Related papers: Involution symmetries and the PMNS matrix
It has been suggested that residual symmetries in the charged-lepton and neutrino mass matrices can possibly reveal the flavour symmetry group of the lepton sector. We review the basic ideas of this purely group-theoretical approach and…
In the absence of a Grand Unified Theory framework, connecting the values of the mixing parameters in the quark and lepton sector is a difficult task, unless one introduces ad-hoc relations among the matrices that diagonalize such different…
We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP…
Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers as a tool for the analysis of features arising from…
Residual symmetry $G_\nu$ of neutrino mass matrix with a massless neutrino and embedding of $G_\nu$ and the residual symmetry $G_l$ of the charged lepton mass matrix into finite discrete groups $G$ is discussed. Massless neutrino results if…
We provide an algorithm for detecting the involutions leaving a surface defined by a polynomial parametrization invariant. As a consequence, the symmetry axes, symmetry planes and symmetry center of the surface, if any, can be determined…
We explore the implications of symmetries that remain unbroken at the self-dual point $\tau=i$ in modular invariant theories. Assuming that (a) the three generations of lepton doublets transform as an irreducible representation of a finite…
A method for constructing evolution equations admitting a master symmetry is proposed. Several examples illustrating the method are presented. It is also noted that for certain evolution equations master symmetries can be useful for…
Investigating the CKM matrix in different parametrization schemes, it is noticed that those schemes can be divided into a few groups where the sine values of the CP phase for each group are approximately equal. Using those relations,…
Symmetry in the parameter space of deep neural networks (DNNs) has proven beneficial for various deep learning applications. A well-known example is the permutation symmetry in Multi-Layer Perceptrons (MLPs), where permuting the rows of…
The PMNS matrix displays an obvious symmetry, but not exact. There are several textures proposed in literature, which possess various symmetry patterns and seem to originate from different physics scenarios at high energy scales. To be…
We propose new lepton-mixing textures that may be enforced through well-defined symmetries in renormalizable models. Each of our textures has four sum rules for the neutrino mass observables. The models are based on the type-I seesaw…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
The observed leptonic mixing pattern could be explained by the presence of a discrete flavour symmetry broken into residual subgroups at low energies. In this scenario, a residual generalised CP symmetry allows the parameters of the PMNS…
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…
After briefly reviewing how the symmetries of the Standard Model (SM) are affected by neutrino masses and mixings, I discuss how these parameters may arise from GUTs and how patterns in the neutrino sector may reflect some underlying family…
We show that large leptonic mixing occurs most naturally in the framework of the Sandard Model just by adding a fourth generation. One can then construct a small $Z_4$ discrete symmetry, instead of the large $S_{4L}\times S_{4R}$, which…
In this paper, we study residual symmetries in the lepton sector. Our first concern is the symmetry of the charged lepton mass matrix in the basis where the Majorana neutrino mass matrix is diagonal, which is strongly constrained by the…
Correlations between light neutrino observables are arguably the strongest predictions of lepton avour models based on (discrete) symmetries, except for the very few cases which unambiguously predict the full set of leptonic mixing angles.…
We study embedding of non-commuting $Z_2$ and $Z_m$, $m\geq 3$ symmetries in discrete subgroups (DSG) of $U(3)$ and analytically work out the mixing patterns implied by the assumption that $Z_2$ and $Z_m$ describe the residual symmetries of…