Maximally correlated multipartite quantum states

We investigate quantum states that posses both maximum entanglement and maximum discord between the pertinent parties. Since entanglement (discord) is defined only for bipartite (two qubit) systems, we shall introduce an appropriate sum over of all bi-partitions as the associated measure. The ensuing definition --not new for entanglement-- is thus extended here to quantum discord. Also, additional dimensions within the parties are considered ({\it qudits}). We also discuss nonlocality (in the form of maximum violation of a Bell inequality) for all multiqubit systems. The emergence of more nonlocal states than local ones, all of them possessing maximum entanglement, will be linked, surprisingly enough, to whether quantum mechanics is defined over the fields of real or complex numbers.Comment: 13 pages, 5 figures, 2 table

The Fine-Tuning Problem of the Electroweak Symmetry Breaking Mechanism in Minimal SUSY Models

We calculate the region of the MSSM parameter space (i.e. $M_{1/2}$, $m_{0}$, $\mu$, \ldots) compatible with a correct electroweak breaking and a realistic top-quark mass. To do so we have included {\em all} the one-loop corrections to the effective potential $V_{1}$ and checked their importance in order to obtain consistent results. We also consider the fine-tuning problem due to the enormous dependence of $M_{Z}$ on $h_{t}$ (the top Yukawa coupling), which is substantially reduced when the one-loop effects are taken into account. We also explore the reliability of the so-called "standard" criterion to estimate the degree of fine-tuning. As a consequence, we obtain a new set of upper bounds on the MSSM parameters or, equivalently, on the supersymmetric masses perfectly consistent with the present experimental bounds.Comment: talk given at the XVI Kazimierz Meeting on Elementary Particle Physics, Kazimierz (Poland) 24-28 May 1993, 4 pages in standard LATEX + 2 figures (not included but available upon request), CERN-TH.7024/9

Large mixing angles for neutrinos from infrared fixed points

Radiative amplification of neutrino mixing angles may explain the large values required by solar and atmospheric neutrino oscillations. Implementation of such mechanism in the Standard Model and many of its extensions (including the Minimal Supersymmetric Standard Model) to amplify the solar angle, the atmospheric or both requires (at least two) quasi-degenerate neutrino masses, but is not always possible. When it is, it involves a fine-tuning between initial conditions and radiative corrections. In supersymmetric models with neutrino masses generated through the Kahler potential, neutrino mixing angles can easily be driven to large values at low energy as they approach infrared pseudo-fixed points at large mixing (in stark contrast with conventional scenarios, that have infrared pseudo-fixed points at zero mixing). In addition, quasi-degeneracy of neutrino masses is not always required.Comment: 36 pages, 7 ps figure

Implications for New Physics from Fine-Tuning Arguments: II. Little Higgs Models

We examine the fine-tuning associated to electroweak breaking in Little Higgs scenarios and find it to be always substantial and, generically, much higher than suggested by the rough estimates usually made. This is due to implicit tunings between parameters that can be overlooked at first glance but show up in a more systematic analysis. Focusing on four popular and representative Little Higgs scenarios, we find that the fine-tuning is essentially comparable to that of the Little Hierarchy problem of the Standard Model (which these scenarios attempt to solve) and higher than in supersymmetric models. This does not demonstrate that all Little Higgs models are fine-tuned, but stresses the need of a careful analysis of this issue in model-building before claiming that a particular model is not fine-tuned. In this respect we identify the main sources of potential fine-tuning that should be watched out for, in order to construct a successful Little Higgs model, which seems to be a non-trivial goal.Comment: 39 pages, 26 ps figures, JHEP forma