scholarly journals Modular $S_3$-invariant flavor model in SU(5) grand unified theory

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Tatsuo Kobayashi ◽  
Yusuke Shimizu ◽  
Kenta Takagi ◽  
Morimitsu Tanimoto ◽  
Takuya H. Tatsuishi
Keyword(s):  
Modular Forms ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Double Beta Decay ◽  
Unified Theory ◽  
Grand Unified Theory ◽  
Mass Matrices ◽  
Charge Parity ◽  
Charged Leptons ◽  
Leptonic Charge

Abstract We present a flavor model with $S_3$ modular invariance in the framework of SU(5) grand unified theory (GUT). The $S_3$ modular forms of weights $2$ and $4$ give the quark and lepton mass matrices with a common complex parameter, the modulus $\tau$. The GUT relation of down-type quarks and charged leptons is imposed by the vacuum expectation value (VEV) of the adjoint 24-dimensional Higgs multiplet in addition to the VEVs of $5$ and $\bar 5$ Higgs multiplets of SU(5). The observed Cabibbo–Kobayashi–Maskawa and Pontecorvo–Maki–Nakagawa–Sakata mixing parameters as well as the mass eigenvalues are reproduced properly. We discuss the leptonic charge–parity phase and the effective mass of the neutrinoless double beta decay with the sum of neutrino masses.

scholarly journals RANDALL–SUNDRUM AND FLIPPED SU(5)

2008 ◽  
Vol 23 (19) ◽  
pp. 2915-2931 ◽  
Author(s):  
BEN DUNDEE ◽  
GERALD CLEAVER
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Matter Content ◽  
Fine Tuning ◽  
Unified Theory ◽  
Grand Unified Theory ◽  
Baryon Decay ◽  
Proton Lifetime ◽  
Bulk Scalar Field ◽  
Dimensional Coupling

In this paper, we construct a model based on a flipped SU(5) partial grand unified theory, within the framework of the Randall–Sundrum (RS1) proposal. Breaking of [Formula: see text] is achieved using a bulk scalar field in the 10 of SU(5), Φ, which gains a vacuum expectation value <Φ> ~ 3 × 1015 GeV . We are able to retain the successes of the [Formula: see text] phenomenology, specifically the confinement of all fields to the smallest (1, [Formula: see text], and 10) representations of SU(5). We derive the beta functions, and point out some constraints on bulk matter content implied by the runnings (and positivity) of the five-dimensional coupling. Finally, we comment on baryon decay and show the fine-tuning problem required to prevent an exponentially short proton lifetime.

scholarly journals Minimal scoto-seesaw mechanism with spontaneous CP violation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
D. M. Barreiros ◽  
F. R. Joaquim ◽  
R. Srivastava ◽  
J. W. F. Valle
Keyword(s):  
Dark Matter ◽  
Cp Violation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Discrete Symmetry ◽  
Double Beta Decay ◽  
Neutrino Masses ◽  
Seesaw Mechanism ◽  
Cosmological Observations ◽  
Scalar Singlet

Abstract We propose simple scoto-seesaw models to account for dark matter and neutrino masses with spontaneous CP violation. This is achieved with a single horizontal $$ {\mathcal{Z}}_8 $$ Z 8 discrete symmetry, broken to a residual $$ {\mathcal{Z}}_2 $$ Z 2 subgroup responsible for stabilizing dark matter. CP is broken spontaneously via the complex vacuum expectation value of a scalar singlet, inducing leptonic CP-violating effects. We find that the imposed $$ {\mathcal{Z}}_8 $$ Z 8 symmetry pushes the values of the Dirac CP phase and the lightest neutrino mass to ranges already probed by ongoing experiments, so that normal-ordered neutrino masses can be cornered by cosmological observations and neutrinoless double beta decay experiments.

scholarly journals Dynamical generation of quark/lepton mass hierarchy in an extra dimension

2019 ◽  
Vol 2019 (12) ◽  
Author(s):  
Yukihiro Fujimoto ◽  
Kouhei Hasegawa ◽  
Kenji Nishiwaki ◽  
Makoto Sakamoto ◽  
Kazunori Takenaga ◽  
...  
Keyword(s):  
Extra Dimension ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Casimir Energy ◽  
Mass Hierarchy ◽  
Point Interactions ◽  
Quark Masses ◽  
Dynamical Generation ◽  
Charged Leptons ◽  
Experimental Values

Abstract We show that the observed quark/lepton mass hierarchy can be realized dynamically on an interval extra dimension with point interactions. In our model, the positions of the point interactions play a crucial role in controlling the quark/lepton mass hierarchy and are determined by the minimization of the Casimir energy. By use of the exact extra-dimensional coordinate-dependent vacuum expectation value of a gauge-singlet scalar, we find that there is a parameter set, where the positions of the point interactions are stabilized and fixed, which can reproduce the experimental values of the quark masses precisely enough, while the charged lepton part is less relevant. We also show that possible mixings among the charged leptons will improve the situation significantly.

scholarly journals FLAVOR SYMMETRY AND VACUUM ALIGNED MASS TEXTURES

2007 ◽  
Vol 16 (05) ◽  
pp. 1427-1436 ◽  
Author(s):  
SATORU KANEKO ◽  
HIDEYUKI SAWANAKA ◽  
TAKAYA SHINGAI ◽  
MORIMITSU TANIMOTO ◽  
KOICHI YOSHIOKA
Keyword(s):  
Scalar Potential ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Flavor Symmetry ◽  
Yukawa Couplings ◽  
Flavor Changing ◽  
Symmetry Approach ◽  
Mass Matrices ◽  
Vanishing Elements ◽  
Higgs Fields

A texture-zeros is an approach to reduce the number of free parameters in Yukawa couplings and it is one of the most attractive ones. In our paper, we discuss the origin of zero-structure in texture-zeros by S3 flavor symmetry approach. Some of electroweak doublet Higgs fields have vanishing vacuum expectation value (VEV) which leads to vanishing elements in quark and lepton mass matrices. Then, the structure of supersymmetric scalar potential is analyzed and Higgs fields have non-trivial S3 charges. As a prediction of our paper, a lower bound of a MNS matrix element, Ue3 ≥ 0.04, is obtained. The suppression of flavor-changing neutral currents (FCNC) mediated by the Higgs fields is discussed and lower bounds of the Higgs masses are derived.

scholarly journals SO(10) × S4 grand unified theory of flavour and leptogenesis

2017 ◽  
Vol 2017 (12) ◽  
Author(s):  
Francisco J. de Anda ◽  
Stephen F. King ◽  
Elena Perdomo
Keyword(s):  
Neutrino Mass ◽  
Discrete Group ◽  
Double Beta Decay ◽  
Neutrino Masses ◽  
Type I ◽  
Unified Theory ◽  
Grand Unified Theory ◽  
Oscillation Phase ◽  
Seesaw Mechanism ◽  
Natural Range

Abstract We propose a Grand Unified Theory of Flavour, based on SO(10) together with a non-Abelian discrete group S 4, under which the unified three quark and lepton 16-plets are unified into a single triplet 3′. The model involves a further discrete group ℤ 4 R  × ℤ 4 3 which controls the Higgs and flavon symmetry breaking sectors. The CSD2 flavon vacuum alignment is discussed, along with the GUT breaking potential and the doublet-triplet splitting, and proton decay is shown to be under control. The Yukawa matrices are derived in detail, from renormalisable diagrams, and neutrino masses emerge from the type I seesaw mechanism. A full numerical fit is performed with 15 input parameters generating 19 presently constrained observables, taking into account supersymmetry threshold corrections. The model predicts a normal neutrino mass ordering with a CP oscillation phase of 260°, an atmospheric angle in the first octant and neutrinoless double beta decay with m ββ = 11 meV. We discuss N 2 leptogenesis, which fixes the second right-handed neutrino mass to be M 2 ≃ 2 × 1011 GeV, in the natural range predicted by the model.

scholarly journals The Family Formula for Leptons and Quarks

2019 ◽  
Author(s):  
Nikola Perkovic
Keyword(s):  
Structure Constant ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Majorana Neutrino ◽  
Fine Structure Constant ◽  
Dirac Fermions ◽  
Strong Argument ◽  
Yukawa Couplings ◽  
Charged Leptons ◽  
G Factors

The problem of Yukawa couplings being arbitrary parameters in the Standard Model Higgs mechanism is a long standing one due to their formulaic dependence on the Higgs Vacuum Expectation Value. We will attempt to solve this problem and provide a strong argument that the Yukawa couplings of charged leptons and down type quarks are not arbitrary parameters in the SM. A new methodology for predicting the Yukawa couplings will be presented by using Compton wavelengths, the Rydberg Constant and g-factors of charged leptons instead of relying on the Higgs VEV. We will then proceed to rewrite this new method in terms of an empirical formula that depends on the running of the fine-structure constant on the Q scale, charge and lepton quantum numbers and g-factors to predict the values of the Yukawa couplings for all three generations of charged leptons and d-type quarks. We will also touch on the subject of neutrinos both as Majorana and Dirac fermions respectively and make a prediction for the lightest possible Majorana neutrino and the differences between Dirac neutrinos and anti-neutrinos. We conclude that the Yukawa couplings are not arbitrary parameters in the SM and that this new formula provides very accurate results.

scholarly journals Towards unification of quark and lepton flavors in $$A_4$$ modular invariance

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Hiroshi Okada ◽  
Morimitsu Tanimoto
Keyword(s):  
Neutrino Mass ◽  
Modular Forms ◽  
Quark Mass ◽  
Mass Matrix ◽  
Neutrino Masses ◽  
Inverted Hierarchy ◽  
Mass Matrices ◽  
The Common ◽  
Charged Leptons ◽  
The One

AbstractWe study quark and lepton mass matrices in the $$A_4$$ A 4 modular symmetry towards the unification of the quark and lepton flavors. We adopt modular forms of weights 2 and 6 for quarks and charged leptons, while we use modular forms of weight 4 for the neutrino mass matrix which is generated by the Weinberg operator. We obtain the successful quark mass matrices, in which the down-type quark mass matrix is constructed by modular forms of weight 2, but the up-type quark mass matrix is constructed by modular forms of weight 6. The viable region of $$\tau $$ τ is close to $$\tau =i$$ τ = i . Lepton mass matrices also work well at nearby $$\tau =i$$ τ = i , which overlaps with the one of the quark sector, for the normal hierarchy of neutrino masses. In the common $$\tau $$ τ region for quarks and leptons, the predicted sum of neutrino masses is 87–120 meV taking account of its cosmological bound. Since both the Dirac CP phase $$\delta _{CP}^\ell $$ δ CP ℓ and $$\sin ^2\theta _{23}$$ sin 2 θ 23 are correlated with the sum of neutrino masses, improving its cosmological bound provides crucial tests for our scheme as well as the precise measurement of $$\sin ^2\theta _{23}$$ sin 2 θ 23 and $$\delta _{CP}^\ell $$ δ CP ℓ . The effective neutrino mass of the $$0\nu \beta \beta $$ 0 ν β β decay is $$\langle m_{ee}\rangle =15$$ ⟨ m ee ⟩ = 15 –31 meV. It is remarked that the modulus $$\tau $$ τ is fixed at nearby $$\tau =i$$ τ = i in the fundamental domain of SL(2, Z), which suggests the residual symmetry $$Z_2$$ Z 2 in the quark and lepton mass matrices. The inverted hierarchy of neutrino masses is excluded by the cosmological bound of the sum of neutrino masses.

scholarly journals Muon anomalous magnetic moment and Higgs potential stability in the 331 model from SU(6)

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Tianjun Li ◽  
Junle Pei ◽  
Wenxing Zhang
Keyword(s):  
Magnetic Moments ◽  
Sufficient Conditions ◽  
Vacuum Expectation ◽  
Higgs Potential ◽  
Unified Theory ◽  
Grand Unified Theory ◽  
Expectation Values ◽  
Muon Anomalous Magnetic Moment ◽  
Muon Mass ◽  
Potential Stability

AbstractWe consider a $$SU(3)_c \times SU(3)_L \times U(1)_X$$ S U ( 3 ) c × S U ( 3 ) L × U ( 1 ) X model from a SU(6) Grand Unified Theory (GUT). In order to explain the anomalous magnetic moments of muon and electron, we introduce two new scalar triplets without vacuum expectation values (VEVs) so that the leading contributions to $$\Delta a_{\mu }$$ Δ a μ and $$\Delta a_{e}$$ Δ a e can avoid the suppression from small muon mass. In addition, the Higgs potential stability of this 331 model is studied by giving a set of sufficient conditions to ensure the boundedness from below of the potential.

scholarly journals Adjoint SU(5) GUT model with modular S4 symmetry

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ya Zhao ◽  
Hong-Hao Zhang
Keyword(s):  
Modular Forms ◽  
Experimental Result ◽  
Fermion Mass ◽  
Neutrino Masses ◽  
Type I ◽  
Neutrino Sector ◽  
Horizontal Symmetry ◽  
Mass Matrices ◽  
Two Generations ◽  
Charged Leptons

Abstract 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 𝒴d𝒴μ/𝒴e𝒴s = 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.

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