Family Symmetry Research Articles

Spontaneous breaking of SO(3) to finite family symmetries with supersymmetry \u2014 an A4 model

We discuss the breaking of SO(3) down to finite family symmetries such as A4, S4 and A5 using supersymmetric potentials for the first time. We analyse in detail the case of supersymmetric A4 and its finite subgroups Z3 and Z2. We then propose a supersymmetric A4 model of leptons along these lines, originating from SO(3) × U(1), which leads to a phenomenologically acceptable pattern of lepton mixing and masses once subleading corrections are taken into account. We also discuss the phenomenological consequences of having a gauged SO(3), leading to massive gauge bosons, and show that all domain wall problems are resolved in this model.

{R}_{K^{left(*right)}} and the origin of Yukawa couplings

We explore the possibility that the semi-leptonic B decay ratios {R}_{K^{left(*right)}} which violate μ − e universality are related to the origin of the fermion Yukawa couplings in the Standard Model. Some time ago, a vector-like fourth family (without a Z′) was used to generate fermion mass hierarchies and mixing patterns without introducing any family symmetry. Recently the idea of inducing flavourful Z′ couplings via mixing with a vector-like fourth family which carries gauged U(1)′ charges has been proposed as a simple way of producing controlled flavour universality violation while elegantly cancelling anomalies. We show that the fusion of these two ideas provides a nice connection between {R}_{K^{left(*right)}} and the origin of Yukawa couplings in the quark sector. However the lepton sector requires some tuning of Yukawa couplings to obtain the desired coupling of Z′ to muons.

Standard Model Fermions and Infinite-Dimensional R Symmetries.

Following up on our earlier work [K. A. Meissner and H. Nicolai, Phys. Rev. D 91, 065029 (2015)] where we showed how to amend a scheme originally proposed by M. Gell-Mann to identify the 48 spin-1/2 fermions of N=8 supergravity that remain after complete breaking of N=8 supersymmetry with the 3×16 quarks and leptons of the standard model, we further generalize the construction to account for the full SU(3)_{c}×SU(2)_{w}×U(1)_{Y} assignments, with an additional family symmetry SU(3)_{f}. Our proposal relies in an essential way on embedding the SU(8) R symmetry of N=8 supergravity into the (infinite-dimensional) "maximal compact" subgroup K(E_{10}) of the conjectured maximal duality symmetry E_{10}. As a by-product, it predicts fractionally charged and possibly strongly interacting massive gravitinos. It also indicates how E_{10} and K(E_{10}) can supersede supersymmetry as a guiding principle for unification.

Electroweak phase transitions in multi-Higgs models: the case of Trinification-inspired THDSM

The rich vacuum structure of multi-Higgs extensions of the Standard Model (SM) may have interesting cosmological implications for the electroweak phase transition (EWPT). As an important example of such class of models, we consider a particularly simple low-energy SM-like limit of a recently proposed Grand-Unified Trinification model with the scalar sector composed of two Higgs doublets and a complex singlet and with a global U(1) family symmetry. The fermion sector of this model is extended with a family of vector-like quarks which enhances CP violation. With the current study, we aim at exploring the generic vacuum structure and uncovering the features of the EWPT in this model relevant for cosmology. We show the existence of different phase transition patterns providing strong departure from thermal equilibrium. Most of these observations are not specific to the considered model and may generically be expected in other multi-Higgs extensions of the SM.

An S4 \xd7 SU(5) SUSY GUT of flavour in 6d

We propose a 6d model with a SUSY SU(5) gauge symmetry. After compactification, it explains the origin of the S4 Family Symmetry with CSD3 vacuum alignment, as well as SU(5) breaking with doublet-triplet splitting. The model naturally accounts for all quark and lepton (including neutrino) masses and mixings, incorporating the highly predictive Littlest Seesaw structure. It spontaneously breaks CP symmetry, resulting in successful CP violation in the quark and lepton sectors, while solving the Strong CP problem. It also explains the Baryon Asymmetry of the Universe (BAU) through leptogenesis, with the leptogenesis phase directly linked to the Dirac and Majorana phases.

Effective alignments as building blocks of flavor models

Flavour models typically rely on flavons - scalars that break the family symmetry by acquiring vacuum expectation values in specific directions. We develop the idea of effective alignments, i.e.\ cases where the contractions of multiple flavons give rise to directions that are hard or impossible to obtain directly by breaking the family symmetry. Focusing on the example where the symmetry is $S_4$, we list the effective alignments that can be obtained from flavons vacuum expectation values that arise naturally from $S_4$. Using those effective alignments as building blocks, it is possible to construct flavour models, for example by using the effective alignments in constrained sequential dominance models. We illustrate how to obtain several of the mixing schemes in the literature, and explicitly construct renormalizable models for three viable cases, two of which lead to trimaximal mixing scenarios.

Muon g−2 and dark matter suggest nonuniversal gaugino masses: SU(5)×A4 case study at the LHC

We argue that in order to account for the muon anomalous magnetic moment $g\ensuremath{-}2$, dark matter and LHC data, nonuniversal gaugino masses ${M}_{i}$ at the high scale are required in the framework of the minimal supersymmetric standard model. We also need a right-handed smuon ${\stackrel{\texttildelow{}}{\ensuremath{\mu}}}_{R}$ with a mass around 100 GeV, evading LHC searches due to the proximity of a neutralino ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}$ several GeV lighter which allows successful dark matter. We discuss such a scenario in the framework of an $SU(5)$ grand unified theory (GUT) combined with ${A}_{4}$ family symmetry, where the three $\overline{5}$ representations form a single triplet of ${A}_{4}$ with a unified soft mass ${m}_{F}$, while the three 10 representations are singlets of ${A}_{4}$ with independent soft masses ${m}_{T1},{m}_{T2},{m}_{T3}$. Although ${m}_{T2}$ (and hence ${\stackrel{\texttildelow{}}{\ensuremath{\mu}}}_{R}$) may be light, the muon $g\ensuremath{-}2$ and relic density also requires light ${M}_{1}\ensuremath{\simeq}250\text{ }\text{ }\mathrm{GeV}$, which is incompatible with universal gaugino masses due to LHC constraints on ${M}_{2}$ and ${M}_{3}$ arising from gaugino searches. After showing that universal gaugino masses ${M}_{1/2}$ at the GUT scale are excluded by gluino searches, we provide a series of benchmarks which show that while ${M}_{1}={M}_{2}\ensuremath{\ll}{M}_{3}$ is in tension with 8 and 13 TeV LHC data, ${M}_{1}<{M}_{2}\ensuremath{\ll}{M}_{3}$ is currently allowed. Even this scenario is almost excluded by the tension between the muon $g\ensuremath{-}2$, relic density, dark matter direct detection and LHC data. We focus on a region of parameter space that has not been studied in detail before being characterized by low Higgsino mass $\ensuremath{\mu}\ensuremath{\approx}\ensuremath{-}300\text{ }\text{ }\mathrm{GeV}$, as required by the muon $g\ensuremath{-}2$. The LHC will be able to fully test this scenario with the upgraded luminosity via muon-dominated tri- and dilepton signatures resulting from Higgsino-dominated ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{\ifmmode\pm\else\textpm\fi{}}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{2}^{0}$ and ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{+}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{\ensuremath{-}}$ production.

Fermion masses and mixings and dark matter constraints in a model with radiative seesaw mechanism

We formulate a predictive model of fermion masses and mixings based on a Δ(27) family symmetry. In the quark sector the model leads to the viable mixing inspired texture where the Cabibbo angle comes from the down quark sector and the other angles come from both up and down quark sectors. In the lepton sector the model generates a predictive structure for charged leptons and, after radiative seesaw, an effective neutrino mass matrix with only one real and one complex parameter. We carry out a detailed analysis of the predictions in the lepton sector, where the model is only viable for inverted neutrino mass hierarchy, predicting a strict correlation between θ23 and θ13. We show a benchmark point that leads to the best-fit values of θ12, θ13, predicting a specific sin2θ23 ≃ 0.51 (within the 3σ range), a leptonic CP-violating Dirac phase δ ≃ 281.6° and for neutrinoless double-beta decay mee ≃ 41.3 meV. We turn then to an analysis of the dark matter candidates in the model, which are stabilized by an unbroken ℤ2 symmetry. We discuss the possibility of scalar dark matter, which can generate the observed abundance through the Higgs portal by the standard WIMP mechanism. An interesting possibility arises if the lightest heavy Majorana neutrino is the lightest ℤ2-odd particle. The model can produce a viable fermionic dark matter candidate, but only as a feebly interacting massive particle (FIMP), with the smallness of the coupling to the visible sector protected by a symmetry and directly related to the smallness of the light neutrino masses.

Heavy charged scalars from coverline{s} fusion: a generic search strategy applied to a 3HDM with U(1) \xd7 U(1) family symmetry

We describe a class of three Higgs doublet models (3HDMs) with a softly broken U(1) × U(1) family symmetry that enforces a Cabibbo-like quark mixing while forbidding tree-level flavour changing neutral currents. The hierarchy in the observed quark masses is partly explained by a softer hierarchy in the vacuum expectation values of the three Higgs doublets. As a consequence, the physical scalar spectrum contains a Standard Model (SM) like Higgs boson h125 while exotic scalars couple the strongest to the second quark family, leading to rather unconventional discovery channels that could be probed at the Large Hadron Collider. In particular, we describe a search strategy for the lightest charged Higgs boson H±, through the process coverline{s}to {H}^{+}to {W}^{+}{h}_{125} , using a multivariate analysis that leads to an excellent discriminatory power against the SM background. Although the analysis is applied to the proposed class of 3HDMs, we employ a model-independent formulation such that it can be applied to any other model with the same discovery channel.

A unified model of quarks and leptons with a universal texture zero

We show that a universal texture zero in the (1,1) position of all fermionic mass matrices, including heavy right-handed Majorana neutrinos driving a type-I see-saw mechanism, can lead to a viable spectrum of mass, mixing and CP violation for both quarks and leptons, including (but not limited to) three important postdictions: the Cabibbo angle, the charged lepton masses, and the leptonic ‘reactor’ angle. We model this texture zero with a non-Abelian discrete family symmetry that can easily be embedded in a grand unified framework, and discuss the details of the phenomenology after electroweak and family symmetry breaking. We provide an explicit numerical fit to the available data and obtain excellent agreement with the 18 observables in the charged fermion and neutrino sectors with just 9 free parameters. We further show that the vacua of our new scalar familon fields are readily aligned along desired directions in family space, and also demonstrate discrete gauge anomaly freedom at the relevant scale of our effective theory.

Accidental Peccei–Quinn symmetry from discrete flavour symmetry and Pati–Salam

We show how an accidental U(1) Peccei–Quinn (PQ) symmetry can arise from a discrete A4 family symmetry combined with a discrete flavour symmetry Z3×Z52, in a realistic Pati–Salam unified theory of flavour. Imposing only these discrete flavour symmetries, the axion solution to the strong CP problem is protected from PQ-breaking operators to the required degree. A QCD axion arises from a linear combination of A4 triplet flavons, which are also responsible for fermion flavour structures due to their vacuum alignments. We find that the requirement of an accidental PQ symmetry arising from a discrete flavour symmetry constrains the form of the Yukawa matrices, providing a link between flavour and the strong CP problem. Our model predicts specific flavour-violating couplings of the flavourful axion and thus puts a strong limit on the axion scale from kaon decays.

Structure of right-handed neutrino mass matrix

Recently, Nishiura and the author have proposed a unified quark-lepton mass matrix model under a family symmetry U(3)$\times$U(3)$'$. The model can give excellent parameter-fitting to the observed quark and neutrino data. The model has a reasonable basis as far as the quark sector, but the form of the right-handed neutrino mass matrix $M_R$ does not have a theoretical grand, that is, it was nothing but a phenomenological assumption. In this paper, it is pointed out that the form of $M_R$ is originated in structure of neutrino mass matrix for $(\nu_i, N_\alpha)$ where $\nu_i$ ($i=1,2,3$) and $N_\alpha$ ($\alpha=1,2,3$) are U(3)-family and U(3)$'$-family triplets, respectively.

A composite axion from a supersymmetric product group

A global U(1)PQ symmetry is protected from gravitational effects in the s-confining SU(N)k product group theory with A + 4Q+Noverline{Q} matter. If the SU(4) family symmetry is gauged and an appropriate tree-level superpotential is added, then the dynamically generated superpotential spontaneously breaks SU(4) × U(1)PQ → SU(3)c and produces a QCD axion. Small values of the CP -violating θ parameter are then possible without any fine-tuning, as long as the product group is suitably large. By introducing a second copy of the s-confining SU(N) product group also coupled to the gauged SU(4), we find that values as small as N = 7 are consistent with overline{theta}<1{0}^{-10} , even under the pessimistic assumption that the dominant contribution to the axion quality is at tree level.

Families from supergroups and predictions for leptonic CP violation

As was shown in 1984 by Caneschi, Farrar, and Schwimmer, decomposing representations of the supergroup SU(M |N ), can give interesting anomaly-free sets of fermion representations of SU(M ) × SU(N ) × U(1). It is shown here that such groups can be used to construct realistic grand unified models with non-abelian gauged family symmetries. A particularly simple three-family example based on SU(5) × SU(2) × U(1) is studied. The forms of the mass matrices, including that of the right-handed neutrinos, are determined in terms of SU(2) Clebsch coefficients; and the model is able to fit the lepton sector and predict the Dirac CP-violating phase of the neutrinos. Models of this type would have a rich phenomenology if part of the family symmetry is broken near the electroweak scale.

Predictions from a flavour GUT model combined with a SUSY breaking sector

We discuss how flavour GUT models in the context of supergravity can be completed with a simple SUSY breaking sector, such that the flavour-dependent (non-universal) soft breaking terms can be calculated. As an example, we discuss a model based on an SU(5) GUT symmetry and A4 family symmetry, plus additional discrete “shaping symmetries” and a ℤ4R symmetry. We calculate the soft terms and identify the relevant high scale input parameters, and investigate the resulting predictions for the low scale observables, such as flavour violating processes, the sparticle spectrum and the dark matter relic density.

Towards a complete Δ(27) × SO(10) GUT of flavour

We propose a renormalisable model based on Δ(27) family symmetry with an SO(10) grand unified theory (GUT) leading to a novel form of spontaneous geometrical CP violation. The symmetries are broken close to the GUT breaking scale to yield the minimal supersymmetric standard model with standard R-parity. Low-scale Yukawa structure is dictated by the coupling of matter to Δ(27) antitriplets whose vacuum expectation values are aligned in the CSD3 directions by the superpotential. Light physical Majorana neutrinos masses emerge from the seesaw mechanism within SO(10). The model predicts a normal neutrino mass hierarchy with the best-fit lightest neutrino mass m1 ∼ 0.3 meV, CP-violating oscillation phase δl ≈ 280° and the remaining neutrino parameters all within 1σ of their best-fit experimental values.

The discrete family symmetries as the possible solution to the flavour problem

In order to explain the fermions masses and mixing parameters appearing in the lepton sector of the Standard Model, one proposes the extension of its symmetry. A discrete, non-abelian subgroup of $U(3)$ is added to the gauge group $SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$ . Apart from that, one assumes the existence of one extra Higgs doublet. This article focuses mainly on the mathematical theorems and computational techniques which brought us to the results.

Left right symmetric model with additional family symmetry

Left right symmetric model with additional family symmetry

Flavon VEV scales in U(3)×U(3)′ model

We have recently proposed a quark and lepton mass matrix model based on U(3)[Formula: see text]×[Formula: see text]U(3)[Formula: see text] family symmetry as the so-called Yukawaon model, in which the U(3) symmetry is broken by VEVs of flavons [Formula: see text] which are [Formula: see text] of U(3)[Formula: see text]×[Formula: see text]U(3)[Formula: see text]. The model has successfully provided the unified description of quark and lepton masses and mixings by using the observed charged lepton masses as only family-number dependent input parameters. However, our final goal is not only to give well-satisfied fitting of quark and lepton masses and mixings, but also to investigate physics behind such a successful parameter fitting. Therefore, our next concern is scales of VEVs of the flavons because we have not paid attention to scales of flavons in the previous study. In order to give consistency among the scales, the previous flavon model is drastically changed together with economizing number of the flavons, but with keeping previous phenomenological success. We estimate that VEVs of flavons with [Formula: see text], [Formula: see text] and [Formula: see text] are of the orders of 10 TeV, 104 TeV and 107 TeV, respectively.

Neutrino mass sum rules and symmetries of the mass matrix

Neutrino mass sum rules have recently gained again more attention as a powerful tool to discriminate and test various flavour models in the near future. A related question which has not yet been discussed fully satisfactorily was the origin of these sum rules and if they are related to any residual or accidental symmetry. We will address this open issue here systematically and find previous statements confirmed. Namely, the sum rules are not related to any enhanced symmetry of the Lagrangian after family symmetry breaking but they are simply the result of a reduction of free parameters due to skillful model building.