Flavor Symmetry Research Articles

Neutrino mass model in the context of Δ(54)⊗Z2 ⊗ Z3 ⊗ Z4 flavor symmetries with Inverse Seesaw mechanism

Our analysis involves enhancing the Δ(54) flavor symmetry model with Inverse Seesaw mechanism along with two SM Higgs through the incorporation of distinct flavons. Additionally, we introduce supplementary Z2⊗Z3⊗Z4 symmetries to eliminate any undesirable components within our investigation. The exact tri-bimaximal neutrino mixing pattern undergoes a deviation as a result of the incorporation of extra flavons, leading to the emergence of a non-zero reactor angle θ13 that aligns with the latest experimental findings. It was found that for our model the atmospheric oscillation parameter occupies the lower octant for normal hierarchy case. We also examine the parameter space of the model for normal hierarchy to explore the Dirac CP (δCP), Jarlskog invariant parameter (J) and the Neutrinoless double-beta decay parameter (mββ) and found it in agreement with the neutrino latest data. Hence our model may be testable in the future neutrino experiments.

The minimal flavor structure of quarks and leptons

A flavor structure with minimal parameters is proposed to address the fermion mass hierarchy and flavor mixing for quarks and leptons. Yukawa interaction is reconstructed in a new basis to show a common flat structure for up-type quarks, down-type quarks, charged leptons, and Dirac neutrinos. A flavor symmetry is found from the hierarchy masses of quarks and leptons, which dominated Cabibbo–Kobayashi–Maskawa (CKM) mixing for quarks and Pontecorvo–Maki–Nakagawa–Sakata mixing for leptons. It results that the minimal flavor structure successfully addresses flavor mixings of quarks and leptons even in the mass hierarchy limit, which means that mass hierarchy and flavor mixing are two independent questions. As a prediction, a sum rule on the mixing angles and CP violation phase (CPV) is suggested, which explains the smallness of s 13 as a natural result of the mass hierarchy. Generalizing the flat structure to quarks and leptons, a unified Yukawa interaction is also achieved for all fermions with only a single coupling.

Modular binary octahedral symmetry for flavor structure of Standard Model

We have investigated the modular binary octahedral group 2O as a flavor symmetry to explain the structure of Standard Model. The vector-valued modular forms in all irreducible representations of this group are constructed. We have classified all possible fermion mass models based on the modular binary octahedral group 2O. A comprehensive numerical analysis is performed, and we present some benchmark quark/lepton mass models in good agreement with the experimental data. Notably we find a minimal modular invariant model for leptons and quarks, which is able to explain simultaneously the masses and mixing parameters of both quarks and leptons in terms of 14 real free parameters including the modulus τ. The fermion mass hierarchies around the vicinity of the modular fixed points are explored.

Constraining BSM discrete flavor symmetries with heavy scalar searches at colliders

Discrete Flavor Symmetries are often employed in BSM constructions to successfully recreate fermion masses and mixing patterns through several known mechanisms. Obvious constraints on these types of scenarios are the non-observation of Flavour Changing Neutral Currents which set stringent limits. In this talk I will discuss the strategy of using the scalar sector phenomenology predicted by such BSM models, and its correlation with the dark matter sector, to further strengthen the constraints by exploiting the large data available from heavy scalar searches in colliders including recent likelihood profiles provided by ATLAS and CMS.

Gauged SU(3)F and loop induced quark and lepton masses

We investigate a local SU(3)F flavour symmetry for its viability in generating the masses for the quarks and charged leptons of the first two families through radiative corrections. Only the third-generation fermions get tree-level masses due to specific choice of the field content and their gauge charges. Unprotected by symmetry, the remaining fermions acquire non-vanishing masses through the quantum corrections induced by the gauge bosons of broken SU(3)F. We show that inter-generational hierarchy between the masses of the first two families arises if the flavour symmetry is broken with an intermediate SU(2) leading to a specific ordering in the masses of the gauge bosons. Based on this scheme, we construct an explicit and predictive model and show its viability in reproducing the realistic charged fermion masses and quark mixing parameters in terms of not-so-hierarchical fundamental couplings. The model leads to the strange quark mass, ms ≈ 16 MeV at MZ, which is ~2.4σ away from its current central value. Large flavour violations are a generic prediction of the scheme which pushes the masses of the new gauge bosons to 103 TeV or higher.

Wrinkles in the Froggatt-Nielsen mechanism and flavorful new physics

When the Froggatt-Nielsen mechanism is used to explain the Standard Model flavor hierarchy, new physics couplings are also determined by the horizontal symmetry. However, additional symmetries or dynamics in the UV can sometimes lead to a departure from this naïve scaling for the new physics couplings. We show that an effective way to keep track of these changes is by using the new spurions of the U(3)5 global flavor symmetry, where we parameterize extra suppression or enhancement factors, referred to as wrinkles, using the same power counting parameter as in the original Froggatt-Nielsen model. As a concrete realization, we consider two flavor spurions of the S1 leptoquark, and demonstrate that wrinkles can be used to make an enhanced value of textrm{BR}left({B}^{+}to {K}^{+}nu overline{nu}right) consistent with other flavor observables. We also present example UV models that realize wrinkles, and comment on choosing consistent charges in ordinary Froggatt-Nielsen models without the typical monotonicity condition.

Minimal left–right symmetric model with A4 modular symmetry

In this paper, we have realized the left–right symmetric model (LRSM) with modular symmetry. Most of the previous works on LRSM have been done considering discrete flavor symmetry, but this work has been carried out using [Formula: see text](3) modular group which is isomorphic to nonabelian discrete symmetry group [Formula: see text]. The advantage of using modular symmetry is the nonrequirement for the use of extra particles called “flavons”. In this model, the Yukawa couplings are expressed in terms of modular forms [Formula: see text]. In this work, we have studied minimal LRSM for both type-I and type-II dominances. Here, we have calculated the values for the Yukawa couplings and then plotted it against the sum of the neutrino masses. The results obtained are well within the experimental limits for the desired values of sum of neutrino masses. We have also briefly analyzed the effects of the implications of modular symmetry on neutrinoless double beta decay with the new physics contributions and the correlation of lepton flavor violation and lightest neutrino mass within the framework of modular symmetric LRSM.

Exploring models with modular symmetry in neutrino oscillation experiments

Our study aims to investigate the viability of neutrino mass models that arise from discrete non-Abelian modular symmetry groups, i.e., ΓN with (N = 1, 2, 3, . ) in the future neutrino experiments T2HK, DUNE, and JUNO. Modular symmetry reduces the usage of flavon fields compared to the conventional discrete flavor symmetry models. Theories based on modular symmetries predict the values of leptonic mixing parameters, and therefore, these models can be tested in future neutrino experiments. In this study, we consider three models based on the A4 modular symmetry, i.e., Model-A, B, and C such a way that they predict different values of the oscillation parameters but still allowed with respect to the current data. In the future, it is expected that T2HK, DUNE, and JUNO will measure the neutrino oscillation parameters very precisely, and therefore, some of these models can be excluded in the future by these experiments. We have estimated the prediction of these models numerically and then used them as input to scrutinize these models in the neutrino experiments. Assuming the future best-fit values of θ23 and δCP remain the same as the current one, our results show that at 5σ C.L, Model-A can be excluded by T2HK whereas Model-B can be excluded by both T2HK and DUNE. Model-C cannot be excluded by T2HK and DUNE at 5σ C.L. Further; our results show that JUNO alone can exclude Model-B at an extremely high confidence level if the future best-fit of θ12 remains at the current-one. We have also identified the region in the θ23 - δCP parameter space, for which Model-A cannot be separated from Model-B in T2HK and DUNE.

Explaining the Bd,s→K∗K¯∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {B}_{d,s}\ o {K}^{\\left(\\ast \\right)}{\\overline{K}}^{\\left(\\ast \\right)} $$\\end{document} non-leptonic puzzle and charged-current B-anomalies via scalar leptoquarks

We present a model based on S1 scalar leptoquarks to solve the tension observed in the recently proposed non-leptonic optimized observables LK∗K¯∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {L}_{K^{\\ast }{\\overline{K}}^{\\ast }} $$\\end{document} and LKK¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {L}_{K\\overline{K}} $$\\end{document}. These observables are constructed as ratios of U-spin related decays based on Bd,s0→K∗0K¯∗0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {B}_{d,s}^0\ o {K}^{\\left(\\ast \\right)0}{\\overline{K}}^{\\left(\\ast \\right)0} $$\\end{document}. The model gives a one-loop contribution to the Wilson coefficient of the chromomagnetic dipole operator needed to explain the tension in both non-leptonic observables, while naturally avoiding large contributions to the corresponding electromagnetic dipoles. The necessary chiral enhancement comes from an O(1) Yukawa coupling with a TeV-scale right-handed neutrino running in the loop. We endow the model with a U(2) flavor symmetry, necessary to protect light-family flavor observables that otherwise would be in tension. Furthermore, we show that the same S1 scalar leptoquark is capable of simultaneously explaining the hints of lepton flavor universality violation observed in charged-current B-decays. The model therefore provides a potential link between two puzzles in B-physics and TeV-scale neutrino mass generation. Finally, the combined explanation of the B-physics puzzles unavoidably results in an enhancement of BB→Kνν¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{B}\\left(B\ o K\ u \\overline{\ u}\\right) $$\\end{document}, yielding a value close to present bounds.

Flavor Symmetry of Hydrogen Atoms Potentially Affecting the Proton Radius Deduced from the Electron-Hydrogen Scattering

Precise knowledge of such fundamental quantity as the proton charge radius rp is extremely important both for the quantum chromodynamics (for quark-gluon structure) and for atomic physics (for atomic hydrogen spectroscopy). Yet the ambiguity in measuring rp persists for over a dozen of years by now—from the time when in 2010 the muonic hydrogen spectroscopy experiment yielded rp ≈ 0.84 fm in contrast to the form factor experiment by the Mainz group that produced rp ≈ 0.88 fm. Important was that this difference corresponded to about seven standard deviations and therefore was inexplicable. In the intervening dozen of years, more experiments of various kinds were performed in this regard. Nevertheless, the controversy remains, which is why several different types of new experiments are being prepared for measuring rp. In one of our previous papers, we pointed out the factor that was never taken into account by the corresponding research community: the flavor symmetry of electronic hydrogen atoms, whose existence was confirmed by four kinds of atomic or molecular experiments and also evidenced by two kinds of astrophysical observations. Specifically, in that paper there was discussed the possible presence of the second flavor of muonic hydrogen atoms (in the corresponding experimental gas) and its effect on the shift of the ground state of muonic hydrogen atoms due to the proton finite size. In the present paper we analyze the effect of the flavor symmetry of electronic hydrogen atoms on the corresponding elastic scattering cross-section and on the proton charge radius rp deduced from the cross-section. As an example, we use our analytical results for reconciling two distinct values of rp obtained in different elastic scattering experiments: 0.88 fm and 0.84 fm (which is by about 4.5% smaller than 0.88 fm). We show that if the ratio of the second flavor of hydrogen atoms to the usual hydrogen atoms in the experimental gas would be about 0.3, then the extraction of rp from the corresponding cross-section would yield by about 4.5% smaller value of rp compared to its true value. We also derive the corresponding general formulas that can be used for interpreting the future electronic and muonic experiments.

Chern-Simons-Trinion theories: One-form symmetries and superconformal indices

We study 3d theories containing N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 3 Chern-Simons vector multiplets coupled to the SU(N)3 flavour symmetry of 3d TN theories with Chern-Simons levels k1, k2 and k3. It was formerly pointed out that these theories flow to infrared SCFTs with enhanced N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 supersymmetry when 1/k1 + 1/k2 + 1/k3 = 0. We examine superconformal indices of these theories which reveal that supersymmetry of the infrared SCFTs may get enhanced to 4 ≤ N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} ≤ 6 if such a condition is satisfied. Moreover, even if the Chern-Simons levels do not obey the aforementioned condition, we find that there is still an infinite family of theories that flows to infrared SCFTs with N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 supersymmetry. The ’t Hooft anomalies of the one-form symmetries of these theories are analysed. As a by-product, we observe that there is generally a decoupled topological sector in the infrared. When the infrared SCFTs have N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} ≥ 4 supersymmetry, we also study the Higgs and Coulomb branch limits of the indices which provide geometric information of the moduli space of the theories in question in terms of the Hilbert series.

A simplest modular S3 model for leptons

We present minimalist constructions for lepton masses and mixing based on flavour symmetry under the modular group ΓN of lowest level N = 2. As opposed to the only existing model of Γ2 ≅ S3 formulated in a SUSY framework, the only non-SM field is the modulus τ, and a generalised CP symmetry is implemented. Charged-leptons masses are reproduced through symmetry arguments, without requiring fine-tuning of the free parameters. As a result, all lepton observables (masses and mixing) are reproduced within 1σ experimental range using a minimum of nine free real parameters (including the real and imaginary parts of the modulus). A normal ordering for the neutrino masses is predicted. We also obtain predictions for the CP violating phases: the Dirac CP phase is predicted around 1.6π, the Majorana phases lie in narrow regions near ±π. The sum of neutrino masses is within the current bound at ∼ 0.09 eV. Furthermore, we provide predictions for the neutrinoless double beta decay and tritium decay effective masses, around 20 meV. Given the reduced number of free input parameters as compared to the existing literature on modular S3, this work renews interest for a unified predictive model of quark-lepton sectors based on Γ2 ≅ S3.

Semileptonic decays D → P/V/Sℓ+νℓ with the SU(3) flavor symmetry/breaking

Many exclusive c→d/sℓ+νℓ(ℓ=e,μ,τ) transitions have been well measured, and they can be used to test the theoretical calculations. Motivated by this, we study the D→P/V/Sℓ+νℓ decays induced by the c→d/sℓ+νℓ transitions with the SU(3) flavor symmetry approach, where P denotes the pseudoscalar meson, V denotes the vector meson, and S denotes the scalar meson with a mass below 1 GeV. The different decay amplitudes of the D→Pℓ+νℓ, D→Vℓ+νℓ or D→Sℓ+νℓ decays can be related by using the SU(3) flavor symmetry and by considering the SU(3) flavor breaking. Using relevant data, we predict the not yet measured or not yet well measured processes in the D→P/V/Sℓ+νℓ decays. We find that the SU(3) flavor symmetry approach works well in the D→P/Vℓ+νℓ decays. Many branching ratios of the D→Sℓ+νℓ decays are predicted by using the data of the Ds+→f0(980)e+νe and D→S(S→P1P2)ℓ+νℓ decays, in addition, the two quark and the four quark scenarios for the light scalar mesons are analyzed. The SU(3) flavor symmetry predictions of the D→Sℓ+νℓ decays need to be further tested, and our predictions of the D→Sℓ+νℓ decays are useful for probing the structure of light scalar mesons. Our results in this work could be used to test the SU(3) flavor symmetry approach in the semileptonic D decays by the future experiments at BESIII, LHCb and BelleII.

Leading directions in the SMEFT

Short-distance new physics at (or slightly) above the TeV scale should not excessively violate the approximate flavor symmetries of the SM in order to comply with stringent constraints from flavor-changing neutral currents. In this respect, flavor symmetries provide an effective organizing principle for the vast parameter space of the SMEFT. In this work, we classify all possible irreducible representations under U(3)5 flavor symmetry of new heavy spin-0, 1/2, and 1 fields which integrate out to dimension-6 operators at the tree level. For a general perturbative UV model, the resulting flavor-symmetric interactions are very restrictive and, in most cases, predict a single Hermitian operator with a definite sign. These leading directions in the SMEFT space deserve particular attention. We derive an extensive set of present experimental constraints by utilizing the existing global SMEFT fits, which incorporate data from top quark, Higgs boson, and electroweak measurements, along with constraints on dilepton and 4-lepton contact interactions. The derived set of bounds comprehensively summarises the present knowledge from indirect searches of flavor-blind new physics mediators.

Second flavor of heavy ions

The existence of the Second Flavor of Hydrogen Atoms (SFHA), predicted theoretically in 2001, has been confirmed by four different types of atomic or molecular experiments, and evidenced by two different types of astrophysical observations. The SFHA is based on the second analytical solution of the standard Dirac equation. Despite this solution is singular at small r, it can be matched with the regular solution inside the proton for the S-states, and thus becomes legitimate. The SFHA have only the S-states: so, in accordance to the selection rules of quantum mechanics they do not couple to the electromagnetic radiation (except for the 21 cm spectral line): they remain dark. In the present paper we extended the legitimacy of the second analytical solution of the Dirac equation outside the nucleus to heavy ions. We predicted the existence of the second flavor of heavy ions and thus the flavor symmetry of these ions. These ions have only the S-states, so that they remain dark just as the SFHA. This theoretical result has the fundamental importance in its own right. Also, it could encourage experimentalists to perform experiments for the verification of the existence of the second flavor of heavy ions. The most probable candidates are ions whose nuclei are double-magic and thus spherical. As an application of the above fundamental result, we referred to the comparison between the nuclear charge radius rn,μ, determined experimentally by the muonic x-ray transition energies, and the nuclear charge radius rn,e, determined experimentally from the elastic electron scattering. The comparison was possible for two spherical nuclei: for 40Ca20, as well as for 48Ca20. In each case, rn,e turned out to be by about 1% smaller, than rn,μ, the difference being well beyond the experimental error margin. We showed in both above examples, that a relatively small admixture (∼10%) of the second flavor of heavy ions in the target reconciles the values of the nuclear charge radius, measured by two different methods, in favor of the larger value. Finally, we noted that while the SFHA is one of the leading candidates for dark matter or a part of it, there are still unsuccessful attempts to find Weakly Interactive Massive Particles (WIMP) as a part of dark matter. We suggested that if there are massive dark matter particles, then more realistically they could be the second flavor of heavy ions, described in the present paper: they are really dark.

Fermion hierarchies in SU(5) grand unification from {Gamma}_6^{prime } modular flavor symmetry

We construct an SU(5) grand unified model in which the hierarchies of the quark and lepton masses and mixing are explained by the {Gamma}_6^{prime } modular flavor symmetry. The hierarchies are realized by the Froggatt-Nielsen-like mechanism due to the residual {Z}_6^T symmetry, approximately unbroken at τ ~ i∞. We argue that the {Gamma}_6^{left({}^{prime}right)} symmetry is the minimal possibility to realize the up-type quark mass hierarchies, since the Yukawa matrix is symmetric. We find a combination of the representations and modular weights and then show numerical values of (1) coefficients for the realistic fermion hierarchies.

CKM and PMNS mixing matrixes from SO(2) flavor symmetry

The relation between quark masses and CKM mixing is studied based on an approximate chiral flavor symmetry of quark mass matrix. In mass hierarchy limit, the mass ratio effect on CKM mixing is suppressed, which separates mass hierarchy and quark flavor mixing into two independent problems. We show that CKM mixing is dominated by two left-handed symmetries while mass hierarchy only provides slight corrections. The same mixing structure is generalized to lepton sector with extended Dirac neutrinos. The common flavor mixing provides a novel comprehension on the relation between quark CKM mixing and lepton PMNS mixing.

Matter matters in moduli fixing and modular flavor symmetries

Modular flavor symmetries provide us with a very compelling approach to the flavor problem. It has been argued that moduli values close to some special values like τ=i or τ=ω provide us with the best fits to data. We point out that the presence of hidden “matter” fields, needed to uplift symmetric AdS vacua, gives rise to a dynamical mechanism that leads to such values of τ.

3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry

The study of 3d mirror symmetry has greatly enhanced our understanding of various aspects of 3d \mathcal{N}=4𝒩=4 theories. In this paper, starting with known mirror pairs of 3d \mathcal{N}=4𝒩=4 quiver gauge theories and gauging discrete subgroups of the flavour or topological symmetry, we construct new mirror pairs with non-trivial 1-form symmetry. By providing explicit quiver descriptions of these theories, we thoroughly specify their symmetries (0-form, 1-form, and 2-group) and the mirror maps between them.

Comments on Non-invertible Symmetries in Argyres-Douglas Theories

We demonstrate the presence of non-invertible symmetries in an infinite family of superconformal Argyres-Douglas theories. This class of theories arises from diagonal gauging of the flavor symmetry of a collection of multiple copies of Dp(SU(N)) theories. The same set of theories that we study can also be realized from 6d mathcal{N} = (1, 0) compactification on a torus. The main example in this class is the (A2, D4) theory. We show in detail that this specific theory bears the same structures of non-invertible duality and triality defects as those of mathcal{N} = 4 super Yang-Mills with gauge algebra \U0001d530\U0001d532(2). We extend this result to infinitely many other Argyres-Douglas theories in the same family, including those with central charges a = c whose conformal manifold is one dimensional, and those with a ≠ c whose conformal manifold has dimension larger than one. Our result is supported by examining certain special cases that can be realized in terms of theories of class \U0001d4ae.