Related papers: Finite flavour groups of fermions
We use the permutational symmetry group $S_{3}$ as a symmetry of flavour, which leads to a unified treatment of masses and mixings of the quarks and leptons. In this framework all mass matrices of the fermions in the theory have the same…
We establish the full list of flavour symmetry groups which may be enforced, without producing any further accidental symmetry, on the Yukawa-coupling matrices of an SO(10) Grand Unified Theory with arbitrary numbers of scalar multiplets in…
The introduction of a Flavour Symmetry can represent an interesting way in which one can try to find an answer to some intriguing problems in Flavour Physics, like the hierarchy between the fermion masses or the particular values of mixing…
We study a finite SU(5) grand unified model based on the non-Abelian discrete symmetry A_4. This model leads to the democratic structure of the mass matrices for the quarks and leptons. In the soft supersymmetry breaking sector, the scalar…
We consider a supersymmetric SO(10) model with a SU(3) symmetry of flavour in which fermion masses emerge via the see-saw mixing with superheavy fermions in 16+16bar representations. In this model the dangerous D=5 operators of proton decay…
Finite symmetries abound in particle physics, from the weak doublets and generation triplets to the baryon octet and many others. These are usually studied by starting from a Lie group, and breaking the symmetry by choosing a particular…
We provide a general classification of flavour symmetries according to their interplay with the proper Poincare' and gauge groups and to their linear or nonlinear action in field space. We focus on the lepton sector and we review the…
We consider the extended electroweak gauge group SU(2)_1 \times SU(2)_2 \times U(1)_Y where the first and second families of fermions couple to SU(2)_1 while the third family couples to SU(2)_2. Bounds based an precision electroweak…
The problem of meson bound states with $N_f$ massive fermions in two dimensional quantum electrodynamics is discussed. We speculate about the spectrum of the lightest particles by means of the effective semiclassical description. In…
We develop a bottom-up approach to constructing a theory of fermion masses and mixing angles based on the gauge group $SU(3)\times G$ where SU(3) is a family symmetry and $G$ contains a unified group such as SO(10) or its Pati-Salam…
Flavour symmetries appropriate for describing a neutrino spectrum with degenerate solar pair and a third massive or massless neutrino are discussed. We demand that the required residual symmetries of the leptonic mass matrices be subgroups…
The heaviness of the third family fermions and the experimental absence of large flavor violating processes suggest, in supersymmetric theories, that the three families belong to a $2+1$ representation of a horizontal symmetry $G_H$. In…
We review the modular flavor symmetric models of quarks and leptons focusing on our works. We present some flavor models of quarks and leptons by using finite modular groups and discuss the phenomenological implications. The modular flavor…
This is the third and final installment of an exposition of an ACL2 formalization of finite group theory. Part I covers groups and subgroups, cosets, normal subgroups, and quotient groups. Part II extends the theory in the developmnent of…
Flavour symmetries are fundamental tools in the search for an explanation to the flavour puzzle: fermion mass hierarchies, the neutrino mass ordering, the differences between the mixing matrices in the quark and lepton sector, can all find…
We discuss our recently proposed S3(down)xS3(up) flavour-permutation-symmetric mixing observables, giving expressions for them in terms of (moduli-squared) of the mixing matrix elements. We outline their successful use in providing…
Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00] (which correspond to the case where H is…
We show that the fermion mass spectrum may naturally be understood in terms of flavour democratic fixed points in supersymmetric theories which have a large domain of attraction in the presence of "strong unification". Our approach provides…
Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…
Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…