We consider a SU(5) x U(1)_F GUT-flavor model in which the number of effects that determine the charged fermions Yukawa matrices is much larger than the number of observables, resulting in a hierarchical fermion spectrum with no particular regularities. The GUT-flavor symmetry is broken by flavons in the adjoint of SU(5), realizing a variant of the Froggatt-Nielsen mechanism that gives rise to a large number of effective operators. By assuming a common mass for the heavy fields and universality of the fundamental Yukawa couplings, we reduce the number of free parameters to one. The observed fermion mass spectrum is reproduced thanks to selection rules that discriminate among various contributions. Bottom-tau Yukawa unification is preserved at leading order, but there is no unification for the first two families. Interestingly, U(1)_F charges alone do not determine the hierarchy, and can only give upper bounds on the parametric suppression of the Yukawa operators.
It is shown that a fermion mass matrix changing in orientation (rotating) with changing scales can give a simple yet near-quantitative explanation for quark mixing, neutrino oscillations and the fermion mass hierarchy.
We show that a simultaneous explanation for fermionic mass hierarchy among and within the fermionic families, quark-mixing, can be obtained in an extension of the standard model, with real singlet scalar fields, which is UV completed by vector-like fermions and a strongly interacting sector.
The introduction of strongly-interacting mirror fermions with masses between the weak scale and 1 TeV could offer a viable alternative to the Higgs mechanism. The framework provided solves the hierarchy problem naturally and predicts a rich phenomenology for present and future experiments.
In non-supersymmetric grand unified models a ``radiative fermion mass hierarchy" can be achieved in which the spectrum of quark and lepton masses is determined entirely by physics at the unification scale, with many relations following from the unified gauge symmetry, and with the masses of the lightest family arising from loops. A simple, realistic, and predictive model of this kind is presented. A "doubly lopsided" structure, known to lead to bilarge neutrino mixing, plays a crucial role in the radiative hierarchy.
We present an SU(9) model of family unification with three light chiral families, and a natural hierarchy of charged fermion masses and mixings. The existence of singlet right handed neutrions with masses about two orders of magnitude smaller than the GUT scale, as needed to understand the light neutrinos masses via the see-saw mechanism, is compelling in our model.
Some phenomenological aspects of a supersymmetric model for fermion mass hierarchy proposed previously are discussed. It is required that the lepton universality violation is near to its current experimental bound. The lepton number violation decay modes $τ\to 2eμ$ and $3μ$ maybe observable in the near future. The Majorana mass of electron-neutrino is predicted to be about 0.1 eV. The fine-tuning problem is discussed.
Recently various phenomenological implications of the existence of extra space-time dimensions have been investigated. In this letter, we construct a model with realistic fermion mass hierarchy with (large) extra dimensions beyond the usual four dimensions. In this model, it is assumed that some matter fields live in the bulk and the others are confined on our four dimensional wall. It can naturally reproduce the quark and lepton mass hierarchy and mixing angles without any symmetry arguments. We also discuss some possibilities of obtaining suitable neutrino masses and mixings for the solar an…
We propose a bottom-up approach that a structure of a high-energy physics is explored by accumulating existence proofs and/or no-go theorems in the standard model or its extension. As an illustration, we study fermion mass hierarchies based on an extension of the standard model with vector-like fermions. It is shown that a magnitude of elements of Yukawa coupling matrices can become $O(1)$ and a Yukawa coupling unification can be realized in a theory beyond the extended model, if vector-like fermions mix with three families. In this case, small Yukawa couplings in the standard model can be hig…
We develop a 5d model for ElectroWeak physics based on a non compact warped extra dimension of finite length, known as the soft wall scenario, where all the dynamical degrees of freedom propagate in the 5d bulk. We solve the equations of motion and find the allowed spectra, showing that the mass of the lightest fermionic mode behaves as a power law of the effective 4d Yukawa coupling constant, with the exponent being the corresponding fermionic 5d bulk mass. Precisely this non universal behavior allows us to reproduce the hierarchy between the Standard Model (SM) fermion masses (from neutrinos…
A non-supersymmetric grand unified theory can exhibit a "radiative fermion mass hierarchy", in which the heavier quarks and leptons get mass at tree level and the lighter ones get mass from loop diagrams. Recently the first predictive model of this type was proposed. Here it is analyzed numerically and it is shown to give an excellent fit to the quark and lepton masses and mixings, including the CP phase violating phase $δ_{CKM}$. A relation between the neutrino angle $θ_{13}$ and the atmospheric neutrino angle is obtained
We propose a renormalizable theory with minimal particle content and symmetries, that successfully explains the number of Standard Model (SM) fermion families, the SM fermion mass hierarchy, the tiny values for the light active neutrino masses, the lepton and baryon asymmetry of the Universe, the dark matter relic density as well as the muon and electron anomalous magnetic moments. In the proposed model, the top quark and the exotic fermions do acquire tree-level masses whereas the SM charged fermions lighter than the top quark gain one-loop level masses. Besides that, the tiny masses for the …
The fermion mass problem is briefly reviewed. The observed hierarchy of quark and charged lepton masses strongly suggests the existence of an approximately conserved chiral flavour symmetry beyond the Standard Model. It is argued that in models of this type, the requirement of a natural explanation for both the atmospheric and solar neutrino problems leads to an essentially unique picture of neutrino masses and mixing angles. The anti-grand unification model is used as an explicit example to illustrate these ideas.
Recently a new mechanism has been proposed to cure the problem of fermion mass hierarchy in the Standard Model (SM) model. In this scenario, all SM charged fermions other than top quark arise from higher dimensional operators involving the SM Higgs field. This model also predicted some interesting phenomenology of the Higgs boson. We generalize this model to accommodate neutrino masses (Dirac & Majorana) and also obtain the mixing pattern in the leptonic sector. To generate neutrino masses, we add extra three right handed neutrinos $(N_{iR})$ in this model.
In this paper we propose a possible explanation to the Fermion mass hierarchy problem by fitting the type-II seesaw mechanism into the Higgs doublet sector, such that their vacuum expectation values are hierarchal. We extend the Standard Model with two extra Higgs doublets as well as a spontaneously broken $U_X(1)$ gauge symmetry. All the fermion Yukawa couplings except that of top quark are of order ${\cal O} (10^{-2})$ in our model. Constraints on the parameter space from Electroweak precision measurements are studied. Besides, the neutral component of the new fields, which are introduced to…
We present a new mechanism for solving the fermionic masses and mixing hierarchies of the standard model through a minimal symmetry $\mathcal{Z}_2 \times \mathcal{Z}_5$. The mechanism is also capable of explaining the neutrino masses and mixing parameters. The phenomenological bounds arising from kaon mixing are also derived on the parameter space of the model.
We discuss a supersymmetric grand unified model which has gauge group SU(5) $\times$ SU(5) $\times$ SU(5), with matter fields transforming asymmetrically under different gauge SU(5) groups. We observe that the gauge structure of the model leads to approximate texture zero structures in fermion mass matrices and a natural hierarchy in the Yukawa couplings. The proton lifetime is estimated to be larger than $10^{34}$ years in this model. As in more conventional supersymmetric GUT models with product gauge groups, this model possesses no tensor fields with rank higher than 2, so that it might ari…
Grand gauge-Higgs unification of five dimensional $SU(6)$ gauge theory on an orbifold $S^1/Z_2$ is discussed. The Standard model (SM) fermions are introduced on one of the boundaries and some massive bulk fields are also introduced so that they couple to the SM fermions through the mass terms on the boundary. Integrating out the bulk fields generates the SM fermion masses with exponentially small bulk mass dependences. The SM fermion masses except for top quark are shown to be reproduced by mild tuning the bulk masses. One-loop Higgs potential is calculated and it is shown that the electroweak…
We suggest simple models which produce the suitable fermion mass hierarchies and flavor mixing angles based on the supersymmetric SO(10) grand unified theory in 6 dimensions compactified on a T^2/Z_2 orbifold. The gauge and Higgs fields propagate in 6 dimensions while ordinal chiral matter fields are localized in 4 dimensions. We introduce extra vector-like heavy fields in the extra dimensions. We show three models according to the configurations of vector-like fields in extra dimensions. The suitable fermion mass hierarchies and flavor mixings are generated by integrating out these vector-lik…
In this paper we explore models in which we add a singlet scalar Higgs to the Standard Model. All of these models explain the origin of the mass hierarchy amongst the fermion masses and mixing angles. We discuss 24 different variations on this model, and explore the different phenomenological possibilities. We find that the phenomenological implications of all the models are very similar except in the Higgs sector. Higgs decays and signals can be altered very significantly in all the models, but break up into two distinct classes. We also describe a systematic method for generating these model…
In this paper, we move from a "proof of concept" to challenging predictions in a flavour model emerging from a single fermion family in six dimensions (6-D) with the two extra dimensions compactified on a sphere. The most striking predictions (beyond the basic ingredients already demonstrated for a realistic quark mass pattern) are for the neutrino sector. Not only can 4-D Majorana masses be generated from 6-D (where no Majorana spinors exist), but Majorana masses are naturally associated to large mixing. The model favours inverted hierarchy and a quasi-Dirac partial suppression of neutrinoles…
We suggest simple models which produce the suitable fermion mass hierarchies and flavor mixing angles based on the 6 dimensional N=1 supersymmetric SO(10) grand unified theory compactified on a $T^2/(Z_2 \times Z_2')$ orbifold. We introduce 6D and 5D matter fields, which contains the 1st and 2nd generation matter fields as the zero modes, respectively. The 3rd generation matter fields are located on a 4D brane. The Yukawa couplings for bulk fields are suppressed by volume factors from extra dimensions. The suitable fermion mass hierarchies and flavor mixings are generated by the volume suppres…
We propose a new model which can naturally explain origins of fermion generations, quark mass hierarchy, and Cabibbo-Kobayashi-Maskawa matrix simultaneously from geometry of an extra dimension. We take the extra dimension to be an interval with point interactions, which are additional boundary points in the bulk space of the interval. Because of the Dirichlet boundary condition for fermion at the positions of point interactions, profiles of chiral fermion zero modes are split and localized, and then we can realize three generations from each five-dimensional Dirac fermion. Our model allows fer…
We propose an extension of the three-Higgs-doublet model (3HDM), where the Standard Model (SM) particle content is enlarged by the inclusion of two inert $SU_{2L}$ scalar doublets, three inert and two active electrically neutral gauge singlet scalars, charged vector like fermions and Majorana neutrinos. These additional particles are introduced to generate the SM fermion mass hierarchy from a sequential loop suppression mechanism. In our model the top and exotic fermion masses appear at tree level, whereas the remaining fermions get their masses radiatively. Specifically, bottom, charm, tau an…
A geometric understanding of the origin of mass hierarchy among the standard model fermions have been addressed in a multiple warped spacetime. We show that the requirement of $10^{16}$ order warping between the Planck and the visible branes without creating any significant hierarchy among the moduli results into splitting of fermion masses in the standard model. Values of the various parameters of the extra dimensional model and the corresponding fermion masses are determined.
A nonuniversal abelian extension $\mathrm{U(1)}_{X}$ free from chiral anomalies is introduced into the Standard Model (SM), in order to evaluate its suitability in addressing the fermion mass hierarchy (FMH) by using seesaw mechanisms (SSM). In order to break the electroweak symmetry, three Higgs doublets are introduced, which give mass at tree-level to the top and bottom quarks, and the muon lepton. With an electroweak singlet scalar field, the $U(1)_{X}$ symmetry is broken and the exotic particles acquire masses. The light particles in the SM obtain their masses via SSM and Yukawa couplings …
We address two fundamental aspects of flavor physics: the mass hierarchy and the large lepton mixing angles. On one side, left-right flavor symmetry realizes the democratic mass matrix patterns and explains why one family is much heavier than the others. On the other side, discrete flavor symmetry such as A4 leads to the observed tribimaximal mixing for the leptons. We show that, by explicitly breaking the left-right flavor symmetry into the diagonal A4, it is possible to explain both the observed charged fermion mass hierarchies and quark and lepton mixing angles. In particular we predict a h…
In the minimal supersymmetric Standard Model with seesaw neutrino masses we show how R-parity can emerge naturally as a discrete gauge symmetry. The same discrete symmetry explains the smallness of the μ-term (the Higgsino mass parameter) via the Giudice--Masiero mechanism. The discrete gauge anomalies are cancelled by a discrete version of the Green--Schwarz mechanism. The simplest symmetry group is found to be Z_4 with a charge assignment that is compatible with grand unification. Several other Z_N gauge symmetries are found for N=10,12,18,36 etc, with some models employing discrete anomaly …
Grand gauge-Higgs unification of five dimensional SU(6) gauge theory on an orbifold S^1/Z_2 with localized gauge kinetic terms is discussed. The Standard model (SM) fermions on one of the boundaries and some massive bulk fermions coupling to the SM fermions on the boundary are introduced, so that they respect an SU(5) symmetry structure. The SM fermion masses including top quark are reproduced by mild tuning the bulk masses and parameters of the localized gauge kinetic terms. Gauge coupling universality is not guaranteed by the presence of the localized gauge kinetic terms and it severely cons…
We build a renormalizable theory where the inverse seesaw mechanism explains the pattern of SM fermion masses. To the best of our knowledge, our model corresponds to the first implementation of the inverse seesaw mechanism for the charged fermion sector. In our theory, the inverse seesaw mechanism is implemented at the tree and one-loop levels in order to generate the masses for the second and first families of the SM charged fermions, respectively. The third family of SM charged fermions obtain tree-level masses from the Higgs doublets $ϕ_{1}$ (for the top quark) and $ϕ_{2}$ (for the bottom q…
We present a common explanation of the fermion mass hierarchy and the large lepton mixing angles in the context of a grand unified flavor and gauge theory (GUTF). Our starting point is a SU(3)xU(1) flavor symmetry and a SO(10) GUT, a basic ingredient of our theory which plays a major role is that two different breaking pattern of the flavor symmetry are at work. On one side, the dynamical breaking of SU(3)xU(1) flavor symmetry into U(2)xZ_3 explains why one family is much heavier than the others. On the other side, an explicit symmetry breaking of SU(3) into a discrete flavor symmetry leads to…
In this talk, I present a new framework to understand the long-standing fermion mass hierarchy puzzle. We extend the Standard Model gauge symmetry by an extra local U(1)_S symmetry, broken spontaneously at the electroweak scale. All the SM particles are singlet with respect to this U(1)_S. We also introduce additional flavor symmetries, U(1)_F's, with flavon scalars F_i, as well as vectorlike quarks and leptons at the TeV scale. The flavon scalars have VEV in the TeV scale. Only the top quark has the usual dimension four Yukawa coupling. EW symmetry breaking to all other quarks and leptons are…
Grand gauge-Higgs unification of five dimensional SU(6) gauge theory on an orbifold $S^1 / Z_2$ with localized gauge kinetic terms is discussed. The Standard model (SM) fermions on the boundaries and some massive bulk fermions coupling to the SM fermions are introduced. The number of the bulk fermions is reduced compared to the previous model, which reproduces the generation mixing of the SM fermions in addition to the SM fermion mass hierarchy by mild tuning the bulk masses and parameters of the localized gauge kinetic terms.
We suggest simple models which produce the suitable fermion mass hierarchies and flavor mixing angles based on the 6 dimensional N=1 supersymmetric SO(10) grand unified theory compactified on a $T^2/(Z_2 \times Z_2')$ orbifold. We introduce extra vector-like heavy fields in the extra dimensions, and the suitable fermion mass hierarchies and flavor mixings are generated by integrating out these heavy fields. We consider gaugino mediation and gauge mediation supersymmetry breaking mechanisms and their flavor structures. The experimental constraints of small flavor changing neutral currents sugge…
We propose a new framework for constructing supersymmetric theories of flavor, in which flavor symmetry breaking is triggered by the dynamical breakdown of supersymmetry at low energies. All mass scales in our scheme are generated from the supersymmetry breaking scale $Λ_{SSB} \approx 10^7$ GeV through radiative corrections. We assume a spontaneously broken flavor symmetry and the Froggatt-Nielsen mechanism for generating the fermion Yukawa couplings. Supersymmetry breaking radiatively induces a vacuum expectation value for a scalar field, which generates invariant masses for the Froggatt-Niel…
We suggest a novel approach towards resolving the fermion mass hierarchy problem within the framework of the Standard Model. It is shown that the observed masses and mixings can be explained with order one couplings using successive higher dimensional operators involving the SM Higgs doublet field. This scenario predicts flavor-dependent enhancement in the the Higgs boson coupling to the fermions (by a factor of 3 to the b-quark and τand by a factor of 5 to μrelative to the SM). It also predicts flavor changing \bar{t}ch^0 interaction with a strength comparable to that of \bar{b}bh^0. This ope…
We propose a new mechanism to produce a fermion mass hierarchy dynamically in a model with a singlet generation of fermions. A five dimensional gauge theory on an interval with point interactions (zero-width branes) takes responsibility for realizing three generations and each massless zero mode localizes at boundaries of the segments on the extra dimension. An extra-dimension coordinate-dependent vacuum expectation value of a scalar field makes large differences in overlap integrals of the localized zero modes and then an exponential fermion mass hierarchy can appear. The positions of the poi…
We present a realistic supersymmetric SU(5) model combined with a non-anomalous U(1)_F symmetry. We find a set of U(1)_F charges which automatically lead to the realistic mass hierarchy and mixing patterns for quarks, leptons and neutrinos. All gauge anomalies, including the [U(1)_F]^3 anomaly, are cancelled in our model without invoking the Green-Schwarz mechanism or having exotic fields. Proton decay mediated by dimension 5 operators is automatically suppressed in our model, because the scale set by the largest right-handed neutrino mass is much less than the GUT scale.
We study the origin of fermion mass hierarchy and flavor mixing in a Lifshitz type extension of the standard model including an extra scalar field. We show that the hierarchical structure can originate from renormalizable interactions. In contrast to the Froggatt-Nielsen mechanism, the higher the dimension of associated operators, the heavier the fermion masses. Tiny masses for left-handed neutrinos are obtained without introducing right-handed neutrinos.
We present a framework to generate the hierarchical flavor structure of Standard Model quarks and leptons from loops of superpartners. The simplest model consists of the minimal supersymmetric standard model with tree level Yukawa couplings for the third generation only and anarchic squark and slepton mass matrices. Agreement with constraints from low energy flavor observables, in particular Kaon mixing, is obtained for supersymmetric particles with masses at the PeV scale or above. In our framework both the second and the first generation fermion masses are generated at 1-loop. Despite this, …
We present a model that gives a natural explanation to the charged lepton mass hierarchy and study the contributions to the electron and the muon $g-2$. In the model, we introduce lepton-flavor-dependent $U(1)_F$ symmetry and three additional Higgs doublets with $U(1)_F$ charges, to realize that each generation of charged leptons couples to one of the three additional Higgs doublets. The $U(1)_F$ symmetry is softly broken by $+1$ charges, and the smallness of the soft breaking naturally gives rise to the hierarchy of the Higgs VEVs, which then accounts for the charged lepton mass hierarchy. Si…
A new non-universal abelian extension $\mathrm{G_{SM}}\otimes \mathrm{U(1)}_{X}$ to the Standard Model free from chiral anomalies is presented. The new $X$ charges distinguish among generations so as the fermion mass matrices get zero-textures from the fermion mass hierarchy can be obtained. Regarding to neutrino physics, the model inclues Majorana fermions which induce see-saw mechanisms to get small neutrino masses. Moreover, the suitability of the model is tested by searching for regions in the parameter space which reproduce current neutrino oscillation data.
We consider quiver theories in four dimensions with a large ultra-violet cutoff. These theories require that an ordered set of vacuum expectation values for the link fields develops dynamically and can be obtained from the coarse deconstruction of extra-dimensional theories in an AdS background. These full-hierarchy quiver theories form a large class which include AdS$_5$ models as a limit, but which have a distinctive phenomenology. As an example, in this paper we show that fermions can be introduced in a way that can at the same time generate the fermion mass hierarchy and have flavor violat…
We show that in supersymmetric models with a gauged flavor symmetry explaining the hierarchy of fermion masses and mixings, the electron, muon, neutron and the deuteron acquire sizable electric dipole moments (EDM) through loop diagrams involving the flavor gaugino/gauge boson near the Planck scale. These EDMs are proportional to the phases in the fermion Yukawa couplings and are typically much larger than the neutrino seesaw induced EDM for the leptons. In a popular class of models based on anomalous U(1) flavor symmetry of string origin, we find d_e ~ (10^{-26}-10^{-27}) e cm, d_μ~ (10^{-24}…
We consider composite two-Higgs doublet models based on gauge-Yukawa theories with strongly interacting fermions generating the top-bottom mass hierarchy. The model features a single "universal" Higgs-Yukawa coupling, $ g $, which is identified with the top quark $ g\equiv g_t \sim \mathcal{O}(1) $. The top-bottom mass hierarchy arises by soft breaking of a $ \mathbb{Z}_2 $ symmetry by a condensate of strongly interacting fermions. A mass splitting between vector-like masses of the confined techni-fermions controls this top-bottom mass hierarchy. This mechanism can be present in a variety of m…
We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space, and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries, and their representations are determined. Symmetries are flavor or gauge-like, with fixed chirality. After spin 0, 1/2, and 1 fields are obtained in this space, we construct associated interactive gauge-invariant renormalizable terms, showing their equivalence to a Lagrangian formulation, using as example the previously studied (5+1)-dimensional case, with …
We have recently proposed a setup of the "Domain-Wall Standard Model" in 5D spacetime, where all the Standard Model (SM) fields are localized in certain domains of the extra 5th dimension. Utilizing this setup, we attempt to solve the fermion mass hierarchy problem of the SM. The mass hierarchy can be naturally explained by suitably distributing the fermions in different positions along the extra dimension. Due to these different localization points, the effective 4D gauge couplings of Kaluza-Klein (KK) mode gauge bosons to the SM fermions become non-universal. As a result, our model is severe…
A framework based on a class of abelian gauge symmetries is proposed in which the masses of only the third generation quarks and leptons arise at the tree level. The fermions of the first and second families receive their masses through radiative corrections induced by the new gauge bosons in the loops. It is shown that the class of abelian symmetries which can viably implement this mechanism are flavour non-universal in nature. Taking the all-fermion generalization of the well-known leptonic $L_μ-L_τ$ and $L_e - L_μ$ symmetries, we construct an explicit renormalizable model based on two $U(1)…
The chiral Gross-Neveu model or equivalently the linearized Bogoliubov-de Gennes equation has been mapped to the nonlinear Schrödinger (NLS) hierarchy in the Ablowitz-Kaup-Newell-Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n-th NLS hierarchy generally has n+1 gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be …
In the SM gauge symmetries and fermion content of neutrinos, charged leptons and quarks, we study the effective four-fermion operators of Einstein-Cartan type and their contributions to the Schwinger-Dyson equations of fermion self-energy functions. The study is motivated by the speculation that these four-fermion operators are probably originated due to the quantum gravity that provides the natural regularization for chiral-symmetric gauge field theories. In the chiral-gauge symmetry breaking phase, as to achieve the energetically favorable ground state, only the top-quark mass is generated v…
