Family Gauge Symmetry Research Articles

Gauge-flavon unification

In this paper we propose the idea that flavons can emerge from extra dimensional gauge fields, referred to as gauge-flavon unification (GFU) analogous to gauge-Higgs unification (GHU). We assume that there is a gauged family symmetry in extra dimensions and that the flavons are the extra dimensional components of the gauge field. This provides a simple mechanism to align the VEVs of the flavons through a combination of Wilson lines and orbifold symmetry breaking. We present some simple 5d examples of GFU based on SO(3) and SU(4) gauged family symmetry, the latter case yielding SU(3) × U(1) gauged family symmetry in 4d, broken by triplet and antitriplet flavons, with effective couplings to fermions. We also present a general formalism for Wilson lines and orbifolds, in any number of dimensions, including non-commutative aspects Wilson lines, which may be useful for aligning additional flavons as required for realistic models.

Formula omitted] gauge family model and new symmetry breaking scale from FCNC processes

Based on the SU(3)F gauge family symmetry model which was proposed to explain the observed mass and mixing pattern of neutrinos, we investigate the symmetry breaking, the mixing pattern in quark and lepton sectors, and the contribution of the new gauge bosons to some flavour changing neutral currents (FCNC) processes at low energy. With the current data of the mass differences in the neutral pseudo-scalar P0–P¯0 systems, we find that the SU(3)F symmetry breaking scale can be as low as 300 TeV and the mass of the lightest gauge boson be about 100 TeV. Other FCNC processes, such as the lepton flavour number violation process μ−→e−e+e− and the semi-leptonic rare decay K→πν¯ν, contain contributions via the new gauge bosons exchanging. With the constrains obtained from P0–P¯0 system, we estimate that the contribution of the new physics is around 10−16, far below the current experimental bounds.

Dynamical generation of flavour

We propose the generation of Standard Model fermion hierarchy by the extension of renormalizable SO(10) GUT with O(N g ) family gauge symmetry. In this scenario, Higgs representations of SO(10) also carry family indices and are called Yukawons. Vacuum expectation values of these Yukawon fields break GUT and family symmetry and generate MSSM Yukawa couplings dynamically. We have demonstrated this idea using ${\mathbf {10}}\oplus {\mathbf {210}} \oplus {\mathbf {126}} \oplus {\overline {\mathbf {126}}}$ Higgs irrep, ignoring the contribution of 1 2 0-plet which is, however, required for complete fitting of fermion mass-mixing data. The effective MSSM matter fermion couplings to the light Higgs pair are determined by the null eigenvectors of the MSSM-type Higgs doublet superfield mass matrix $\mathcal {H}$ . A consistency condition on the doublet ([1,2,±1]) mass matrix ( $\text {Det}(\mathcal {H})=$ 0) is required to keep one pair of Higgs doublets light in the effective MSSM. We show that the Yukawa structure generated by null eigenvectors of $\mathcal {H}$ are of generic kind required by the MSSM. A hidden sector with a pair of (S a b ; ϕ a b ) fields breaks supersymmetry and facilitates $D_{O(N_{g})}\hspace *{-1pt}=$ 0. SUSY breaking is communicated via supergravity. In this scenario, matter fermion Yukawa couplings are reduced from 15 to just 3 parameters in MSGUT with three generations.

SO(10) grand unified theories with dynamical Yukawa couplings

Renormalizable SO(10) grand unified theories (GUTs), extended by $O(N_g)_F$ family gauge symmetry, generate minimal supersymmetric Standard Model flavour structure dynamically via vacuum expectation values of "Yukawon" Higgs multiplets. For concrete illustration and calculability, we work with the fully realistic minimal supersymmetric GUTs based on the $\bf{210 \oplus {\overline{126}}\oplus 126} $ GUT Higgs system - which were already parameter counting minimal relative to other realistic models. $SO(10)$ fermion Higgs channels $\bf{{\overline{126}},10}$($\mathbf{120}$) extend to symmetric(antisymmetric) representations of $O(N_g)_F$, while $\mathbf{210,126}$ are symmetric. $N_g=3$ dynamical Yukawa generation reduces the matter fermion Yukawas from 15 to 3 (21 to 5) without (with) the $\bf{120}$ Higgs. Yukawon GUTs are thus ultraminimal in parameter counting terms. Consistent symmetry breaking is ensured by a hidden sector Bajc-Melfo(BM) superpotential with a pair of symmetric $O(N_g)$ multiplets $\phi,S $, of which the latter's singlet part $S_s$ breaks supersymmetry and the traceless part $\hat S $ furnishes flat directions to cancel the $O(N_g)$ D-term contributions of the visible sector. Novel dark matter candidates linked to flavour symmetry arise from both the BM sector and GUT sector minimal supersymmetric Standard Model singlet pseudo-Goldstones. These relics may be viable light($< 50 $ GeV) cold dark matter as reported by DAMA/LIBRA. In contrast to the new minimal supersymmetric SO(10) grand unified theory (NMSGUT) even sterile neutrinos can appear in certain branches of the flavour symmetry breaking without the tuning of couplings.

Dirac leptogenesis with a non-anomalous U(1)′ family symmetry

We propose a model for Dirac leptogenesis based on a non-anomalous U(1)′ gauged family symmetry. The anomaly cancellation conditions are satisfied with no new chiral fermions other than the three right-handed neutrinos, giving rise to stringent constraints among the charges. Realistic masses and mixing angles are obtained for all fermions. The model predicts neutrinos of the Dirac type with naturally suppressed masses. Dirac leptogenesis is achieved through the decay of the flavon fields. The cascade decays of the vector-like heavy fermions in the Froggatt-Nielsen mechanism play a crucial role in the separation of the primodial lepton numbers. We find that a large region of parameter space of the model gives rise to a sufficient cosmological baryon number asymmetry through Dirac leptogenesis.

THE MASS DIFFERENCE OF $F-\bar{F}$ WITH SO(3) FAMILY GAUGE SYMMETRY

As a simple extension, a non-Abelian family gauge symmetry SO(3), as well as three family Majorana neutrinos, was introduced to explain the tri-bimaximal mixing matrix of neutrinos. We discuss the effect of the possible SO(3) family gauge interaction to the mass differences of [Formula: see text] and [Formula: see text], and get the constrains to the new gauge bosons.

SU(3) gauge family symmetry and prediction for the lepton-flavor mixing and neutrino masses with maximal spontaneous CP violation

A model for the lepton-flavor mixing and CP violation is proposed based on the SUF(3) gauge family symmetry and the Majorana feature of neutrinos. A consistent prediction for the lepton-flavor mixing and masses is shown to be resulted from the appropriate vacuum structure of SUF(3) gauge symmetry breaking. By choosing the SUF(3) gauge fixing condition to possess a residual Z2 symmetry and requiring the vacuum structure of spontaneous symmetry breaking to have approximate global U(1) family symmetries, we obtain naturally the tri-bimaximal mixing matrix and largely degenerate neutrino masses in the neutrino sector and the small mixing matrix in the charged-lepton sector. With a simple ansatz that all the smallness due to the approximate global U(1) family symmetries is characterized by a single Wolfenstein parameter λ≃0.22, and the charged-lepton mixing matrix has a similar hierarchy structure as the CKM quark mixing matrix, we arrive at a consistent prediction for the MNSP lepton-flavor mixing with a maximal spontaneous CP violation: δ=π/2, sin2θ13≃12λ2≃0.024 (sin22θ13≃0.094), sin2θ12≃13(1−2λ3)≃0.326 and sin2θ23≃12(1−λ2)≃0.48, which agree well with the current experimental data. The CP-violating Jarlskog-invariant is obtained to be JCP≃16λ(1−λ2/2−λ3)sinδ≃0.035, which is detectable in next generation neutrino experiment. The small masses of the neutrinos and charged leptons are simply attributed to the standard seesaw mechanism. The largely degenerate neutrino masses with the normal hierarchy and inverse hierarchy are discussed and found to be at the order mνi≃O(λ2)≃0.04–0.06 eV with a total mass ∑mν∼0.15 eV, which is testable in future precision astrophysics and cosmology.

Searching for a Z′ gauge boson in an anomaly-free U(1)′ gauge family model

We study a simple ultraviolet complete and anomaly-free Z′ model based on a U(1)′ gauge family symmetry without introducing extra fermions beyond the standard model. The U(1)′ group is diagonal in the three-family space in which the U(1)′ charges of the first and second families are the same but different from those of the third family. After spontaneous symmetry breaking and rotating to the mass eigenstates of quarks and leptons, there exist, in general, both flavor-conserving and flavor-changing couplings. In the flavor-conserving case, we use the latest dijet and dilepton search at the LHC to constrain the mass and gauge couplings of Z′. Also we show that in the flavor-changing and left–right asymmetry case, the t-channel Z′ process can only contribute to part of the forward–backward asymmetry in the top quark pair production observed at the Tevatron by taking into account the constraint from the same sign top production at the LHC.

Tests of a family gauge symmetry model at 103 TeV scale

Based on a specific model with U(3) family gauge symmetry at 103 TeV scale, we show its experimental signatures to search for. Since the gauge symmetry is introduced with a special purpose, its gauge coupling constant and gauge boson mass spectrum are not free. The current structure in this model leads to family number violations via exchange of extra gauge bosons. We investigate present constraints from flavor changing processes and discuss visible signatures at LHC and lepton colliders.

Family gauge symmetry as an origin of Koide's mass formula and charged lepton spectrum

Koide's mass formula is an empirical relation among the charged lepton masses which holds with a striking precision. We present a model of charged lepton sector within an effective field theory with U(3) \times SU(2) family gauge symmetry, which predicts Koide's formula within the present experimental accuracy. Radiative corrections as well as other corrections to Koide's mass formula have been taken into account. We adopt a known mechanism, through which the charged lepton spectrum is determined by the vacuum expectation value of a 9-component scalar field \Phi. On the basis of this mechanism, we implement the following mechanisms into our model: (1) The radiative correction induced by family gauge interaction cancels the QED radiative correction to Koide's mass formula, assuming a scenario in which the U(3) family gauge symmetry and SU(2)_L weak gauge symmetry are unified at 10^2-10^3 TeV scale; (2) A simple potential of \Phi invariant under U(3) \times SU(2) leads to a realistic charged lepton spectrum, consistent with the experimental values, assuming that Koide's formula is protected; (3) Koide's formula is stabilized by embedding U(3) \times SU(2) symmetry in a larger symmetry group. Formally fine tuning of parameters in the model is circumvented (apart from two exceptions) by appropriately connecting the charged lepton spectrum to the boundary (initial) conditions of the model at the cut-off scale.

Family gauge symmetry and Koide's mass formula

Koide's mass formula is an empirical relation among the charged lepton masses which holds with a striking precision. We propose a mechanism for cancelling the QED correction to Koide's formula. This is discussed in an effective theory with U ( 3 ) family gauge symmetry and a scenario in which this symmetry is unified with SU ( 2 ) L symmetry at 10 2 – 10 3 TeV scale.

SU(3)family gauge symmetry and the axion

We analyze the structure of a recently proposed effective field theory (EFT) for the generation of quark and lepton mass ratios and mixing angles, based on the spontaneous breaking of an $SU(3)$ family gauge symmetry at a high scale $F$. We classify the Yukawa operators necessary to seed the masses, making use of the continuous global symmetries that they preserve. One global $U(1)$, in addition to baryon number and electroweak hypercharge, remains unbroken after the inclusion of all operators required by standard model fermion phenomenology. An associated vacuum symmetry insures the vanishing of the first-family quark and charged-lepton masses in the absence of the family gauge interaction. If this $U(1)$ symmetry is taken to be exact in the EFT, broken explicitly by only the QCD-induced anomaly, and if the breaking scale $F$ is taken to lie in the range ${10}^{9}--{10}^{12}\text{ }\text{ }\mathrm{GeV}$, then the associated Nambu-Goldstone boson is a potential QCD axion.

Tri-bimaximal neutrino mixing from discrete subgroups of SU(3) and SO(3) family symmetry

It has recently been shown how tri-bimaximal neutrino mixing can be achieved, using the see-saw mechanism with constrained sequential dominance, through the vacuum alignment of a broken non-Abelian gauged family symmetry such as SO(3) or SU(3). Generalising the approach of Altarelli and Feruglio developed for an $A_4$ model we show how the reduction of the underlying symmetry to a discrete subgroup of SO(3) or SU(3) renders this alignment a generic property of such models. This means near tri-bimaximal mixing can be quite naturally accommodated in a complete unified theory of quark and lepton masses.

Towards a complete theory of fermion masses and mixings with SO(3) Family Symmetry and 5d SO(10) unification

We construct a complete 4d model of fermion masses and mixings in the Pati-Salam SU(4) x SU(2)_L x SU(2)_R framework governed by an SO(3) gauged Family Symmetry. The relevant low energy effective Yukawa operators are constructed so that the SO(3) flavons enter at the simplest possible one-flavon level, with couplings enforced by an additional U(1) x Z_2 symmetry. The simplicity of the flavon sector allows the messenger sector to be fully specified, allowing the ultraviolet completion of the model at the 4d renormalizable level. The model predicts approximate tri-bimaximal lepton mixing via the see-saw mechanism with sequential dominance, and vacuum alignment of flavons, with calculable deviations described by the neutrino sum rule. We perform a numerical analysis of the emerging charged fermion spectra and mixings. The 4d model is shown to result from a 5d orbifold GUT model based on SO(3) x SO(10), where small flavon vacuum expectation values originate from bulk volume suppression.

Mass ratios and mixing angles from a SU(3) gauge family symmetry

The effective field theory description of a gauged horizontal SU(3) symmetry successfully reproduces many of the small parameters in the mass matrices of the fermions of the Standard Model. Few observables in flavour physics appear in the effective Lagrangian as free parameters, suggesting that these specific quantities give us information about scales much larger than the flavour scale.

Flavor changing effects in family nonuniversalZ′ models

Flavor-changing and CP-violating interactions of Z' to fermions are generally present in models with extra U(1) gauge symmetry that are string-inspired or related to broken gauged family symmetry. We study the consequences of such couplings in fermion electric dipole moments, muon g-2, and K and B meson mixings. From experimental limits or measured values, we constrain the off-diagonal Z' couplings to fermions. Some of these constraints are comparable or stronger than the existing constraints obtained from other observables.

Quark mass ratios and mixing angles from SU(3) family gauge symmetry

We explore a framework for the computation of quark mass ratios and CKM mixing angles based on an SU(3) family gauge symmetry. The four ratios md/mb, ms/mb, mu/mt, and mc/mt can be fit at one-loop in the family gauge interaction. The same is true of the quark mixing angles theta12 and theta23, although the result for theta13 is too small. The CP violating phase is naturally O(1).

Family unification in five and six dimensions

In family unification models, all three families of quarks and leptons are grouped together into an irreducible representation of a simple gauge group, thus unifying the Standard Model gauge symmetries and a gauged family symmetry. Large orthogonal groups, and the exceptional groups $E_7$ and $E_8$ have been much studied for family unification. The main theoretical difficulty of family unification is the existence of mirror families at the weak scale. It is shown here that family unification without mirror families can be realized in simple five-dimensional and six-dimensional orbifold models similar to those recently proposed for SU(5) and SO(10) grand unification. It is noted that a family unification group that survived to near the weak scale and whose coupling extrapolated to high scales unified with those of the Standard model would be evidence accessible in principle at low energy of the existence of small (Planckian or GUT-scale) extra dimensions.

Flavor universal dynamical electroweak symmetry breaking

The top condensate see-saw mechanism of Dobrescu and Hill allows electroweak symmetry to be broken while deferring the problem of flavour to an electroweak singlet, massive sector. We provide an extended version of the singlet sector that naturally accommodates realistic masses for all the standard model fermions, which play an equal role in breaking electroweak symmetry. The models result in a relatively light composite Higgs sector with masses typically in the range of (400-700)~GeV. In more complete models the dynamics will presumably be driven by a broken gauged family or flavour symmetry group. As an example of the higher scale dynamics a fully dynamical model of the quark sector with a GIM mechanism is presented, based on an earlier top condensation model of King using broken family gauge symmetry interactions (that model was itself based on a technicolour model of Georgi). The crucial extra ingredient is a reinterpretation of the condensates that form when several gauge groups become strong close to the same scale. A related technicolour model of Randall which naturally includes the leptons too may also be adapted to this scenario. We discuss the low energy constraints on the massive gauge bosons and scalars of these models as well as their phenomenology at the TeV scale.

Atmospheric neutrino oscillations and maximal νμ− ντ mixing in unified models

The recent data describing the evidence for neutrino oscillations by Super Kamiokande implies that two neutrinos are very strongly mixed. We ask the question: can approximate maximal neutrino mixing be natural in unified (GUT or string) models? We attempt to answer this question in as much generality as possible. Without specifying a particular model, we are able to show that a gauged family symmetry can naturally provide the required maximal mixing between μ and τ neutrinos. The second and third family neutrino mass eigenstates are almost degenerate with masses of order 0.2 eV.