Related papers: Family Gauge Symmetry and Koide's Mass Formula
The sets of charged-lepton (L) and quark (D,U) masses may be parametrized in a Z_3-symmetric language appropriate for the discussion of Koide's formula. Experiment suggests that at the low-energy scale the relevant phase parameters \delta_f…
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…
Unification based on the group SO(10)^3 \times S_3 is studied. Each family has its own SO(10) group, and the S_3 permutes the three families and SO(10) factors. This is the maximal local symmetry for the known fermions. Family unification…
Spontaneous breaking of inter-family (horizontal) gauge symmetries can be at the origin of the mass hierarchy between the fermion families. The corresponding gauge bosons have flavor-nondiagonal couplings which generically induce the…
Family Replicated Gauge Group models of the type SU(n)^N\times SU(m)^N, (SMG)^3 and (SMG\times U(1)_{B-L})^3 are reviewed, where SMG=SU(3)_{c}\times SU(2)_{L}\times U(1)_{Y} is the gauge symmetry group of the Standard Model, $B$ is the…
The pattern of quark and lepton mass matrices is unexplained in the standard model of particle interactions. I propose the novel idea of a progressive gauge U(1) symmetry where it is a reflection of the regressive electroweak symmetry…
A gauge $U(1)$ family symmetry is proposed, spanning the quarks and leptons as well as particles of the dark sector. The breaking of $U(1)$ to $Z_2$ divides the two sectors and generates one-loop radiative masses for the first two families…
The charged lepton masses may be parametrized in a Z3-symmetric language appropriate to the discussions of Koide's formula. The phase parameter \delta_L appearing in this parametrization is experimentally indistinguishable from 2/9. We…
A U(3) family gauge boson model is investigated based on U(3)$\times$[U(1)]$^3$ gauge symmetry. In this model, of nine U(3) family gauge bosons $A_i^{\ j}$, those with $i=j$ are considerable heavy compared with those with $i \neq j$, so…
The charged lepton mass relation $K \equiv (m_e +m_\mu+m_\tau)/(\sqrt{m_e} %+\sqrt{m_\mu} +\sqrt{m_\tau})^2= 2/3 $ is excellently satisfied by observed masses (pole masses). However, the formula $K=2/3$ should be never satisfied with the…
Two empirical formulae for the lepton and quark masses (i.e. Kartavtsev's extended Koide formulae), $K_l=(\sum_l m_l)/(\sum_l\sqrt{m_l})^2=2/3$ and $K_q=(\sum_q m_q)/(\sum_q\sqrt{m_q})^2=2/3$, are explored in this paper. For the lepton…
A spontaneously broken non-Abelian SU(3) family symmetry can generate a realistic form for quark, charged lepton and neutrino masses and mixing angles. It also gives a new solution to the SUSY flavour problem by ensuring near family…
A quark and lepton mass matrix model with family symmetries U(3)$\times$O(3) is investigated on the basis of the so-called yukawaon model. In the present model, quarks and leptons are assigned to $(\ell, e^c, u^c) \sim ({\bf 3}, {\bf 3},…
We calculate quark and lepton masses and quark mixing angles in the framework of a supersymmetric SU(4)$\otimes$SU(2)$_L\otimes$SU(2)$_R$ model where the gauge group is broken at 10$^{16}$ GeV. The model predicts third family top-bottom-tau…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
It is known that the charged lepton masses obey to high precision an interesting empirical relation (Koide relation). In turn, the light neutrino masses cannot obey such a relation. We note that if neutrinos acquire their mass via the…
To explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor…
Koide's charged-lepton relation suggests that $(\sqrt{m_e},\sqrt{m_\mu},\sqrt{m_\tau})$ is the natural family vector. We construct an effective compact-cycle model in which this vector is sampled from one real amplitude $Z(\phi)$ on an…
We discuss whether quark, charged lepton and neutrino masses and mixing angles may be related by an extended flavour and family symmetry group. We show that current measurements of all fermion masses and mixing angles are consistent with a…
The observed replication of fermions in three families is undoubtedly a reflection of a deeper symmetry underlying the standard model. In this paper we investigate one very elementary possibility, that physics above the grand unification…