Related papers: Finite flavour groups of fermions
Let FL_s(K) be the finitary linear group of degree s over an associative ring K with unity. We prove that the torsion subgroups of FL_s(K) are locally finite for certain classes of rings K. A description of some f.g. solvable subgroups of…
Every mathematician is familiar with the beautiful structure of finite commutative groups. What is less well known is that finite commutative semigroups also have a neat and well-described structure. We prove this in an efficient fashion.…
We present new lattice investigations of finite-temperature transitions for SU(3) gauge theory with Nf=8 light flavors. Using nHYP-smeared staggered fermions we are able to explore renormalized couplings $g^2 \lesssim 20$ on lattice volumes…
We discuss the role of flavour physics in building effective theories at the TeV scale. Particular attention is devoted to the Minimal Flavour Violation hypothesis, both in the quark and in the lepton sector. Alternative flavour-protection…
In this paper, we explain the importance of finite decomposition semigroups and present two theorems related to their structure.
An introduction to the heavy quark effective theory and its symmetries is given. Some implications of the heavy quark spin and flavor symmetries are discussed. Recent results on fragmentation to quarkonium states are reviewed.
We review and compare theoretically and phenomenologically a number of possible family symmetries, which when combined with unification, could be important in explaining quark, lepton and neutrino masses and mixings, providing new results…
The coming flavour precision era will allow to uncover various patterns of flavour violation in different New Physics scenarios. We discuss different classes of them. A simple extension of the Standard Model that generally introduces new…
We show how two principles - strong coupling and discrete symmetry - can work together to generate the flavour structure of the Standard Model. We propose that in the UV the full theory has a discrete flavour symmetry, typically only…
A nonabelian finite flavor group $G \subset SO(3)$ can have double covering $G^{'} \subset SU(2)$ such that $G \not\subset G^{'}$. This situation is not contradictory, but quite natural, and we give explicit examples such as $G=D_n,…
After 100 years of effort, the classification of all the finite subgroups of SU(3) is yet incomplete. The most recently updated list can be found in P.O. Ludl, J. Phys. A: Math. Theor. 44 255204 (2011), where the structure of the series (C)…
We use the SmallGroups Library to find the finite subgroups of U(3) of order smaller than 512 which possess a faithful three-dimensional irreducible representation. From the resulting list of groups we extract those groups that can not be…
First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…
U(1)-family symmetries have led to successful predictions of the fermion mass spectrum and the mixing angles of the hadronic sector. In the context of the supersymmetric unified theories, they further imply a non-trivial mass structure for…
Motivated by the idea of Comprehensive Unification, we consider a gauged $SO(3)$ flavor extension of the Standard Model, including right-handed neutrinos and a Peccei-Quinn symmetry. The model accommodates the observed fermion masses and…
This note presents Galois theory for finite fields. It was written as a handout for the MAT401 course ``Polynomial equations and fields'' taught at the University of Toronto in Spring 2026. We use without proofs some basic properties of…
Discrete flavor symmetries provide a promising approach to understand the flavor sector of the standard model of particle physics. Top-down (TD) explanations from string theory reveal two different types of such flavor symmetries:…
This paper gives a quick overview of the author's recent result that all finitely presented groups are QSF.
In this short note, we describe the finite groups $G$ having $|G|-1$ cyclic subgroups. This leads to a nice characterization of the symmetric group $S_3$.
A grand unified $SU(5)$ theory is constructed with a hierarchical breaking of a $U(2)$ flavor symmetry. The small parameters of the squark and slepton mass matrices, necessary to solve the supersymmetric flavor-changing problem, and the…