Mapping and Probing Froggatt-Nielsen Solutions to the Quark Flavor Puzzle
Claudia Cornella, David Curtin, Ethan T. Neil, Jedidiah O. Thompson
备注：
7 pages, 3 figures + Appendices. File "charges.csv" included in arXiv source. v2: added references. v3: updated phenomenological analysis in terms of observables instead of operators, matches published version
The Froggatt-Nielsen (FN) mechanism is an elegant solution to the flavor problem. In its minimal application to the quark sector, the different quark types and generations have different charges under a $U(1)_X$ flavor symmetry. The SM Yukawa couplings are generated below the flavor breaking scale with hierarchies dictated by the quark charge assignments. Only a handful of charge assignments are generally considered in the literature. We analyze the complete space of possible charge assignments with $|X_{q_i}| \leq 4$ and perform both a set of Bayesian-inspired numerical scans and an analytical spurion analysis to identify those charge assignments that reliably generate SM-like quark mass and mixing hierarchies. The resulting set of top-20 flavor charge assignments significantly enlarges the viable space of FN models but is still compact enough to enable focused phenomenological study. We then apply our numerical methodology to demonstrate that these distinct charge assignments result in the generation of correlated flavor-violating four-quark operators characterized by significantly varied strengths, potentially differing substantially from the possibilities previously explored in the literature. Future precision measurement of $ΔF =2 $ observables, along with increasingly accurate SM predictions, may therefore enable us to distinguish among otherwise equally plausible FN charges, thus shedding light on the UV structure of the flavor sector.
In this paper, we propose a Generalized Froggatt-Nielsen mechanism in which non-renormalizable operators involving a GUT group and $U(1)_H$ non-singlet Higgs field are introduced. Thus the GUT gauge symmetry breaking and the generation of hierarchical flavor hierarchy have a common origin in this mechanism. In this Generalized Froggatt-Nielsen mechanism, we propose universality conditions for coefficients corresponding to different contractions in the group productions. We find that the predictions in Generalized Froggatt-Nielsen mechanism for SU(5) GUT is different to that of ordinary Froggat…
We embed Two Higgs Doublet Models (2HDMs) in the Froggatt Nielsen (FN) framework. We find that the approximate FN symmetry predicts i) approximate Natural Flavor Conservation (NFC) of Types II or IV in the Yukawa sector, and ii) approximate Peccei-Quinn (PQ) symmetry in the scalar sector. We discuss the phenomenological consequences of these features.
We systematically investigate the embedding of U(1)_X Froggatt-Nielsen models in (four-dimensional) local supersymmetry. We restrict ourselves to models with a single flavon field. We do not impose a discrete symmetry by hand, e.g. R-parity, baryon-parity or lepton-parity. Thus we determine the order of magnitude of the baryon- and/or lepton violating coupling constants through the Froggatt-Nielsen mechanism. We then scrutinize whether the predicted coupling constants are in accord with weak or GUT scale constraints. Many models turn out to be incompatible.
Superheavy neutrinos can, via the seesaw model, provide a mechanism for lepton number violation. If they are combined with flavor violation as characterized by the Froggatt-Nielsen mechanism, then the phenomenology for the neutrinos in oscillation experiments, neutrinoless double beta decay, and other experiments can be described by a relatively few number of parameters. We describe the low-energy neutrino mass matrix and show that the results are consistent with currently available data.
We study the neutrino mass matrix derived from the seesaw mechanism in which the neutrino Yukawa couplings and the heavy Majorana neutrino mass matrix are controlled by the Froggatt-Nielsen mechanism. In order to obtain the large neutrino mixings, two Froggatt-Nielsen fields are introduced with a complex vacuum expectation values. As a by-product, CP violation is systematically induced even if the order one couplings of FN fields are real. We show several predictions of this model, such as theta_{13}, the Dirac CP phase, two Majorana CP phases, the effective mass of the neutrinoless double bet…
On the basis of the Froggatt-Nielsen mechanism, we study quark flavor mixings in the $SU(6) \times SU(2)_R$ model. The characteristic structure of the CKM matrix is attributed to the hierarchical effective Yukawa couplings due to the Froggatt-Nielsen mechanism and also to the state-mixings beyond the MSSM. We elucidate the detailed form of the CKM matrix elements and find interesting relations between the \textit{CP} violating phase and three mixing angles. Taking the existing data of three mixing angles, we estimate the quark \textit{CP}-phase at $δ= (75 \pm 3)^{\circ}$. This result is in acc…
We propose UV-completions of Froggatt-Nielsen-Peccei-Quinn models of fermion masses and mixings with flavored axions, by incorporating heavy fields. Here, the $U(1)$ Froggatt-Nielsen symmetry is identified with the Peccei-Quinn symmetry to solve the strong CP problem along with the mass hierarchies of the Standard Model fermions. We take into account leading order contributions to the fermion mass matrices giving rise to Nearest-Neighbour-Interaction structure in the quark sector and $A_2$ texture in the neutrino sector. A comprehensive numerical analysis has been performed for the fermion mas…
In this paper, we introduce an extension of the Standard Model, based on SU(3)$_\mathrm{C}\times $SU(3)$_\mathrm{L}\times $U(1)$_X$ gauge symmetry (331-model). The 331-models traditionally explain the number of fermion familes in nature. In our model the Froggatt-Nielsen mechanism is incorporated into the 331-setting in a particularly economical fashion. The model utilizes the both the Froggatt-Nielsen and linear seesaw mechanisms to explain the observed fermion mass hierarchies and lightness of neutrinos. In our numerical analysis we found that a $\sim$ 50 TeV new physics scale is able to rep…
The Froggatt-Nielsen mechanism provides an elegant explanation for the hierarchies of fermion masses and mixings in terms of a U(1) symmetry. Promoting such a family symmetry to an R-symmetry, we explicitly construct supersymmetric Froggatt-Nielsen models which are gauged, family dependent U(1)_R completions of the Z_4^R symmetry proposed by Lee, Raby, Ratz, Ross, Schieren, Schmidt-Hoberg and Vaudrevange in 2010. Forbidden by Z_4^R, the mu-term is generated around the supersymmetry breaking scale m_3/2 from either the Kahler potential or the superpotential. Neutrinos acquire their mass via the…
We describe a simple connection between the Froggatt-Nielsen, Stueckelberg and Higgs mechanisms, all three of them combined in a consistent way. This is illustrated in the context of a class of generalizations of the Standard Model with a gauge structure extended by a certain number of anomalous U(1) factors. These are built in the effective action in a way that gauge invariance and unitarity are preserved. Among other features, a physical axion with properties different from those of a Peccei-Quinn axion emerges.
The models with the gauge group $SU(3)_c\times SU(3)_L \times U(1)_X$ (331-models) have been advocated to explain why there are three fermion generations in Nature. As such they can provide partial understanding of the flavour sector. The hierarchy of Yukawa-couplings in the Standard Model is another puzzle which remains without compelling explanation. We propose to use Froggatt-Nielsen -mechanism in a 331-model to explain both fundamental problems. It turns out that no additional representations in the scalar sector are needed to take care of this. The traditional 331-models predict scalar fl…
The extensions of the Standard Model based on the $SU(3)_c\times SU(3)_L\times U(1)_X$ gauge group (331-models) have been advocated to explain the number of fermion families in nature. It has been recently shown that the Froggatt-Nielsen mechanism, a popular way to explain the mass hierarchy of the charged fermions, can be incorporated into the 331-setting in an economical fashion (FN331). In this work we extend the FN331-model to include three right-handed neutrino singlets. We show that the seesaw mechanism is realized in this model. The scale of the seesaw mechanism is near the $SU(3)_L\tim…
We analyze in detail lepton-flavor violation (LFV) in the charged-lepton sector such as $μ\to e γ$, $τ\to μγ$, $μ\to eee$ and the $μ\to e$ conversion in nuclei, within the framework of supersymmetric models with lopsided Froggatt--Nielsen charges, in which the large mixing in the neutrino sector as well as small mixings in the quark sector can be naturally accommodated. We show that the present experimental limits on the LFV processes already exclude some of the models. The future proposed search for LFV, especially in muon processes, can provide a significant probe to this framework. We also …
We discuss the Dirac CP violating phase $δ_{CP}$ in the Froggatt-Nielsen model for a neutrino mass matrix $M_ν$ imposing a condition ${\rm det} [M_ν]=0$. This additional condition restricts the CP violating phase $δ_{CP}$ drastically. We find that the phase $δ_{CP}$ is predicted in the region of $\pm (0.4- 2.9)$ radian, which is consistent with the recent T2K and NO$ν$A data. There is a remarkable correlation between $δ_{CP}$ and $\sin^2θ_{23}$. The phase $δ_{CP}$ converges on $\sim \pm π/2$ if $\sin^2θ_{23}$ is larger than $0.5$. Thus, accurate measurements of $\sin^2θ_{23}$ are important for…
The flavour problem of the Standard Model can be addressed through the Froggatt-Nielsen (FN) mechanism. In this work, we develop an approach to the study of FN textures building a direct link between FN-charge assignments and the measured masses and mixing angles via unitary transformations in flavour space. We specifically focus on the quark sector to identify the most economic FN models able to provide a dynamical and natural understanding of the flavour puzzle. Remarkably, we find viable FN textures, involving charges under the horizontal symmetry that do not exceed one in absolute value (i…
In the model of gauge mediation of SUSY breaking in the presence of tree-level mediation, the Froggatt-Nielsen mechanism provides a different hierarchy of sparticle masses. We study the spectra and show the results to be like those in an effective supersymmetric model.
Flavor mixings together with fermion mass spectra are studied in detail in the $SU(6) \times SU(2)_R$ model, in which state-mixings beyond the minimal supersymmetric standard model (MSSM) take place. Characteristic patterns of fermion spectra are attributed to the hierarchical structure of effective Yukawa interactions via the Froggatt-Nielsen mechanism and also to the state-mixings beyond the MSSM. It is shown explicitly that the neutrino mass matrix in the mass diagonal basis for charged leptons has no hierarchical structure. This is due to the cancellation among the hierarchical factors by …
We study UV-complete Froggatt-Nielsen-like models for the generation of mass and mixing hierarchies, assuming that the integrated heavy fields are chiral with respect to an abelian Froggatt-Nielsen symmetry. It modifies the mixed anomalies with respect to the Standard Model gauge group, which opens up the possibility to gauge the Froggatt-Nielsen symmetry without the need to introduce additional spectator fermions, while keeping mass matrices usually associated to anomalous flavour symmetries. We give specific examples where this happens, and we study the flavourful axion which arises from an …
We construct a model of decaying, TeV-scale scalar dark matter motivated by data from the PAMELA and Fermi-LAT experiments. By introducing an appropriate Abelian discrete symmetry and an intermediate scale of vector-like states that are responsible for generating lepton Yukawa couplings, we show that Planck-suppressed corrections may lead to decaying dark matter that is leptophilic and has the desired lifetime. The dark matter candidate decays primarily to lepton/anti-lepton pairs, and at a subleading rate to final states with a lepton, anti-lepton and standard model Higgs boson. We show that …
The flavor symmetry-breaking scale in the Froggatt-Nielsen (FN) mechanism is very weakly constrained by present experiments, and can lie anywhere from a few TeV to the Planck scale. We construct two minimal, non-supersymmetric, ultraviolet (UV) complete models that generate the FN mechanism, with a global $U(1)_{\rm{FN}}$ flavor symmetry and a single flavon field. Using the one-loop finite temperature effective potential, we explore the possibility of a strong first order phase transition (SFOPT) induced by the flavon. We show that if the flavor symmetry-breaking occurs at intermediate scales …
Can the cosmological dynamics responsible for settling down the present values of the Cabibbo-Kobayashi-Maskawa matrix be related to electroweak symmetry breaking? If the Standard Model Yukawa couplings varied in the early universe and started with order one values before electroweak symmetry breaking, the CP violation associated with the CKM matrix could be the origin of the matter-antimatter asymmetry. The large effective Yukawa couplings which lead to the enhanced CP violation can also help in achieving a strong first-order electroweak phase transition. We study in detail the feasibility of…
We study the structure of Yukawa matrices derived from the supersymmetric Yang-Mills theory on magnetized orbifolds, which can realize the observed quark and charged lepton mass ratios as well as the CKM mixing angles, even with a small number of tunable parameters and without any critical fine-tuning. As a reason behind this, we find that the obtained Yukawa matrices possess a Froggatt-Nielsen like structure with Gaussian hierarchies, which provides a suitable texture for them favored by the experimental data.
We discuss vacuum stability in Froggatt-Nielsen (FN) models. One concern in FN models is that for large flavon VEVs the running of the quartic Higgs coupling is enhanced what might lead to a more severe instability compared to the Standard Model (SM). We study this issue using the renormalization-group improved scalar potential. Another issue is that the mixing between the Higgs and the flavon can potentially destabilize the potential. However, taking current bounds on the flavon phenomenology into account, we find that both effects do not lead to an instability that is more severe than in the…
We study how to incorporate CP violation in the Froggatt--Nielsen (FN) mechanism. To this end, we introduce non-renormalizable interactions with a flavor democratic structure to the fermion mass generation sector. It is found that at least two iso-singlet scalar fields with imposed a discrete symmetry are necessary to generate CP violation due to the appearance of the relative phase between their vacuum expectation values. In the simplest model, ratios of quark masses and the Cabibbo-Kobayashi-Maskawa (CKM) matrix including the CP violating phase are determined by the CKM element |V_{us}| and …
We introduce two anomaly free versions of Froggatt-Nielsen (FN) models, based on either $G_{\rm FN}=U(1)^3$ or $G_{\rm FN}=U(1)$ horizontal symmetries, that generate the SM quark and lepton flavor structures. The structure of these "inverted" FN models is motivated by the clockwork mechanism: the chiral fields, singlets under $G_{\rm FN}$, are supplemented by chains of vector-like fermions charged under $G_{\rm FN}$. Unlike the traditional FN models the hierarchy of quark and lepton masses is obtained as an expansion in $M/\langle ϕ\rangle$, where $M$ is the typical vector-like fermion mass, a…
A natural composite Higgs demands the presence of light resonances at the TeV scale, that in general are in conflict with bounds from flavor and CP violation. We propose a composite model with a Froggatt-Nielsen mechanism, that offers new possibilities for the origin of flavor. We analyse the interplay of partial compositeness and the horizontal U(1) symmetry in achieving the quark masses and mixing angles. We study the contributions to $ΔF=2$ 4-fermion operators, as well as to $ΔF=1$ and neutron dipole operators. We find scenarios in which the contribution to Left-Right and Right-handed opera…
We present a doubly parametric extension of the standard Froggatt--Nielsen (FN) mechanism. As is well known, mass matrices of the up- and down-type quark sectors and the charged lepton sector in the standard model can be parametrized well by a parameter $λ$ which is usually taken to be the sine of the Cabibbo angle ($λ= \sinθ_\text{C} \simeq 0.225$). However, in the neutrino sector, there is still room to realize the two neutrino mass squared differences $Δm_\text{sol}^2$ and $Δm_\text{atm}^2$, two large mixing angles $θ_{12}$ and $θ_{23}$, and non-zero $θ_{13}$. Then we consider an extension …
This paper studies F-theory SU(5) GUT models where the three generations of the standard model come from three different curves. All the matter is taken to come from curves intersecting at a point of enhanced E8 gauge symmetry. Giving a vev to some of the GUT singlets naturally implements a Froggatt-Nielsen approach to flavour structure. A scan is performed over all possible models and the results are filtered using phenomenological constraints. We find a unique model that fits observations of quark and lepton masses and mixing well. This model suffers from two drawbacks: R-parity must be impo…
Sterile neutrinos with a mass around the keV scale are an attractive particle physics candidate for Warm Dark Matter. Although many frameworks have been presented in which these neutrinos can fulfill all phenomenological constraints, there are hardly any models known that can explain such a peculiar mass pattern, one sterile neutrino at the keV scale and the other two considerably heavier, while at the same time being compatible with low-energy neutrino data. In this paper, we present models based on the Froggatt-Nielsen mechanism, which can give such an explanation. We explain how to assign F…
We study Froggatt-Nielsen (FN) like flavor models with modular symmetry. The FN mechanism is a convincing solution to the flavor puzzle in quark sector. The FN mechanism requires an extra $U(1)$ gauge symmetry which is broken at high energy. Alternatively, in the framework of modular symmetry the modular weights can play the role of the FN charges of the extra $U(1)$ symmetry. Based on the FN-like mechanism with modular symmetry we present new flavor models for quark sector. Assuming that the three generations have a common representation under modular symmetry, our models simply reproduce the…
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…
In F-theory, U(1) gauge symmetries are encoded in rational sections, which generate the Mordell-Weil group of the elliptic fibration of the compactification space. Recently the possible U(1) charges for global SU(5) F-theory GUTs with smooth rational sections were classified arXiv:1504.05593 [hep-th]. In this paper we utilize this classification to probe global F-theory models for their phenomenological viability. After imposing an exotic-free MSSM spectrum, anomaly cancellation (related to hypercharge flux GUT breaking in the presence of U(1) gauge symmetries), absence of dimension four and f…
We consider Randall-Sundrum set up (RS) to be a theory of flavour, as an alternative to Froggatt-Nielsen models instead of as a solution to the hierarchy problem. We consider a modified RS framework between the Planck scale and the GUT scale. This also alleviates constraints from flavour physics. Fermion masses and mixing angles are fit at the GUT scale. The ranges of the bulk mass parameters are determined using a $χ^2$ fit taking in to consideration the variation in $\mathcal{O}(1)$ parameters. In the hadronic sector, the heavy top quark requires large bulk mass parameters localising the rig…
Contents (Part 1): 1.Derivation of Lorentz Invariance and Three Space Dimensions in Generic Field Theory (C D. Froggatt and H. B. Nielsen) 2.Unitary Representations, Noncompact Groups SO(q; d - q)...(N. Mankoc Borstnik, H. B. Nielsen and D. Lukman) 3.Weyl Spinor of SO(1; 13), Families of Spinors ...(A. Borstnik Bracic and N. Mankoc Borstnik) 4.A Tight Packing Problem (A. Kleppe) 5.Why so Few Particle Species? ... (D.L. Bennett and A. Kleppe) 6.About Number of Families (D. Lukman, A. Kleppe and N.S. Mankoc Borstnik) 7.Coupling Constant Unification in Spin-Charge Unifying Model ....(N. Mankoc Bo…
Contents (Part 2): 8.Renormalization of Coupling Constants in the Minimal SUSY Models (R. B. Nevzorov, K. A. Ter-Martirosyan and M. A. Trusov) 9.Multiple Point Model and Phase Transition Couplings ...(L.V. Laperashvili, D.A. Ryzhikh and H.B. Nielsen) 10.Family Replicated Fit of All Quark and Lepton Masses and Mixings (H. B. Nielsen and Y. Takanishi) 11.Family Replicated Calculation of Baryogenesis (H. B. Nielsen and Y. Takanishi) 12. Neutrino Oscillations in Vacuum on the Large Distance (D.A. Ryzhikh and K.A. Ter-Martirosyan) 13. Possibility of an Additional Source of Time Reversal Violation f…
Two Flavon Froggatt-Nielsen Models with Genetic Algorithms
Institute for Particle Physics Phenomenology, Department of Physics, Durham University（杜伦大学粒子物理现象学研究所）；School of Physics and Astronomy, University of Southampton（南安普顿大学物理与天文学院）
In this paper, we apply reinforcement learning to particle physics model building. As an example environment, we use the space of Froggatt-Nielsen type models for quark masses. Using a basic policy-based algorithm we show that neural networks can be successfully trained to construct Froggatt-Nielsen models which are consistent with the observed quark masses and mixing. The trained policy networks lead from random to phenomenologically acceptable models for over 90% of episodes and after an average episode length of about 20 steps. We also show that the networks are capable of finding models pr…
The Froggatt-Nielsen mechanism and the multi-local field theory are interesting and promising candidates for solving the naturalness problem in the universe. These theories are based on the different physical principles: The former assumes the micro-canonical partition function $\int {\cal{D}}ϕ \prod_i δ(S_i^{}-I_i^{})$, and the latter assumes the partition function $\int {\cal{D}}ϕ \exp\left(iS_M^{}\right)$ where $S_M^{}$ is the multi-local action $\sum_i c_i^{}S_i^{}+\sum_{i,j}c_{i,j}^{}S_i^{}S_j^{}+\cdots $. Our main purpose is to show that they are equivalent in the sense that they predict…
We present a Froggatt-Nielsen flavor model that yields a minimal realization of the type-I seesaw mechanism. This seesaw model is minimal for three reasons: (i) It features only two rather than three right-handed sterile neutrinos: N_1 and N_2, which form a pair of pseudo-Dirac neutrinos; (ii) the neutrino Yukawa matrix exhibits flavor alignment, i.e., modulo small perturbations, it contains only three independent parameters; and (iii) the N_1,2 coupling to the electron flavor is parametrically suppressed compared to the muon and tau flavors, i.e., the neutrino Yukawa matrix exhibits an approx…
We constructed a model of neutrino masses using Froggatt-Nielsen mechanism with $U(1) \times Z_3 \times Z_2$ flavor symmetry. The model predicts that $(2/3)m_2/m_3 \sim \sqrt{2}\sinθ_{13}$ at lepton number violating scale $M_1$. It is shown that the small values for $m_2/m_3$ and $\sinθ_{13}$ are consequences of breaking discrete symmetries.
We introduce a set of clockwork models of flavor that can naturally explain the large hierarchies of the Standard Model quark masses and mixing angles. Since the clockwork only contains chains of new vector-like fermions without any other dynamical fields, the flavor constraints allow for relatively light new physics scale. For two benchmarks with gear masses just above 1 TeV, allowed by flavor constraints, we discuss the collider searches and the possible ways of reconstructing gear spectra at the LHC. We also examine the similarities and differences with the other common solutions to the SM …
We consider a large class of models where an SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a quiver gauge theory. Such quiver models are very restrictive and therefore have strong predictive power. In particular, under mild assumptions neutrino mass anarchy is predicted.
