Scattering in one dimension: The coupled Schroedinger equation, threshold behaviour and Levinson's theorem

We formulate scattering in one dimension due to the coupled Schr\"{o}dinger equation in terms of the $S$ matrix, the unitarity of which leads to constraints on the scattering amplitudes. Levinson's theorem is seen to have the form $\eta(0) = \pi (n_b + 1/2 n - 1/2 N)$, where $\eta(0)$ is the phase of the $S$ matrix at zero energy, $n_b$ the number of bound states with nonzero binding energy, $n$ the number of half-bound states, and $N$ the number of coupled equations. In view of the effects due to the half-bound states, the threshold behaviour of the scattering amplitudes is investigated in general, and is also illustrated by means of particular potential models.Comment: to appear in Journal of Mathematic Physics, RevTex, 16 pages, 3 figures (PostScript

Higgs Sector of the Left-Right Model with Explicit CP Violation

We explore the Higgs sector of the Minimal Left-Right (LR) Model based on the gauge group SU(2)_L x SU(2)_R x U(1)_{B-L} with explicit CP violation in the Higgs potential. Since flavour-changing neutral current experiments and the small scale of neutrino masses both place stringent constraints on the Higgs potential, we seek to determine whether minima of the Higgs potential exist that are consistent with current experimental bounds. We focus on the case in which the right-handed symmetry-breaking scale is only ``moderately'' large, of order 15-50 TeV. Unlike the case in which the Higgs potential is CP-invariant, the CP noninvariant case does yield viable scenarios, although these require a small amount of fine-tuning. We consider a LR model supplemented by an additional U(1) horizontal symmetry, which results in a Higgs sector consistent with current experimental constraints and a realistic spectrum of neutrino masses.Comment: 20 pages, 2 figure

Factor PD-Clustering

Factorial clustering methods have been developed in recent years thanks to the improving of computational power. These methods perform a linear transformation of data and a clustering on transformed data optimizing a common criterion. Factorial PD-clustering is based on Probabilistic Distance clustering (PD-clustering). PD-clustering is an iterative, distribution free, probabilistic, clustering method. Factor PD-clustering make a linear transformation of original variables into a reduced number of orthogonal ones using a common criterion with PD-Clustering. It is demonstrated that Tucker 3 decomposition allows to obtain this transformation. Factor PD-clustering makes alternatively a Tucker 3 decomposition and a PD-clustering on transformed data until convergence. This method could significantly improve the algorithm performance and allows to work with large dataset, to improve the stability and the robustness of the method

Neutrinos in a left-right model with a horizontal symmetry

We analyze the lepton sector of a Left-Right Model based on the gauge group SU(2)_L x SU(2)_R x U(1), concentrating mainly on neutrino properties. Using the seesaw mechanism and a horizontal symmetry, we keep the right-handed symmetry breaking scale relatively low, while simultaneously satisfying phenomenological constraints on the light neutrino masses. We take the right-handed scale to be of order 10's of TeV and perform a full numerical analysis of the model's parameter space, subject to experimental constraints on neutrino masses and mixings. The numerical procedure yields results for the right-handed neutrino masses and mixings and the various CP-violating phases. We also discuss phenomenological applications of the model to neutrinoless double beta decay, lepton-flavor-violating decays (including decays such as \tau \to 3\mu) and leptogenesis.Comment: 26 pages, 4 figure

Bootstrap confidence intervals for principal covariates regression

Principal covariate regression (PCOVR) is a method for regressing a set of criterion variables with respect to a set of predictor variables when the latter are many in number and/or collinear. This is done by extracting a limited number of components that simultaneously synthesize the predictor variables and predict the criterion ones. So far, no procedure has been offered for estimating statistical uncertainties of the obtained PCOVR parameter estimates. The present paper shows how this goal can be achieved, conditionally on the model specification, by means of the bootstrap approach. Four strategies for estimating bootstrap confidence intervals are derived and their statistical behaviour in terms of coverage is assessed by means of a simulation experiment. Such strategies are distinguished by the use of the varimax and quartimin procedures and by the use of Procrustes rotations of bootstrap solutions towards the sample solution. In general, the four strategies showed appropriate statistical behaviour, with coverage tending to the desired level for increasing sample sizes. The main exception involved strategies based on the quartimin procedure in cases characterized by complex underlying structures of the components. The appropriateness of the statistical behaviour was higher when the proper number of components were extracted

Candecomp/Parafac with zero constraints at arbitrary positions in a loading matrix

When one interprets Candecomp/Parafac (CP) solutions for analyzing three-way data, small loadings are often ignored, that is, considered to be zero. Rather than just considering them zero, it seems better to actually model such values as zero. This can be done by successive modeling approaches as well as by a simultaneous modeling approach. This paper offers algorithms for three such approaches, and compares them on the basis of empirical data and a simulation study. The conclusion of the latter was that, under realistic circumstances, all approaches recovered the underlying structure well, when the number of values to constrain to zero was given. Whereas the simultaneous modeling approach seemed to perform slightly better, differences were very small and not substantial. Given that the simultaneous approach is far more time consuming than the successive approaches, the present study suggests that for practical purposes successive approaches for modeling zeros in the CP model seem to be indicated

A New Opinion Polarization Index Developed by Integrating Expert Judgments

Opinion polarization is increasingly becoming an issue in today’s society, producing both unrest at the societal level, and conflict within small scale communications between people of opposite opinion. Often, opinion polarization is conceptualized as the direct opposite of agreement and consequently operationalized as an index of dispersion. However, in doing so, researchers fail to account for the bimodality that is characteristic of a polarized opinion distribution. A valid measurement of opinion polarization would enable us to predict when, and on what issues conflict may arise. The current study is aimed at developing and validating a new index of opinion polarization. The weights of this index were derived from utilizing the knowledge of 58 international experts on polarization through an expert survey. The resulting Opinion Polarization Index predicted expert polarization scores in opinion distributions better than common measures of polarization, such as the standard deviation, Van der Eijk’s polarization measure and Esteban and Ray’s polarization index. We reflect on the use of expert ratings for the development of measurements in this case, and more in general

CP Violation in Three-Body Chargino Decays

CP violation in supersymmetry can give rise to rate asymmetries in the decays of supersymmetric particles. In this work we compute the rate asymmetries for the three-body chargino decays \tilde\chi^\pm_2 \to \tilde\chi^\pm_1 HH, \tilde\chi^\pm_2 \to \tilde\chi^\pm_1 ZZ, \tilde\chi^\pm_2 \to \tilde\chi^\pm_1 W^+ W^- and \tilde\chi^\pm_2 \to tilde\chi^\pm_1 ZH. Each of the decays contains contributions mediated by neutral Higgs bosons that can possibly go on shell. Such contributions receive a resonant enhancement; furthermore, the strong phases required for the CP asymmetries come from the widths of the exchanged Higgs bosons. Our results indicate that the rate asymmetries can be relatively large in some cases, while still respecting a number of important low-energy bounds such as those coming from B meson observables and electric dipole moments. For the parameters that we consider, rate asymmetries of order 10% are possible in some cases.Comment: 17 pages, 4 figures, published versio