Fermion Mass Matrices Research Articles

Minimal eclectic flavor group Q8 ⋊ S3 and neutrino mixing

We perform a comprehensive analysis of the minimal eclectic flavor group Q8 ⋊ S3 which is isomorphic to GL(2, 3), and all its irreducible representations are induced from the irreducible representations of Q8 and S3. The consistency conditions between EFG and generalized CP (gCP) symmetry are revisited, and we find the gCP symmetry compatible with the minimal EFG Q8 ⋊ S3. The most general forms of Kähler potential and superpotential based on Q8 ⋊ S3 are discussed, and the corresponding fermion mass matrices are presented. A concrete lepton model invariant under Q8 ⋊ S3 and gCP is constructed, in which the experimental data of all six lepton masses and six mixing parameters can be successfully described through seven real input parameters. The model predicts a vanishing effective mass mββ in neutrinoless double beta decay.

Proton Decay and Gauge Coupling Unification in an Extended SU(5) GUT with 45D Higgs

Abstract We present a comprehensive study of an extended SU(5) grand unified theory (GUT) that incorporates a 45D Higgs representation to address the shortcomings of the minimal SU(5) GUT, such as the inability to generate realistic fermion mass hierarchies and insufficient proton stability. By considering a hierarchical mass spectrum for the scalar components of the 45D Higgs, we demonstrate that successful gauge coupling unification (GCU) can be achieved. The color octet scalar, color triplet scalar, and color antitriplet scalar play crucial roles in realizing GCU when their masses are significantly lighter than other components of the 45D Higgs. We focus on the proton decay channels mediated by the exchange of the color antitriplet scalar. Assuming that the 45D Higgs couples to all three generations of fermions, we determine the 45D Higgs Yukawa couplings with which the observed fermion mass matrices at low energies are realized. We calculate proton decay rates using the Yukawa couplings obtained from renormalization group evolutions and matching conditions at the GUT scale, thereby exploring the dependence of proton decay rates on model parameters. We find that the $p \rightarrow \nu \pi$ mode imposes the most stringent constraint on the mass of the color antitriplet scalar $M_{S_1}$. We also study the correlations between the lower bounds on $M_{S_1}$ derived from different proton decay modes.

Pati-Salam models with A4 modular symmetry

The flavor structure of quarks and leptons and quark-lepton unification are studied in the framework of Pati-Salam models with A4 modular symmetry. The three generations of the left-handed and right-handed fermions are assigned to be triplet or singlets of A4. The light neutrino masses are generated through the type-I seesaw mechanism. We perform a systematic classification of Pati-Salam models according to the transformations of matter fields under the A4 modular symmetry, and the general form of the fermion mass matrix is given. We present four phenomenologically viable benchmark models which provide excellent descriptions of masses and flavor mixing of quarks and leptons, including neutrinos. In such models we find that the normal ordered neutrino mass spectrum is preferred over the inverted case, with neutrinoless double beta decay predicted to be too small to be observed by the next generation of experiments.

Anomalous dispersion, superluminality, and instabilities in two-flavor theories with local non-Hermitian mass mixing

Pseudo-Hermitian field theories possess a global continuous “similarity” symmetry, interconnecting the theories with the same physical particle content and an identical mass spectrum. In their regimes with real spectra, within this family of similarity transformations, there is a map from the non-Hermitian theory to its Hermitian similarity partner. We promote the similarity transformation to a local symmetry, which requires the introduction of a new vector similarity field as a connection in the similarity space of non-Hermitian theories. In the case of non-Hermitian two-flavor scalar or fermion mixing and by virtue of a novel IR/UV mixing effect, the effect of inhomogeneous non-Hermiticity then reveals itself via anomalous dispersion, instabilities, and superluminal group velocities at very high momenta, thus setting an upper bound on the particle momentum propagating through inhomogeneous backgrounds characterized by Lagrangians with non-Hermitian mass matrices. Such a non-Hermitian extension of the Standard Model of particle physics, encoded in a weak inhomogeneity of the non-Hermitian part of the fermion mass matrix, may nevertheless provide us with a low-energy particle spectrum consistent with experimentally observed properties. Published by the American Physical Society 2024

Eclectic flavor group ∆(27) ⋊ S3 and lepton model building

We have performed a systematical study of the eclectic flavor group ∆(27) ⋊ S3 which is the extension of the traditional flavor symmetry ∆(27) by the finite modular symmetry S3. Consistency between ∆(27) and S3 requires that the eight nontrivial singlet representations of ∆(27) should be arranged into four reducible doublets. The modular transformation matrices are determined for various ∆(27) multiplets, and the CP-like symmetry compatible with ∆(27) ⋊ S3 are discussed. We study the general form of the Kähler potential and superpotential invariant under ∆(27) ⋊ S3, and the corresponding fermion mass matrices are presented. We propose a bottom-up model for lepton masses and mixing based on ∆(27) ⋊ S3, a numerical analysis is performed and the experimental data can be accommodated.

Leptogenesis in a Left-Right Symmetric Model with double seesaw

We explore the connection between the low-scale CP-violating Dirac phase (δ) and high-scale leptogenesis in a Left-Right Symmetric Model (LRSM) with scalar bidoublet and doublets. The model’s fermion sector includes one sterile neutrino (SL) per generation to enable a double seesaw mechanism in the neutral fermion mass matrix, implemented by performing type-I seesaw twice. The first seesaw generates the Majorana mass term for heavy right-handed (RH) neutrinos (NR), and in the second, the light neutrino mass is linearly dependent on S L mass. We use charge conjugation (C) as the discrete left-right (LR) symmetry, aiding in deriving the Dirac neutrino mass matrix (MD) in terms of light and heavy RH neutrino masses and the light neutrino mixing matrix UPMNS (containing δ). We demonstrate the feasibility of unflavored thermal leptogenesis via RH neutrino decay using the obtained MD and RH neutrino masses as input. A thorough analysis of the Boltzmann equations describing asymmetry evolution is conducted in the unflavored regime, showing that the CP-violating Dirac phase alone can generate the required leptonic asymmetry for given input parameters, with or without Majorana phases. Finally, we discuss constraining our model with current and upcoming oscillation experiments aimed at refining the value of δ.

The structure of flavor mixing and reconstruction of the mass matrix

The fermion flavor structure is investigated by bilinear decomposition of the mass matrix after EW symmetry breaking, and the roles of factorized matrices in flavor mixing and mass generation are explored. On a new Yukawa basis, the minimal parameterization of flavor mixing is realized containing two relative phases and two free [Formula: see text] rotation angles. It is shown that flavor mixing can be addressed from four independent parameters. The validity of the flavor mixing structure is checked in both the lepton and quark sectors. Under the decomposition of flavor mixing, fermion mass matrices are reconstructed in the hierarchy limit. A flat mass matrix with all elements equal to 1 arises naturally from the requirement that homology exists between up-type and down-type fermion mass matrices. Some hints of a flat matrix and flavor breaking are also discussed.

Neutrino mass and mixing models with eclectic flavor symmetry ∆(27) ⋊ T′

The Kähler potentials of modular symmetry models receive unsuppressed contributions which may be controlled by a flavor symmetry, where the combination of the two symmetry types is referred to as eclectic flavor symmetry. After briefly reviewing the consistency conditions of eclectic flavor symmetry models, including those with generalised (g)CP, we perform a comprehensive bottom-up study of eclectic flavor symmetry models based on Ω(1) ≅ ∆(27) ⋊ T′, consisting of the flavor symmetry ∆(27) in a semi-direct product with the modular symmetry T′. The modular transformations of different ∆(27) multiplets are given by solving the consistency condition. The eight nontrivial singlets of ∆(27) are related by T′ modular symmetry, and they have to be present or absent simultaneously in any Ω(1) model. The most general forms of the superpotential and Kähler potential invariant under Ω(1) are discussed, and the corresponding fermion mass matrices are presented. Based on the eclectic flavor group Ω(1), two concrete lepton models which can successfully describe the experimental data of lepton masses and mixing parameters are constructed. For the two models without gCP, all six mixing parameters vary in small regions. A nearly maximal atmospheric mixing angle θ23 and Dirac CP phase δCP are obtained in the first model. After considering the compatible gCP symmetry and the assumption of mathfrak{R}tau = 0 in the first model, the μ − τ reflection symmetry is preserved in the charged lepton diagonal basis. As a consequence, the atmospheric mixing angle and Dirac CP phase are predicted to be maximal, and two Majorana CP phases are predicted to be π.

Texture-zero patterns of lepton mass matrices from modular symmetry

Texture zeros in fermion mass matrices have been widely considered in tackling the Standard Model flavour puzzle. In this work, we perform a systematic analysis of texture zeros in lepton mass matrices in the framework of {Gamma}_3^{prime}cong {T}^{prime } modular symmetry. Assuming that the lepton fields transform as irreducible representations of T′, we obtain all possible texture-zero patterns for both charged-lepton and neutrino mass matrices which can be achieved from T′ modular symmetry. We provide representative models for the phenomenologically-viable textures which can accommodate the experimental data. The predictions for lepton mixing angles, CP-violating phases, light neutrino masses and effective neutrino mass relevant for neutrinoless double beta decay, are discussed. We find that the minimal viable lepton model depends on only 7 real free parameters including the modulus τ (the corresponding charged-lepton mass matrix contains 4 vanishing entries, and the neutrino mass matrix has 1 texture zero). Finally, we study in detail three benchmark models, one for each neutrino mass generation mechanism considered (Dirac, Majorana via Weinberg operator and Majorana via minimal type-I seesaw mechanism).

Scale-invariant 3-3-1-1 model with B−L symmetry

Motivated by a possible interplay between the mechanism of dynamical symmetry breaking and the seesaw mechanism for generating fermion masses, we present a scale-invariant model that extends the gauge symmetry of the Standard Model electroweak sector to SU(3)$_L\otimes$U(1)$_X\otimes$U(1)$_N$, with a built-in $B-L$ symmetry. The model is based on the symmetry structure of the known 3-3-1 models and, thus, it relates the number of the three observed fermion generations with the cancellation of gauge anomalies. Symmetry breaking is triggered via the Coleman-Weinberg mechanism taking into account a minimal set of scalar field multiplets. We establish the stability conditions for the tree-level scalar potential imposing the copositivity criteria and use the method of Gildener-Weinberg for computing the one-loop effective potential when one has multiple scalar fields. With the addition of vectorial fermions, getting their mass mainly through the vacuum expectation value of scalar singlets at $10^3$ TeV, the $B-L$ symmetry leads to textures for the fermion mass matrices, allowing seesaw mechanisms for neutrinos and quarks to take place. In particular, these mechanisms could partly explain the mass hierarchies of the quarks. Once the breakdown of the SU(3)$_L$ symmetry is supposed to occur around 10 TeV, the model also predicts new particles with TeV-scale masses, such as a neutral scalar, $H_{1}$, a charged scalar, $H^\pm$, and the gauge bosons $Z^{\prime}$, $W^{\prime\pm}$ and $Y^0$, that could be searched with the high-luminosity LHC.

Gauged N=3 , D=4 supergravity: A new web of marginally connected vacua

We analyze the vacuum structure of $\mathcal{N}=3,D=4$ supergravity coupled to 9 vector multiplets with gauge group ${\rm SO}(3)\times {\rm SU}(3)$. Aside from the central $\mathcal{N}=3$ AdS$_4$ vacuum at the origin, on which the supermultiplet structure reproduces the massless sector of M-theory compactified on $\mathrm{N^{0,1,0}}$, we find a rich structure of AdS$_4$ vacua preserving $\mathcal{N}=0,1,2,3$ supersymmetry. These new vacua are arranged in a manifold spanned by scalar fields corresponding to exactly marginal deformations of the dual CFT. This manifold has the form $T^3/K$, where $K$ is a discrete subgroup of the gauge group: $\mathcal{N}=3,2$ and $1$ vacua correspond, respectively, to a point, a line and a surface in the three-dimensional vacuum manifold. We study RG flows from the central $\mathcal{N}=3$ vacuum and elaborate on the possible higher dimensional origin of the new vacua. For the reader's convenience we also provide a review of the embedding tensor formulation of $D=4$, $\mathcal{N}=3$ gauged supergravities. In particular we provide formulas involving the fermion shift tensors and mass matrices in $\mathcal{N}=3$ theories, which can be applied to a generic gauging.

The minimal flavor structure from decomposition of the fermion mass matrix

The minimal flavor structures for both quarks and leptons are proposed to address fermion mass hierarchy and flavor mixings by bi-unitary decomposition of the fermion mass matrix. The real matrix M0f is completely responsive to family mass hierarchy, which is expressed by a close-to-flat matrix structure. The left-handed unitary phase FLf provides the origin of CP violation in quark and lepton mixings, which can be explained as a quantum effect between Yukawa interaction states and weak gauge states. The minimal flavor structure is realized by just 10 parameters without any redundancy, corresponding to 6 fermion masses, 3 mixing angles and 1 CP violation in the quark/lepton sector. This approach provides a general flavor structure independent of the specific quark or lepton flavor data. We verify the validation of the flavor structure by reproducing quark/lepton masses and mixings. Some possible scenarios that yield the flavor structure are also discussed.

A translational flavor symmetry in the mass terms of Dirac and Majorana fermions

Requiring the effective mass term for a category of fundamental Dirac or Majorana fermions of the same electric charge to be invariant under the translational transformations ψ αL(R) → ψ αL(R) + n α z ψL(R) in the flavor space, where n α and z ψL(R) stand respectively for the flavor-dependent complex numbers and a constant spinor field anticommuting with the fermion fields, we show that n α can be identified as the elements U αi in the ith column of the unitary matrix U used to diagonalize the corresponding Hermitian or symmetric fermion mass matrix M ψ , and m i = 0 holds accordingly. We find that the reverse is also true. Now that the mass spectra of charged leptons, up- and down-type quarks are all strongly hierarchical and current experimental data allow the lightest neutrino to be massless, we argue that the zero mass limit for the first-family fermions and the translational flavor symmetry behind it should be a natural starting point for building viable fermion mass models.

Flavor mixing and CP violation from the interplay of an S4 modular group and a generalized CP symmetry

We have performed a systematical analysis of lepton and quark masses models based on $\Gamma_4\cong S_4$ modular symmetry with gCP symmetry. We have considered both cases that neutrinos are Majorana particles and Dirac particles. All possible nontrivial representation assignments of matter fields are considered, and the most general form of fermion mass matrices are given. The phenomenologically viable models with the lowest number of free parameters together with the results of fit are presented. We find out nine lepton models with seven real free parameters including the real and imaginary parts of modulus for Majorana neutrinos, which can accommodate the lepton masses and neutrino oscillation data. The prediction for leptogenesis is studied in an example lepton model. The observed baryon asymmetry as well as lepton masses and mixing angles can be explained. For Dirac neutrinos, four lepton models with five real free couplings are compatible with experimental data. Ten quark models containing seven couplings are found to be able to accommodate the hierarchical quark masses and mixing angles and CP violation phase. Furthermore, the $S_4$ modular symmetry can provide a unified description of lepton and quark flavor structure, and a benchmark model is presented.

SU(5) × U(1)′ Models with a Vector-like Fermion Family

Motivated by experimental measurements indicating deviations from the Standard Model predictions, we discuss F-theory-inspired models, which, in addition to the three chiral generations, contain a vector-like complete fermion family. The analysis takes place in the context of SU(5)×U(1)′ GUT embedded in an E8 covering group, which is associated with the (highest) geometric singularity of the elliptic fibration. In this context, the U(1)′ is a linear combination of four abelian factors subjected to the appropriate anomaly cancellation conditions. Furthermore, we require universal U(1)′ charges for the three chiral families and different ones for the corresponding fields of the vector-like representations. Under the aforementioned assumptions, we find 192 models that can be classified into five distinct categories with respect to their specific GUT properties. We exhibit representative examples for each such class and construct the superpotential couplings and the fermion mass matrices. We explore the implications of the vector-like states in low-energy phenomenology, including the predictions regarding the B-meson anomalies. The rôle of R-parity violating terms appearing in some particular models of the above construction is also discussed.

Flavored axion in the UV-complete Froggatt\u2013Nielsen models

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 mass matrices. Subsequently, we investigate the resulting axion flavor violating couplings and the axion-photon coupling arising from the model.

Modular invariant dynamics and fermion mass hierarchies around \u03c4 = i

We discuss fermion mass hierarchies within modular invariant flavour models. We analyse the neighbourhood of the self-dual point τ = i, where modular invariant theories possess a residual Z4 invariance. In this region the breaking of Z4 can be fully described by the spurion ϵ ≈ τ − i, that flips its sign under Z4. Degeneracies or vanishing eigenvalues of fermion mass matrices, forced by the Z4 symmetry at τ = i, are removed by slightly deviating from the self-dual point. Relevant mass ratios are controlled by powers of |ϵ|. We present examples where this mechanism is a key ingredient to successfully implement an hierarchical spectrum in the lepton sector, even in the presence of a non-minimal Kähler potential.

Fermion mass hierarchies, large lepton mixing and residual modular symmetries

In modular-invariant models of flavour, hierarchical fermion mass matrices may arise solely due to the proximity of the modulus τ to a point of residual symmetry. This mechanism does not require flavon fields, and modular weights are not analogous to Froggatt-Nielsen charges. Instead, we show that hierarchies depend on the decomposition of field representations under the residual symmetry group. We systematically go through the possible fermion field representation choices which may yield hierarchical structures in the vicinity of symmetric points, for the four smallest finite modular groups, isomorphic to S3, A4, S4, and A5, as well as for their double covers. We find a restricted set of pairs of representations for which the discussed mechanism may produce viable fermion (charged-lepton and quark) mass hierarchies. We present two lepton flavour models in which the charged-lepton mass hierarchies are naturally obtained, while lepton mixing is somewhat fine-tuned. After formulating the conditions for obtaining a viable lepton mixing matrix in the symmetric limit, we construct a model in which both the charged-lepton and neutrino sectors are free from fine-tuning.

Adjoint SU(5) GUT model with modular S4 symmetry

We study the textures of SM fermion mass matrices and their mixings in a supersymmetric adjoint SU(5) Grand Unified Theory with modular S4 being the horizontal symmetry. The Yukawa entries of both quarks and leptons are expressed by modular forms with lower weights. Neutrino sector has an adjoint SU(5) representation 24 as matter superfield, which is a triplet of S4. The effective light neutrino masses is generated through Type-III and Type-I seesaw mechanism. The only common complex parameter in both charged fermion and neutrino sectors is modulus τ . Down-type quarks and charged leptons have the same joint effective operators with adjoint scalar in them, and their mass discrepancy in the same generation depends on Clebsch-Gordan factor. Especially for the first two generations the respective Clebsch-Gordan factors made the double Yukawa ratio \U0001d4b4d\U0001d4b4μ/\U0001d4b4e\U0001d4b4s = 12, in excellent agreement with the experimental result. We reproduce proper CKM mixing parameters and all nine Yukawa eigenvalues of quarks and charged leptons. Neutrino masses and MNS parameters are also produced properly with normal ordering is preferred.

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.’