B Physics: CP Violation Beyond the SM

We analyse the present experimental evidence for a complex CKM matrix, even allowing for New Physics contributions to $\epsilon_{K}$, $a_{J/\Psi K_{S}}$%, $\Delta M_{B_{d}}$, $\Delta M_{B_{s}}$, and the $\Delta I=1/2$ piece of $\rho \rho$ and $B\to \rho \pi$. We emphasize the crucial r\^{o}le played by the angle $\gamma$ in both providing irrefutable evidence for a 3$\times$3 complex CKM matrix and placing constraints on the size of NP contributions. It is shown that even if one allows for New Physics a real CKM matrix is excluded at a 99.92% C.L., and the probability for the phase $\gamma$ to be in the interval $[-170^{\circ};-10^{\circ}]\cup \lbrack 10^{\circ};170^{\circ}]$ is 99.7%. Large value of the phase $\chi$, e.g. of order $\lambda$, is only possible in models where the unitarity of the $3\times 3$ Cabibbo-Kobayashi-Maskawa matrix is violated through the introduction of extra $Q=2/3$ quarks. We study the allowed range for $\chi$ and the effect of a large $\chi$ on various low-energy observables, such as CP asymmetries in $B$ meson decays. We also discuss the correlated effects which would be observable at high energy colliders, like decays $t\to cZ$, etc..Comment: 14 pages, 7 figures. Presented at the Symposium in Honour of Gustavo C. Branco "CP Violation and the Flavour Puzzle", Lisbon, Portugal, 19-20 July 2005. To appear in Acta Physica Polonica

Coexistence of periods in a bisecting bifurcation

The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.Comment: 13 pages, 5 figure

A Novel Kind of Neutrino Oscillation Experiment

A novel method to look for neutrino oscillations is proposed based on the elastic scattering process $\bar{\nu}_{i} e^{-}\rightarrow \bar{\nu}_{i} e^{-}$, taking advantage of the dynamical zero present in the differential cross section for $\bar{\nu}_{e} e^{-}\rightarrow \bar{\nu}_{e} e^{-}$. An effective tunable experiment between the "appearance" and "disappearance" limits is made possible. Prospects to exclude the allowed region for atmospheric neutrino oscillations are given.Comment: 11 pages (+3 figures, available upon request),Standard Latex, FTUV/94-3

Bifurcations in the Lozi map

We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.Comment: 17 pages, 12 figure

Invariant approach to flavour-dependent CP-violating phases in the MSSM

We use a new weak basis invariant approach to classify all the observable phases in any extension of the Standard Model (SM). We apply this formalism to determine the invariant CP phases in a simplified version of the Minimal Supersymmetric SM with only three non-trivial flavour structures. We propose four experimental measures to fix completely all the observable phases in the model. After these phases have been determined from experiment, we are able to make predictions on any other CP-violating observable in the theory, much in the same way as in the Standard Model all CP-violation observables are proportional to the Jarlskog invariant.Comment: 25 pages, 12 figure

Vacuum Induced CP Violation Generating a Complex CKM Matrix with Controlled Scalar FCNC

We propose a viable minimal model with spontaneous CP violation in the framework of a Two Higgs Doublet Model. The model is based on a generalised Branco-Grimus-Lavoura model with a flavoured $\mathbb{Z}_2$ symmetry, under which two of the quark families are even and the third one is odd. The lagrangian respects CP invariance, but the vacuum has a CP violating phase, which is able to generate a complex CKM matrix, with the rephasing invariant strength of CP violation compatible with experiment. The question of scalar mediated flavour changing neutral couplings is carefully studied. In particular we point out a deep connection between the generation of a complex CKM matrix from a vacuum phase and the appearance of scalar FCNC. The scalar sector is presented in detail, showing that the new scalars are necessarily lighter than 1 TeV. A complete analysis of the model including the most relevant constraints is performed, showing that it is viable and that it has definite implications for the observation of New Physics signals in, for example, flavour changing Higgs decays or the discovery of the new scalars at the LHC. We give special emphasis to processes like $t\to {\rm h} c,{\rm h} u$, as well as ${\rm h}\to bs, bd$, which are relevant for the LHC and the ILC.Comment: 36 pages, 11 figure