Comments on the classification of the finite subgroups of SU(3)

Many finite subgroups of SU(3) are commonly used in particle physics. The classification of the finite subgroups of SU(3) began with the work of H.F. Blichfeldt at the beginning of the 20th century. In Blichfeldt's work the two series (C) and (D) of finite subgroups of SU(3) are defined. While the group series Delta(3n^2) and Delta(6n^2) (which are subseries of (C) and (D), respectively) have been intensively studied, there is not much knowledge about the group series (C) and (D). In this work we will show that (C) and (D) have the structures (C) \cong (Z_m x Z_m') \rtimes Z_3 and (D) \cong (Z_n x Z_n') \rtimes S_3, respectively. Furthermore we will show that, while the (C)-groups can be interpreted as irreducible representations of Delta(3n^2), the (D)-groups can in general not be interpreted as irreducible representations of Delta(6n^2).Comment: 15 pages, no figures, typos corrected, clarifications and references added, proofs revise

Lepton mixing from the hidden sector

Experimental results indicate a possible relation between the lepton and quark mixing matrices of the form U_PMNS \approx V_CKM^\dagger U_X, where U_X is a matrix with special structure related to the mechanism of neutrino mass generation. We propose a framework which can realize such a relation. The main ingredients of the framework are the double seesaw mechanism, SO(10) Grand Unification and a hidden sector of theory. The latter is composed of singlets (fermions and bosons) of the GUT symmetry with masses between the GUT and Planck scale. The interactions in this sector obey certain symmetries G_hidden. We explore the conditions under which symmetries G_hidden can produce flavour structures in the visible sector. Here the key elements are the basis-fixing symmetry and mediators which communicate information about properties of the hidden sector to the visible one. The interplay of SO(10) symmetry, basis-fixing symmetry identified as Z2 x Z2 and G_hidden can lead to the required form of U_X. A different kind of new physics is responsible for generation of the CKM mixing. We present the simplest realizations of the framework which differ by nature of the mediators and by symmetries of the hidden sector.Comment: 30 pages, 6 figures; typo corrected, one reference added, version for publication in Phys. Rev.

Finite flavour groups of fermions

We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations and character tables. In a specialized part, we attempt to give a fairly comprehensive review of finite subgroups of SO(3) and SU(3), in which we apply and illustrate the general theory. Moreover, we also provide a concise description of the symmetric and alternating groups and comment on the relationship between finite subgroups of U(3) and finite subgroups of SU(3). Though in this review we give a detailed description of a wide range of finite groups, the main focus is on the methods which allow the exploration of their different aspects.Comment: 89 pages, 6 figures, some references added, rearrangement of part of the material, section on SU(3) subgroups substantially extended, some minor revisions. Version for publication in J. Phys. A. Table 12 corrected to match eq.(256), table 14 and eq.(314) corrected to match the 2-dimensional irreps defined on p.6

Two-parameter neutrino mass matrices with two texture zeros

We reanalyse Majorana-neutrino mass matrices M_nu with two texture zeros, by searching for viable hybrid textures in which the non-zero matrix elements of M_nu have simple ratios. Referring to the classification scheme of Frampton, Glashow and Marfatia, we find that the mass matrix denoted by A1 allows the ratios (M_nu)_{mu mu} : (Mnu)_{tau tau} = 1:1 and (M_nu)_{e tau} : (Mnu)_{mu tau} = 1:2. There are analogous ratios for texture A2. With these two hybrid textures, one obtains, for instance, good agreement with the data if one computes the three mixing angles in terms of the experimentally determined mass-squared differences Delta m^2_21 and Delta m^2_31. We could not find viable hybrid textures based on mass matrices different from those of cases A1 and A2.Comment: 10 pages, no figures, minor changes, some references adde

Principal series of finite subgroups of SU(3)

We attempt to give a complete description of the "exceptional" finite subgroups Sigma(36x3), Sigma(72x3) and Sigma(216x3) of SU(3), with the aim to make them amenable to model building for fermion masses and mixing. The information on these groups which we derive contains conjugacy classes, proper normal subgroups, irreducible representations, character tables and tensor products of their three-dimensional irreducible representations. We show that, for these three exceptional groups, usage of their principal series, i.e. ascending chains of normal subgroups, greatly facilitates the computations and illuminates the relationship between the groups. As a preparation and testing ground for the usage of principal series, we study first the dihedral-like groups Delta(27) and Delta(54) because both are members of the principal series of the three groups discussed in the paper.Comment: 43 pages, no figures; typos corrected, clarifications and references added, version matches publication in J. Phys.

Correlations of the elements of the neutrino mass matrix

Assuming Majorana nature of neutrinos, we re-investigate, in the light of the recent measurement of the reactor mixing angle, the allowed ranges for the absolute values of the elements of the neutrino mass matrix in the basis where the charged-lepton mass matrix is diagonal. Apart from the derivation of upper and lower bounds on the values of the matrix elements, we also study their correlations. Moreover, we analyse the sensitivity of bounds and correlations to the global fit results of the neutrino oscillation parameters which are available in the literature.Comment: 37 pages, 146 figures, minor corrections, 17 additional figures, version for publication in JHE

Predicting leptonic CP violation in the light of Daya Bay result

In the light of the recent Daya Bay result the reactor angle is about 9 degrees, we reconsider the model presented in arXiv:1005.3482 showing that, when all neutrino oscillation parameters are taken at their best fit values of Schwetz et al and the reactor angle to be the central value of Daya Bay, the predicted value of the CP phase is approximately 45 degrees.Comment: 4 pages, 2 figures, update of arXiv:1005.348

Development of two-photon polymerised scaffolds for optical interrogation and neurite guidance of human iPSC-derived cortical neuronal networks

Recent progress in the field of human induced pluripotent stem cells (iPSCs) has led to the efficient production of human neuronal cell models for in vitro study. This has the potential to enable the understanding of live human cellular and network function which is otherwise not possible. However, a major challenge is the generation of reproducible neural networks together with the ability to interrogate and record at the single cell level. A promising aid is the use of biomaterial scaffolds that would enable the development and guidance of neuronal networks in physiologically relevant architectures and dimensionality. The optimal scaffold material would need to be precisely fabricated with submicron resolution, be optically transparent, and biocompatible. Two-photon polymerisation (2PP) enables precise microfabrication of three-dimensional structures. In this study, we report the identification of two biomaterials that support the growth and differentiation of human iPSC-derived neural progenitors into functional neuronal networks. Furthermore, these materials can be patterned to induce alignment of neuronal processes and enable the optical interrogation of individual cells. 2PP scaffolds with tailored topographies therefore provide an effective method of producing defined in vitro human neural networks for application in influencing neurite guidance and complex network activity

Mining and Filtering Multi-level Spatial Association Rules with ARES

In spatial data mining, a common task is the discovery of spatial association rules from spatial databases. We propose a distributed system, named ARES that takes advantage of the use of a multi-relational approach to mine spatial association rules. It supports spatial database coupling and discovery of multi-level spatial association rules as a means for spatial data exploration. We also present some criteria to bias the search and to filter the discovered rules according to user's expectations. Finally, we show the applicability of our proposal to two different real world domains, namely, document image processing and geo-referenced analysis of census data

Proceedings of the 2nd Workshop on Flavor Symmetries and Consequences in Accelerators and Cosmology (FLASY12)

These are the proceedings of the 2nd Workshop on Flavor Symmetries and Consequences in Accelerators and Cosmology, held 30 June 2012 - 4 July 2012, Dortmund, Germany.Comment: Order 400 pages, several figures including the group picture v2: corrected author list and contributio