Long range forces induced by neutrinos at finite temperature

We revisit and extend previous work on neutrino mediated long range forces in a backround at finite temperature. For Dirac neutrinos, we correct existing results. We also give new results concerning spin-dependent as well as spin-independent long range forces associated to Majorana neutrinos. An interesting outcome of the investigation is that, for both types of neutrinos whether massless or not, the effect of the relic neutrino heat bath is to convert those forces into attractive ones in the supra-millimeter scale while they stay repulsive within the sub-millimeter scale.Comment: 8 pages, Latex, 1 figur

Flavour-conserving oscillations of Dirac-Majorana neutrinos

We analyze both chirality-changing and chirality-preserving transitions of Dirac-Majorana neutrinos. In vacuum, the first ones are suppressed with respect to the others due to helicity conservation and the interactions with a (``normal'') medium practically does not affect the expressions of the probabilities for these transitions, even if the amplitudes of oscillations slightly change. For usual situations involving relativistic neutrinos we find no resonant enhancement for all flavour-conserving transitions. However, for very light neutrinos propagating in superdense media, the pattern of oscillations $\nu_L \to \nu^C_L$ is dramatically altered with respect to the vacuum case, the transition probability practically vanishing. An application of this result is envisaged.Comment: 14 pages, latex 2E, no 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

Coherence of neutrino flavor mixing in quantum field theory

In the simplistic quantum mechanical picture of flavor mixing, conditions on the maximum size and minimum coherence time of the source and detector regions for the observation of interference---as well as the very viability of the approach---can only be argued in an ad hoc way from principles external to the formalism itself. To examine these conditions in a more fundamental way, the quantum field theoretical $S$-matrix approach is employed in this paper, without the unrealistic assumption of microscopic stationarity. The fully normalized, time-dependent neutrino flavor mixing event rates presented here automatically reveal the coherence conditions in a natural, self-contained, and physically unambiguous way, while quantitatively describing the transition to their failure.Comment: 12 pages, submitted to Phys. Rev.

Towards a unique formula for neutrino oscillations in vacuum

We show that all correct results obtained by applying quantum field theory to neutrino oscillations can be understood in terms of a single oscillation formula. In particular, the model proposed by Grimus and Stockinger is shown to be a subcase of the model proposed by Giunti, Kim and Lee, while the new oscillation formulas proposed by Ioannisian and Pilaftsis and by Shtanov are disproved. We derive an oscillation formula without making any relativistic assumption and taking into account the dispersion, so that the result is valid for both neutrinos and mesons. This unification gives a stronger phenomenological basis to the neutrino oscillation formula. We also prove that the coherence length can be increased without bound by more accurate energy measurements. Finally, we insist on the wave packet interpretation of the quantum field treatments of oscillations.Comment: 30 pages, 1 figure; the proof that plane wave oscillations do no exist is extended to stationary models; the influence of dispersion is explained in more detail

Three heavy jet events at hadron colliders as a sensitive probe of the Higgs sector

Assuming that a non-standard neutral Higgs with an enhanced Yukawa coupling to a bottom quark is observed at future hadron experiments, we propose a method for a better understanding of the Higgs sector. Our procedure is based on "counting" the number of events with heavy jets (where "heavy" stands for a c or b jet) versus b jets, in the final state of processes in which the Higgs is produced in association with a single high p_T c or b jet. We show that an observed signal of the type proposed, at either the Tevatron or the LHC, will rule out the popular two Higgs doublet model of type II as well as its supersymmetric version - the Minimal Supersymmetric Standard Model (MSSM), and may provide new evidence in favor of some more exotic multi Higgs scenarios. As an example, we show that in a version of a two Higgs doublet model which naturally accounts for the large mass of the top quark, our signal can be easily detected at the LHC within that framework. We also find that such a signal may be observable at the upgraded Tevatron RunIII, if the neutral Higgs in this model has a mass around 100 GeV and \tan\beta > 50 and if the efficiency for distinguishing a c jet from a light jet will reach the level of 50%.Comment: Revtex, 11 pages, 4 figures embedded in the text. Main changes with respect to Version 1: Numerical results re-calculated using the CTEQ5L pdf, improved discussion on the experimental consequences, new references added. Conclusions remain unchanged. As will appear in Phys. Rev.

Simplicity transformations for three-way arrays with symmetric slices, and applications to Tucker-3 models with sparse core arrays

AbstractTucker three-way PCA and Candecomp/Parafac are two well-known methods of generalizing principal component analysis to three way data. Candecomp/Parafac yields component matrices A (e.g., for subjects or objects), B (e.g., for variables) and C (e.g., for occasions) that are typically unique up to jointly permuting and rescaling columns. Tucker-3 analysis, on the other hand, has full transformational freedom. That is, the fit does not change when A,B, and C are postmultiplied by nonsingular transformation matrices, provided that the inverse transformations are applied to the so-called core array G̲. This freedom of transformation can be used to create a simple structure in A,B,C, and/or in G̲. This paper deals with the latter possibility exclusively. It revolves around the question of how a core array, or, in fact, any three-way array can be transformed to have a maximum number of zero elements. Direct applications are in Tucker-3 analysis, where simplicity of the core may facilitate the interpretation of a Tucker-3 solution, and in constrained Tucker-3 analysis, where hypotheses involving sparse cores are taken into account. In the latter cases, it is important to know what degree of sparseness can be attained as a tautology, by using the transformational freedom. In addition, simplicity transformations have proven useful as a mathematical tool to examine rank and generic or typical rank of three-way arrays. So far, a number of simplicity results have been attained, pertaining to arrays sampled randomly from continuous distributions. These results do not apply to three-way arrays with symmetric slices in one direction. The present paper offers a number of simplicity results for arrays with symmetric slices of order 2×2,3×3 and 4×4. Some generalizations to higher orders are also discussed. As a mathematical application, the problem of determining the typical rank of 4×3×3 and 5×3×3 arrays with symmetric slices will be revisited, using a sparse form with only 8 out of 36 elements nonzero for the former case and 10 out of 45 elements nonzero for the latter one, that can be attained almost surely for such arrays. The issue of maximal simplicity of the targets to be presented will be addressed, either by formal proofs or by relying on simulation results