Related papers: Involution symmetries and the PMNS matrix
In this talk I review the present status of neutrino masses and mixing and some of their implications for particle physics phenomenology. I first discuss the minimum extension of the Standard Model of particle physics required to…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The lepton mixing angles of the PMNS matrix are predicted based on the lepton flavor symmetry of a finite group $C_2\times D_3$, where the cyclic group $C_2$ acts on the charged lepton mass terms and the dihedral group $D_3$ on the neutrino…
We propose a supersymmetric extra U(1) model, which can generate small neutrino masses and necessary $\mu$ terms, simultaneously. Fields including quarks and leptons are embedded in three ${\bf 27}$s of $E_6$ in a different way among…
The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…
The elementary symmetric partition function is a map on the set of partitions. It sends a partition lambda to the partition whose parts are the summands in the evaluation of the elementary symmetric function on the parts of lambda. These…
Deep learning can be used to extract meaningful results from images. In this paper, we used convolutional neural networks combined with recurrent neural networks on images of plasmonic structures and extract absorption data form them. To…
The renormalization evolution of all parameters in the neutrino mass matrix depends only on one variable, the energy scale. This fact, coupled with rephasing considerations, leads to a set of renormalization invariants, correlating the…
We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classical, while the second appears in the geometry of certain…
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -- a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M…
Complex, multivariable systems are often analyzed by grouping their constituent units into components, sometimes referred to as latent features, which afford physical or biological interpretation. However, a priori many different types of…
A predictive Leptogenesis scenario is presented based on the Minimal Lepton Flavour Violation symmetry. In the realisation with three right-handed neutrinos transforming under the same flavour symmetry of the lepton electroweak doublets,…
We give unique recovery guarantees for matrices of bounded rank that have undergone permutations of their entries. We even do this for a more general matrix structure that we call ladder matrices. We use methods and results of commutative…
We revisit the production of leptonic asymmetries in minimal extensions of the Standard Model that can explain neutrino masses, involving extra singlets with Majorana masses in the GeV scale. We study the quantum kinetic equations both…
It is shown that each integrable mapping is connected with a hierarchical completely integrable sytem of equations of evolution type which are invariant with respect to the transformation described by this mapping.
We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show…
Many scientific and geometric problems exhibit general linear symmetries, yet most equivariant neural networks are built for compact groups or simple vector features, limiting their reuse on matrix-valued data such as covariances, inertias,…
We predict new particles at the Tera scale based on the assumptions that the standard model gauge interactions are unified around the gravitational scale with a big desert and new particles originate from hypermultiplets as remnants of…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
In this paper we postulate an algebraic model to explain how the symmetry of three lepton species plays its role in the Lorentz extension. Inspired by the two-to-one mapping between the group SL (2, C) and the Lorentz group, we design a…