Anarchy and Neutrino Physics

The neutrino sector of a seesaw-extended Standard Model is investigated under the anarchy hypothesis. The previously derived probability density functions for neutrino masses and mixings, which characterize the type I-III seesaw ensemble of $N\times N$ complex random matrices, are used to extract information on the relevant physical parameters. For $N=2$ and $N=3$, the distributions of the light neutrino masses, as well as the mixing angles and phases, are obtained using numerical integration methods. A systematic comparison with the much simpler type II seesaw ensemble is also performed to point out the fundamental differences between the two ensembles. It is found that the type I-III seesaw ensemble is better suited to accommodate experimental data. Moreover, the results indicate a strong preference for the mass splitting associated to normal hierarchy. However, since all permutations of the singular values are found to be equally probable for a particular mass splitting, predictions regarding the hierarchy of the mass spectrum remains out of reach in the framework of anarchy.Comment: 1+22 pages, 8 figures, typos fixed, added referenc

Phénoménologie des neutrinos dans une théorie de matrices aléatoires

Le mécanisme permettant d’expliquer l’origine de la masse des neutrinos demeure, encore aujourd’hui, un mystère complet dont la résolution est susceptible de modifier considérablement la structure du modèle standard en physique des particules élémentaires. Dans la littérature, plusieurs candidats potentiels sont donc proposés afin de combler cette lacune et, ainsi, faire la lumière sur certaines des propriétés les plus étranges des neutrinos. Parmi ceux-ci, les mécanismes seesaw de type I, II et III constituent sans doute les approches les plus attrayantes et les plus étudiées. Cependant, bien que ces mécanismes offrent un cadre de travail simple et élégant pour expliquer la faible masse des neutrinos (l’ordre de grandeur), ceux-ci n’offrent aucune prédiction sur les paramètres fondamentaux caractérisant le phénomène d’oscillation, soit les angles de mélange, les phases complexes et la hiérarchie des masses. Afin d’obtenir des prédictions concrètes sur la phénoménologie des neutrinos, certaines hypothèses de travail supplémentaires doivent donc être formulées pour contraindre la structure des matrices de masse obtenue. Dans ce travail, l’hypothèse anarchique propre au secteur des neutrinos est adoptée. Les matrices de masse générées par les trois mécanismes seesaw dans la limite des basses énergies sont traitées dans le contexte d’une théorie de matrices aléatoires, ce qui permet de définir et d’analyser de nouveaux ensembles matriciels aléatoires appelés ensembles seesaw. Un cadre théorique unifié est donc présenté pour la construction de ces ensembles. Grâce au formalisme élaboré, qui repose sur les outils traditionnels relevant de la théorie des matrices aléatoires, les densités de probabilité jointes caractérisant ces ensembles sont obtenues de façon analytique. Une étude détaillée de leurs propriétés est alors réalisée, ce qui permet d’extraire les tendances dominantes propres à ces mécanismes de masse et d’analyser leurs conséquences pour le secteur des neutrinos du modèle standard étendu. En ce qui concerne le spectre de masse, les résultats obtenus indiquent que les mécanismes seesaw de type I et de type III sont plus adéquats pour reproduire les observations expérimentales. De plus, une forte préférence pour la différence de masses associée à la hiérarchie normale est observée. En contrepartie, il est également démontré que pour une différence de masses donnée entre les trois générations, toutes les permutations des masses sont équiprobables, ce qui rend hors de portée toute prédiction concernant la hiérarchie du spectre (normale ou inverse) sous l’hypothèse anarchique. En ce qui concerne les variables du groupe de symétrie (les angles de mélange et les phases complexes), on constate, d’une part, que la notion de mélange quasi-maximal est naturellement favorisée et, d’autre part, que la matrice PMNS peut être décrite comme une matrice unitaire générique tirée au hasard d’un ensemble matriciel caractérisé par la mesure de Haar du groupe de Lie correspondant. Par ailleurs, il est également démontré que ces conclusions sont indépendantes du mécanisme de masse considéré.The neutrino mass generation mechanism remains, to this day, a complete mystery which is likely to play an important role in understanding the foundations of the Standard Model of particle physics. In an effort to fill this gap and, ultimately, shed some light on some of the most intriguing properties of neutrinos, many theoretical models are proposed in the literature. Among the many candidates, the type I, type II and type III seesaw mechanisms may very well be the most attractive and the most studied propositions. However, despite the fact that these mechanisms provide a simple and elegant framework for explaining the smallness of neutrino masses (the order of magnitude), no prediction can be made on the fundamental parameters governing neutrino oscillations (the mixing angles, the CP-violating phases and the mass differences). Thus, to obtain concrete results regarding neutrino phenomenology, additional working assumptions must be made in order to constrain the structure of the corresponding mass matrices. In this work, the anarchy hypothesis relevant to the neutrino sector is investigated. The mass matrices generated by the three seesaw mechanisms in the low-energy limit are studied within the framework of random matrix theory, which leads to the development and the analysis of the seesaw ensembles. A unified and precise theoretical formalism, based on the usual tools of random matrix theory, is presented for the construction of these new random matrix ensembles. Using this formalism, the joint probability density functions characterizing these ensembles are obtained analytically, thus paving the way for a detailed study of their properties. This study is then carried out, revealing the underlying trends in these ensembles and, thereby, offering a thorough analysis of their consequences for the neutrino sector of the seesaw-extended Standard Model. Regarding the mass spectrum, it is found that the type I and type III seesaw mechanisms are better suited to accommodate experimental data. Moreover, the results indicate a strong preference for the mass splitting associated to normal hierarchy. However, since all permutations of the masses are found to be equally probable for a particular mass splitting between the three generations, predictions concerning the hierarchy of the mass spectrum (normal or inverted) remains out of reach in the framework of anarchy. Regarding the group variables (the mixing angles an CP-violating phases), it is found that near-maximal mixing is naturally favored by these ensembles and, that the PMNS matrix can be described as a generic unitary matrix drawn at random from a matrix ensemble characterized by the Haar measure of the corresponding Lie group. Furthermore, these conclusions are found to be independent of the mass mechanism considered

Paramétrisation du champ de pion dans une extension quasi-BPS du modèle de Skyrme

Le modèle de Skyrme, dont la première apparition remonte au milieu du 20ième siècle, est maintenant interprété comme une théorie efficace de la chromodynamique quantique dans la limite des basses énergies. Dans ce modèle, une description des noyaux atomiques les plus stables s’avère possible à l’aide d’une structure solitonique qui possède une charge topologique conservée. Ce présent travail s’appuie sur une récente extension du modèle de Skyrme original suggérée par Marleau et coll., c’est-à-dire le modèle de Skyrme quasi-BPS, et propose l’étude de deux hypothèses de départ (ansatz) pour la paramétrisation du champ mésonique. Les résultats obtenus à partir de ces deux hypothèses de départ ont été comparés et analysés selon deux approches principales, la première favorisant un développement perturbatif des équations de champs (qui permet des solutions analytiques) et la seconde s’appuyant sur un algorithme de recuit simulé pour obtenir des solutions numériques complètes du modèle au niveau classique

Probability Density Functions for CP-Violating Rephasing Invariants

The implications of the anarchy principle on CP violation in the lepton sector are investigated. A systematic method is introduced to compute the probability density functions for the CP-violating rephasing invariants of the PMNS matrix from the Haar measure relevant to the anarchy principle. Contrary to the CKM matrix which is hierarchical, it is shown that the Haar measure, and hence the anarchy principle, are very likely to lead to the observed PMNS matrix. Predictions on the CP-violating Dirac rephasing invariant $|j_D|$ and Majorana rephasing invariant $|j_1|$ are also obtained. They correspond to $\langle|j_D|\rangle_\text{Haar}=\pi/105\approx0.030$ and $\langle|j_1|\rangle_\text{Haar}=1/(6\pi)\approx0.053$ respectively, in agreement with the experimental hint from T2K of $|j_D^\text{exp}|\approx0.032\pm0.005$ (or $\approx0.033\pm0.003$) for the normal (or inverted) hierarchy.Comment: 1+15 pages, 2 figure

Optimization of culture conditions for porcine corneal endothelial cells

Purpose : To optimize the growth condition of porcine corneal endothelial cells (PCEC), we evaluated the effect of coculturing with a feeder layer (irradiated 3T3 fibroblasts) with the addition of various exogenous factors, such as epidermal growth factor (EGF), nerve growth factor (NGF), bovine pituitary extract (BPE), ascorbic acid, and chondroitin sulfate, on cell proliferation, size, and morphology. Methods : PCEC cultures were seeded at an initial cell density of 400 cells/cm2 in the presence or absence of 20,000 murine-irradiated 3T3 fibroblast/cm2 in the classic media Dulbecco's Modified Eagle's Medium (DMEM) supplemented with 20% fetal bovine serum (FBS). Mean cell size and bromodeoxyuridine incorporation was assessed at various passages. Growth-promoting factors were studies by seeding PCEC at 8,000 cells/cm2 in DMEM with 20% FBS or Opti-MEM I supplemented with 4% FBS and one of the following additives: EGF (0.5, 5, 25 ng/ml), NGF (5, 20, 50 ng/ml), BPE (25, 50, 100, 200 μg/ml), ascorbic acid (10, 20, 40 μg/ml) and chondroitin sulfate (0.03, 0.08, 1.6%), alone or in combination. Cell number, size and morphology of PCEC were assessed on different cell populations. Each experiment was repeated at least twice in three sets. In some cases, cell cultures were maintained after confluence to observe post-confluence changes in cell morphology. Results : Co-cultures of PCEC grown in DMEM 20% FBS with a 3T3 feeder layer improved the preservation of small polygonal cell shape. EGF, NGF, and chondroitin sulfate did not induce proliferation above basal level nor did these additives help maintain a small size. However, chondroitin sulfate did help preserve a good morphology. BPE and ascorbic acid had dose-dependent effects on proliferation. The combination of BPE, chondroitin sulfate, and ascorbic acid significantly increased cell numbers above those achieved with serum alone. No noticeable changes were observed when PCEC were cocultured with a 3T3 feeder layer in the final selected medium. Conclusions : Improvements have been made for the culture of PCEC. The final selected medium consistently allowed the growth of a contact-inhibited cell monolayer of small, polygonal-shaped cells

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference

Glucosamine-Anchored Graphene Oxide Nanosheets: Fabrication, Ultraviolet Irradiation, and Electrochemical Properties

A biofunctionalized graphene oxide (GO) nanosheet with improved physicochemical properties is useful for electrocatalysis and sensor development. Herein, a new class of functionalized GO with a chemically anchored biomolecule glucosamine is developed. Structural and chemical analyses confirm the glucosamine anchoring. Ultraviolet irradiation transforms the surface chemistry of GO. Glucosamine-anchored GO nanosheets exhibit improved cyclic voltammetric and amperometric sensing activity toward the model redox probe, ruthenium­(II) and <i>N</i>-acetylneuraminic acid, respectively. The biomolecular anchoring and ultraviolet irradiation helped to tune and enhance the properties of GO, which may find multiple applications in optimizing sensor platforms