相关论文: A novel mathematical construct for the family of l…
Recent stringent experiment data of neutrino oscillations induces partial symmetries such as $Z_{2}$, $Z_{2}\times CP$ to derive lepton mixing patterns. New partial symmetries expressed with elements of group algebras are studied. A…
Discrete groups are widely used in the expression of flavor symmetries of leptons. In this paper, we employ a novel mathematical object called group-algebra (GA) to describe symmetries of the leptonic mass matrices. A GA element is…
We investigate the possibility of expressing the charged leptons and neutrino mass matrices as linear combinations of generators of a single finite group. Constraints imposed on the resulting mixing matrix by current data restrict the group…
Recent data of reactor neutrino experiments set more stringent constraint on leptonic mixing patterns. We examine all possible patterns on the basis of combinations of elementary correlations of elements of leptonic mixing matrix. we obtain…
Following the newly formulated notion of form invariance of the neutrino mass matrix, a complete model of leptons is constructed. It is based on a specific unitary 3 X 3 matrix U in family space, such that U^2 is the simple discrete…
Experimentally viable lepton mixing parameters can be predicted in so-called direct flavour models with Majorana neutrinos using $\Delta(6n^2)$ groups as a flavour group. In direct models, in which the flavour group is broken to a…
We have used the SmallGroups library of groups, together with the computer algebra systems GAP and Mathematica, to search for groups with a three-dimensional irreducible representation in which one of the group generators has a…
Assuming three generations of Majorana neutrinos, we study the different mixing patterns that arise from the non-trivial breaking of the flavor group A5 and CP to the residual symmetries Z3, Z5 or Z2 x Z2 in the charged lepton and to Z2 x…
We survey the mixing patterns which can be derived from the discrete groups Sigma (36 x 3), Sigma (72 x 3), Sigma (216 x 3) and Sigma (360 x 3), if these are broken to abelian subgroups Ge and Gnu in the charged lepton and neutrino sector,…
Amid the uncertainty regarding the fundamental nature of neutrinos, we adhere to the Dirac description, and construct a model in the framework of $\Delta(27)$ symmetry. The model successfully accounts for the hierarchical patterns of both…
We perform a detailed study of lepton mixing patterns arising from a scenario with three Majorana neutrinos in which a discrete flavor group Gf=Delta (3 n^2) or Gf=Delta(6 n^2) and a CP symmetry are broken to residual symmetries Ge=Z3 and…
The pattern of lepton mixing can emerge from breaking a flavor symmetry in different ways in the neutrino and charged lepton Yukawa sectors. In this framework, we derive the conditions imposed on the mixing matrix by the structure of…
In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups. We create a database of all 2-generated…
We present a model that extends the standard model by incorporating the simplest discrete symmetry groups, $Z_2$ and $Z_3$. This model introduces vector-like leptons and a real scalar singlet. Based on this framework, we generate Dirac…
The recent discovery of a non-zero value of the mixing angle theta_13 has ruled out tri-bimaximal mixing as the correct lepton mixing pattern generated by some discrete flavor symmetry (barring large next-to-leading order corrections in…
Hernandez and Smirnov discovered an interesting formula to parametrize each column of a neutrino mixing matrix by six integers related to the residual symmetry. We point out that these six integers are not independent, and propose a way to…
By assuming there exist three massive non-degenerate Majorana neutrinos, it is possible to describe neutrino mixing with a residual, unbroken discrete Klein subgroup of a larger spontaneously broken flavor symmetry group. Motivated by…
We construct a family of finitely generated infinite periodic groups. The basic example is a 2-group, called the tetrahedron group. We generalize the construction by suggesting a family of infinite finitely generated dice groups. We provide…
To a first approximation, the quark mixing matrix has $\theta^q_{13} = \theta^q_{23} = 0$, whereas the lepton mixing matrix has $\theta^l_{23} = \pi/4$. We show how this structure may be understood if the family symmetry is $Q_8$, the…
We consider a scenario with three Majorana neutrinos in which a discrete, finite flavour group G_f is combined with a generalized CP transformation. We derive conditions for consistently defining such a setup. We show that in general lepton…