Family Symmetry Research Articles

Decoding fermion mass pattern from mass hierarchy

Abstract Building an organized Yukawa structure of quarks and leptons is an essential mission to understand fermion mass hierarchy and flavor mixing in particle physics. Inspired by the similarity of CKM and PMNS mixings, a common mass pattern for up-type and down-type quarks, charged leptons, and Dirac neutrinos is realized in terms of hierarchal masses. An organized structure of Yukawa couplings can be expressed on a Yukawa basis. The CKM mixing and PMNS mixing have the same mathematical forms due to SO(2) family symmetry. By fitting the CKM/PMNS mixing experiment, the flat pattern becomes a successful flavor structure. The fundamental fermions can be explained by a new picture to show the relationship between gauge structure and flavor structure.

Phenomenological aspects of the fermion and scalar sectors of a S4 flavored 3-3-1 model

We proposed a viable and predictive model based on the SU(3)C×SU(3)L×U(1)X gauge symmetry, supplemented by the global U(1)Lg symmetry, the S4 family symmetry and several auxiliary cyclic symmetries, which successfully reproduces the experimentally observed SM fermion mass and mixing pattern. The tiny active neutrino masses are generated through an inverse seesaw mechanism mediated by right-handed Majorana neutrinos. The model is consistent with the SM fermion masses and mixings and successfully accommodates the current Higgs diphoton decay rate constraints as well as the constraints arising from oblique S, T and U parameters and we studied the meson mixing due to flavor changing neutral currents mediated by heavy scalars, finding parameter space consistent with experimental constraints.

Quark-lepton mass relations from modular flavor symmetry

The so-called Golden Mass Relation provides a testable correlation between charged-lepton and down-type quark masses, that arises in certain flavor models that do not rely on Grand Unification. Such models typically involve broken family symmetries. In this work, we demonstrate that realistic fermion mass relations can emerge naturally in modular invariant models, without relying on ad hoc flavon alignments. We provide a model-independent derivation of a class of mass relations that are experimentally testable. These relations are determined by both the Clebsch-Gordan coefficients of the specific finite modular group and the expansion coefficients of its modular forms, thus offering potential probes of modular invariant models. As a detailed example, we present a set of viable mass relations based on the Γ4 ≅ S4 symmetry, which have calculable deviations from the usual Golden Mass Relation.

An unfamiliar way to generate the hierarchy of standard model fermion masses

While the properties of the observed Higgs boson agree with the Standard Model predictions, the hierarchy of fermion masses lacks an explanation within the model. In this work, we consider a fresh approach to this problem, involving a different Higgs doublet responsible for each quark mass. We construct a model with a gauged, non-anomalous U(1) family symmetry that fixes which fermion couples to which doublet with an O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(1) Yukawa coupling. The hierarchy of masses is generated by the hierarchy of vacuum expectation values of the Higgs fields. The model generically predicts a light, weakly coupled pseudoscalar. We verify that the model satisfies constraints from flavour changing neutral currents, Higgs phenomenology and electroweak precision tests.

Three generations of colored fermions with S_3 family symmetry from Cayley–Dickson sedenions

An algebraic representation of three generations of fermions with SU(3)_C color symmetry based on the Cayley–Dickson algebra of sedenions {mathbb {S}} is constructed. Recent constructions based on division algebras convincingly describe a single generation of leptons and quarks with Standard Model gauge symmetries. Nonetheless, an algebraic origin for the existence of exactly three generations has proven difficult to substantiate. We motivate mathbb {S} as a natural algebraic candidate to describe three generations with SU(3)_C gauge symmetry. We initially represent one generation of leptons and quarks in terms of two minimal left ideals of mathbb {C}ell (6), generated from a subset of all left actions of the complex sedenions on themselves. Subsequently we employ the S_3 automorphism of order three, which is an automorphism of mathbb {S} but not of mathbb {O}, to generate two additional generations. Given the relative obscurity of sedenions, efforts have been made to present the material in a self-contained manner.

Global monopoles in the two-Higgs-doublet-model

We discuss monopoles formed due to the spontaneous breakdown of a global SO(3)HF symmetry within the global two-Higgs doublet model. We explain that the Higgs sector dynamics can be described in terms of two vectors one of which is null, RA=(R0,Ra,R4,R5) for a=1,2,3, with 5 independent components describing the Higgs family symmetry and another, na, with 3 independent components related to the “would-be” Goldstone bosons. When formed from random initial conditions we find that monopoles are formed with a charged vacuum in the centre which couples the two fields together. We find a spherically symmetric solution which is an approximately uniform, unit winding of the sphere in both the Ra and na vectors. These global monopoles are closely related to the Nambu monopole. The additional complexity and structure contained in these monopoles does not appear to prevent the scaling of their density.

Fermion masses and mixings, dark matter, leptogenesis and $$g-2$$ muon anomaly in an extended 2HDM with inverse seesaw

We propose a predictive \(Q_4\) flavored 2HDM model, where the scalar sector is enlarged by the inclusion of several gauge singlet scalars and the fermion sector by the inclusion of right-handed Majorana neutrinos. In our model, the \(Q_4\) family symmetry is supplemented by several auxiliary cyclic symmetries, whose spontaneous breaking produces the observed pattern of SM charged fermion masses and quark mixing angles. The light active neutrino masses are generated from an inverse seesaw mechanism at one loop level thanks to a remnant preserved \(Z_2\) symmetry. Our model successfully reproduces the measured dark matter relic abundance and is consistent with direct detection constraints for masses of the DM candidate around \(\sim\) 6.3 TeV. Furthermore, our model is also consistent with the lepton and baryon asymmetries of the Universe as well as with the muon anomalous magnetic moment.

Fermion masses and mixings and g-2 muon anomaly in a 3-3-1 model with D_4 family symmetry

We propose a predictive model based on the SU(3)_Ctimes SU(3)_Ltimes U(1)_X gauge symmetry, which is supplemented by the D_4 family symmetry and several auxiliary cyclic symmetries whose spontaneous breaking produces the observed SM fermion mass and mixing pattern. The masses of the light active neutrinos are produced by an inverse seesaw mechanism mediated by three right handed Majorana neutrinos. To the best of our knowledge the model corresponds to the first implementation of the D_4 family symmetry in a SU(3)_Ctimes SU(3)_Ltimes U(1)_X theory with three right handed Majorana neutrinos and inverse seesaw mechanism. Our proposed model successfully accommodates the experimental values of the SM fermion mass and mixing parameters, the muon anomalous magnetic moment as well as the Higgs diphoton decay rate and meson oscillations constraints. The consistency of our model with the muon anomalous magnetic moment requires charged exotic vector like leptons at the TeV scale.

Scotogenic Majorana neutrino masses in a predictive orbifold theory of flavor

The use of extra space-time dimensions provides a promising approach to the flavour problem. The chosen compactification of a 6-dimensional orbifold implies a remnant family symmetry $A_4$. This makes interesting predictions for quark and lepton masses, for neutrino oscillations and neutrinoless double beta decay, providing also a very good global description of all flavour observables. Due to an auxiliary $\mathbb{Z}_4$ symmetry, we implement a scotogenic Majorana neutrino mass generation mechanism with a viable WIMP dark matter candidate.

Controlled fermion mixing and FCNCs in a \u2206(27) 3+1 Higgs Doublet Model

We propose a 3+1 Higgs Doublet Model based on the ∆(27) family symmetry supplemented by several auxiliary cyclic symmetries leading to viable Yukawa textures for the Standard Model fermions, consistent with the observed pattern of fermion masses and mixings. The charged fermion mass hierarchy and the quark mixing pattern is generated by the spontaneous breaking of the discrete symmetries due to flavons that act as Froggatt-Nielsen fields. The tiny neutrino masses arise from a radiative seesaw mechanism at one loop level, thanks to a preserved {Z}_2^{(1)} discrete symmetry, which also leads to stable scalar and fermionic dark matter candidates. The leptonic sector features the predictive cobimaximal mixing pattern, consistent with the experimental data from neutrino oscillations. For the scenario of normal neutrino mass hierarchy, the model predicts an effective Majorana neutrino mass parameter in the range 3 meV ≲ mββ ≲ 18 meV, which is within the declared range of sensitivity of modern experiments. The model predicts Flavour Changing Neutral Currents which constrain the model, for instance, μ→e nuclear conversion processes and Kaon mixing are found to be within the reach of the forthcoming experiments.

Trimaximal neutrino mixing from scotogenic A4 family symmetry

We propose a flavor theory of leptons implementing an A4 family symmetry. Our scheme provides a simple way to derive trimaximal neutrino mixing from first principles, leading to simple and testable predictions for neutrino mixing and CP violation. Dark matter mediates neutrino mass generation, as in the simplest scotogenic model.

Reconstructing effective Lagrangians embedding residual family symmetries

We consider effective Lagrangians which, after electroweak- and family-symmetry breaking, yield fermionic mass matrices and/or other flavoured couplings exhibiting residual family symmetries (RFS). Thinking from the bottom up, these RFS intimately link ultraviolet (UV) Beyond-the-Standard Model (BSM) physics to infrared flavour phenomenology without direct reference to any (potentially unfalsifiable) UV dynamics. While this discussion is typically performed at the level of RFS group generators and the UV flavour groups they can close, we now also focus on the RFS-implied shape of the low-energy mass/coupling matrices. We then show how this information can be used to algorithmically guide the reconstruction of an effective Lagrangian, thereby forming top-down models realizing the typical bottom-up phenomenological conclusions. As a first application we take results from scans of finite groups capable of controlling (through their RFS) CKM or PMNS mixing within the SM alone. We then extend this to recently studied scenarios where RFS also control special patterns of leptoquark couplings, thus providing proof-in-principle completions for such ‘Simplified Models of Flavourful Leptoquarks.’

Predictions from warped flavor dynamics based on the T′ family group

We propose a realistic theory of fermion masses and mixings using a five-dimensional warped scenario where all fermions propagate in the bulk and the Higgs field is localized on the IR brane. The assumed $T'$ flavor symmetry is broken on the branes by flavon fields, providing a consistent scenario where fermion mass hierarchies arise from adequate choices of the bulk mass parameters, while quark and lepton mixing angles are restricted by the family symmetry. Neutrino mass splittings, mixing parameters and the Dirac CP phase all arise from the type-I seesaw mechanism and are tightly correlated, leading to predictions for the neutrino oscillation parameters, as well as expected \znbb decay rates within reach of upcoming experiments. The scheme also provides a good global description of flavor observables in the quark sector.

Scotogenic dark matter in an orbifold theory of flavor

We propose a flavour theory in which the family symmetry results naturally from a six-dimensional orbifold compactification. “Diracness” of neutrinos is a consequence of the spacetime dimensionality, and the fact that right-handed neutrinos live in the bulk. Dark matter is incorporated in a scotogenic way, as a result of an auxiliary ℤ3 symmetry, and its stability is associated to the conservation of a “dark parity” symmetry. The model leads naturally to a “golden” quark-lepton mass relation.

Fermion mass splitting in the technicolor coupled scenario

We discuss fermion mass generation in unified models where QCD and technicolor (or any two strongly interacting theories) have their Schwinger–Dyson equations coupled. In this case the technicolor (TC) and QCD self-energies are modified in comparison with the behavior observed in the isolated theories. In these models the pseudo-Goldstone boson masses are much higher than the ones obtained in different contexts, and phenomenological signals, except from a light scalar composite boson, will be quite difficult to be observed at present collider energies. The most noticeable fact of these models is how the mass splitting between the different ordinary fermions is generated. We discuss how a necessary horizontal (or family) symmetry can be implemented in order to generate the mass splitting between fermions of different generations; how the fermionic mass spectrum may be modified due to GUT interactions, as well as how the mass splitting within the same fermionic generation are generated due to electroweak and GUT interactions.

Probing the predictions of an orbifold theory of flavor

We examine the implications of a recently proposed theory of fermion masses and mixings in which an ${A}_{4}$ family symmetry emerges from orbifold compactification. We analyze two variant schemes concerning their predictions for neutrino oscillations, neutrinoless double-beta decay, and the golden quark-lepton unification mass relation. We find that upcoming experiments DUNE as well as LEGEND and nEXO offer good chances of exploring a substantial region of neutrino parameters.

Generating the Cabibbo angle in flavored gauge mediation models with discrete non-Abelian symmetries

We explore the generation of fermion masses and quark mixing angles within flavored gauge mediation models of supersymmetry breaking in which the Higgs and messenger doublets are connected by a discrete non-Abelian symmetry. In this framework, the Higgs-messenger symmetry, which we take for concreteness to be the discrete group $\mathcal{S}_3$, also plays the role of a (partial) family symmetry. We investigate mechanisms for generating mass hierarchies for the lighter quark generations and generating the Cabibbo angle within this class of models. While perturbations of the couplings at the renormalizable level do not lead to phenomenologically viable quark mixing parameters, we show that the Cabibbo angle can be generated via couplings at the nonrenormalizable level and explore the phenomenological implications of this scenario.

Littlest inverse seesaw model

We propose a minimal predictive inverse seesaw model based on two right-handed neutrinos and two additional singlets, leading to the same low energy neutrino mass matrix as in the Littlest Seesaw (LS) (type I) model. In order to implement such a Littlest Inverse Seesaw (LIS) model, we have used an S4 family symmetry, together with other various symmetries, flavons and driving fields. The resulting LIS model leads to an excellent fit to the low energy neutrino parameters, including the prediction of a normal neutrino mass ordering, exactly as in the usual LS model. However, unlike the LS model, the LIS model allows charged lepton flavor violating (CLFV) processes and lepton conversion in nuclei within reach of the forthcoming experiments.

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.

SU(5) grand unified theory with A4 modular symmetry

We present the first example of a grand unified theory (GUT) with a modular symmetry interpreted as a family symmetry. The theory is based on supersymmetric $SU(5)$ in 6d, where the two extra dimensions are compactified on a $T_2/\mathbb{Z}_2$ orbifold. We have shown that, if there is a finite modular symmetry, then it can only be $A_4$ with an (infinite) discrete choice of moduli, where we focus on $\tau = \omega=e^{i2\pi/3}$, the unique solution with $|\tau|=1$. The fields on the branes respect a generalised CP and flavour symmetry $A_4\ltimes \mathbb{Z}_2$ which is isomorphic to $S_4$ which leads to an effective $\mu-\tau$ reflection symmetry at low energies, implying maximal atmospheric mixing and maximal leptonic CP violation. We construct an explicit model along these lines with two triplet flavons in the bulk, whose vacuum alignments are determined by orbifold boundary conditions, analogous to those used for $SU(5)$ breaking with doublet-triplet splitting. There are two right-handed neutrinos on the branes whose Yukawa couplings are determined by modular weights. The charged lepton and down-type quarks have diagonal and hierarchical Yukawa matrices, with quark mixing due to a hierarchical up-quark Yukawa matrix.