Higgs particles. We present total cross-sections and event rates for the important discovery channels at the LHC and SSC. Promising physics signatures are given by $h \to \gamma \gamma$, $H \to \gamma \gamma$ or $Z^* Z^*$ or $\tau^+ \tau^-$, $A \to \tau^+ \tau^-$, and $t \to b H^+$ followed by $H^+ \to \tau^+ \nu_{\tau}$, which should allow for an almost complete coverage of the parameter space of the model.Comment: 51 pages, 30 figures (not enclosed and not available via e-mail

Waiting for Precise Measurements of K^+->pi^+ nu nu and K_L->pi^0 nu nu

In view of future plans for accurate measurements of the theoretically clean branching ratios Br(K+ -> pi+ nu nu) and Br(KL -> pi0 nu nu), that should take place in the next decade, we collect the relevant formulae for quantities of interest and analyze their theoretical and parametric uncertainties. We point out that in addition to the angle beta in the unitarity triangle (UT) also the angle gamma can in principle be determined from these decays with respectable precision and emphasize in this context the importance of the recent NNLO QCD calculation of the charm contribution to K+ -> pi+ nu nu and of the improved estimate of the long distance contribution by means of chiral perturbation theory. In addition to known expressions we present several new ones that should allow transparent tests of the Standard Model (SM) and of its extensions. While our presentation is centered around the SM, we also discuss models with minimal flavour violation and scenarios with new complex phases in decay amplitudes and meson mixing. We give a brief review of existing results within specific extensions of the SM, in particular the Littlest Higgs Model with T-parity, Z' models, the MSSM and a model with one universal extra dimension. We derive a new "golden" relation between B and K systems that involves (beta,gamma) and Br(KL -> pi0 nu nu) and investigate the virtues of (R_t,beta), (R_b,gamma), (beta,gamma) and (etabar,gamma) strategies for the UT in the context of K -> pi nu nu decays with the goal of testing the SM and its extensions.Comment: 56 pages, 18 figures, Section on Long Distance Contributions, 2 Figures and few References added, Uses Rev Mod Phys Style; Includes new results of NNLO calculation as well as matrix elements, extended and modified sections on new physic