Related papers: On Leptonic Unitary Triangles and Boomerangs
In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of…
We present an application of the basic mathematical concept of complex functions as topological solitons, a most interesting area of research in physics. Such application of complex theory is virtually unknown outside the community of…
In this paper, we develop the theory of symmetric triads with multiplicities. First, we classify abstract symmetric triads with multiplicities. Second, we determine the symmetric triads with multiplicities corresponding to commutative…
After the observation of non-zero $\theta_{13}$ the goal has shifted to observe $CP$ violation in the leptonic sector. Neutrino oscillation experiments can, directly, probe the Dirac $CP$ phases. Alternatively, one can measure $CP$…
I review some aspects of supersymmetric grand unification and emphasize a recent development in the area of gauge coupling unification.
This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…
We review the present understanding of neutrino masses and mixings, discussing what are the unknowns in the three family oscillation scenario. Despite the anticipated success coming from the planned long baseline neutrino experiments in…
The extension of chiral theories to the description of resonances, via the incorporation of unitarity in coupled channels, has provided us with a new theoretical perspective on the nature of some of the observed excited hadrons. In this…
Some models for the lepton sector, based on seesaw extensions of the Standard Model, are discussed in which the mu-tau interchange symmetry is realized in various ways. The symmetries defining such models and their characteristic…
Restrictions on the neutrino masses and lepton mixing are reviewed. Solar, atmospheric and relic neutrinos give the indications of existence of nonzero neutrino masses and mixing. The data pick up two regions of mixing angles which are or…
To generate a triangle of unit perimeter, break a stick of length 1 in two places at random, with the condition that triangle inequalities are satisfied. Is there a similarly natural method for generating triangles of unit area? Study of a…
In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to study attributes of triangles. Using the new definition, this…
We study the lepton flavor models, whose flavor symmetries are finite subgroups of the modular group such as $S_3$ and $A_4$. In our models, couplings are also nontrivial representations of these groups and modular functions of the modulus.…
Leptonic mixing patterns are usually extracted on the basis of groups or algebraic structures. In this paper, we introduce an alternative geometric method to study the correlations between the leptonic mixing parameters. At the 3$\sigma$…
We investigate the possibility of a fourth sequential generation in the lepton sector. Assuming neutrinos to be Majorana particles and starting from a recent - albeit weak - evidence for a non-zero admixture of a fourth generation neutrino…
Using renormalization group techniques, we examine several interesting relations among masses and mixing angles of quarks and leptons in the Standard Model. We extend the analysis to the minimal supersymmetric extension to determine its…
Our present knowledge of neutrinos can be summarized in terms of the "standard neutrino scenario". Phenomenology of this scenario as well as attempts to uncover physics behind neutrino mass and mixing are described. Goals of future studies…
Non-unitarity of the neutrino mixing matrix is expected in many scenarios with physics beyond the Standard Model. Motivated by the search for deviations from unitary, we study two neutrino counting observables: the neutrino-antineutrino…
We phenomenologically build a neutrino mass matrix obeying $\mu-\tau$ symmetry with only two parameters, Cabibbo angle $(\lambda)$ and a flavour twister parameter $(\eta)$. For vanishing $\eta$, the model assumes TBM mixing. When…
We study a supersymmetric E6 grand unified model in which the SU(5) 5^* components are twisted in the third generation 27. Supplementing the adjoint Higgs field to a model analyzed previously, we calculate the mass matrices for the up and…