arXiv subjects

Gui-Jun Ding

Publications and source records attributed to Gui-Jun Ding.

At least 55 records · Page 3Linked to original sources

arXiv2021

Modular symmetry at level 6 and a new route towards finite modular groups

We propose to construct the finite modular groups from the quotient of two principal congruence subgroups as $Γ(N')/Γ(N")$, and the modular group $SL(2,\mathbb{Z})$ is extended to a principal congruence subgroup $Γ(N')$. The original modular invariant theory is reproduced when $N'=1$. We perform a comprehensive study of $Γ'_6$ modular symmetry corresponding to $N'=1$ and $N"=6$, five types of models for lepton masses and mixing with $Γ'_6$ modular symmetry are discussed and some example models are studied numerically. The case of $N'=2$ and $N"=6$ is considered, the finite modular group is $Γ(2)/Γ(6)\cong T'$, and a benchmark model is constructed.

hep-ph↗

arXiv2021

Flavor mixing and CP violation from the interplay of $S_4$ modular group and gCP

We have performed a systematical analysis of lepton and quark masses models based on $Γ_4\cong S_4$ 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.

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arXiv2021

Fermion Masses and Mixing from Double Cover and Metaplectic Cover of $A_5$ Modular Group

We perform a comprehensive study of the homogeneous finite modular group $A'_5$ which is the double covering of $A_5$. The integral weight and level 5 modular forms have been constructed up to weight 6 and they are decomposed into the irreducible representations of $A'_5$. Then we perform a systematical analysis of the $A'_5$ modular models for lepton masses and mixing. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find out 15 models with 9 real free parameters which can accommodate the experimental data of lepton sector. After including generalized CP symmetry, 9 viable models with 7 free parameters are found out. We apply $A'_5$ modular symmetry to the quark sector, and a quark-lepton unification model is given. The framework of modular invariance is extended to include the rational weight modular forms of level 5. The ring of modular forms at level 5 can be generated by two algebraically independent weight $1/5$ modular forms denoted by $F_1(τ)$ and $F_2(τ)$. We give the expressions of the rational weight modular forms of level 5 up to weight $3$ and arrange them into the irreducible multiplets of finite metaplectic group $\widetildeΓ_5\cong A'_5\times Z_5$. A neutrino mass model with $\widetildeΓ_5$ modular symmetry is presented, and the phenomenological predictions of the model are analyzed numerically.

hep-ph↗

arXiv2021

Modular Invariant Quark and Lepton Models in Double Covering of $S_4$ Modular Group

We perform a comprehensive analysis of the homogeneous finite modular group $Γ'_4\equiv S'_4$ which is the double covering of $S_4$ group. The weight 1 modular forms of level 4 are constructed in terms of Dedekind eta function, and they transform as a triplet $\mathbf{\hat{3}'}$ of $S'_4$. The integral weight modular forms until weight 6 are built from the tensor products of weight 1 modular forms. We perform a systematical classification of $S'_4$ modular models for lepton masses and mixing with/without generalized CP, where the left-handed leptons are assigned to triplet of $S'_4$ and right-handed charged leptons transform as singlets under $S'_4$, and we consider both scenarios where the neutrino masses arise from Weinberg operator or type I seesaw mechanism. The phenomenological implications of the minimal models for lepton masses, mixing angles, CP violation phases and neutrinoless double decay are discussed. The $S'_4$ modular symmetry is extended to quark sector, we present several predictive models which use nine or ten free parameters including real and imaginary parts of $τ$ to describe quark masses and Cabibbo-Kobayashi-Maskawa mixing matrix. We give a quark-lepton unified model which can explain the flavor structure of quarks and leptons simultaneously for a common value of $τ$.

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arXiv2021

CP Symmetry and Symplectic Modular Invariance

We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus $g\ge 3$ the definition of CP is unique, while two independent possibilities are allowed when $g\le 2$. We discuss the transformation properties of moduli, matter multiplets and modular forms in the Siegel upper half plane, as well as in invariant subspaces. We identify CP-conserving surfaces in the fundamental domain of moduli space. We make use of all these elements to build a CP and symplectic invariant model of lepton masses and mixing angles, where known data are well reproduced and observable phases are predicted in terms of a minimum number of parameters.

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arXiv2021

$SU(5)$ GUTs with $A_4$ modular symmetry

We combine $SU(5)$ Grand Unified Theories (GUTs) with $A_4$ modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. Classifying the models according to the representation assignments of the matter fields under $A_4$, we find that there are seven types of $SU(5)$ models with $A_4$ modular symmetry. We present 53 benchmark models with the fewest free parameters. The parameter space of each model is scanned to optimize the agreement between predictions and experimental data, and predictions for the masses and mixing parameters of quarks and leptons are given at the best fitting points. The best fit predictions for the leptonic CP violating Dirac phase, the lightest neutrino mass and the neutrinoless double beta decay parameter when displayed graphically are observed to cover a wide range of possible values, but are clustered around particular regions, allowing future neutrino experiments to discriminate between the different types of models.

hep-ph↗

arXiv2020

Modular Invariant $A_{4}$ Models for Quarks and Leptons with Generalized CP Symmetry

We perform a systematical analysis of the $A_4$ modular models with generalized CP for the masses and flavor mixing of quarks and leptons, and the most general form of the quark and lepton mass matrices is given. The CP invariance requires all couplings real in the chosen basis and thus the vacuum expectation value of the modulus $τ$ uniquely breaks both the modular symmetry and CP symmetry. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find 20 models with 7 real free parameters that can accommodate the experimental data of lepton sector. We then apply $A_4$ modular symmetry to the quark sector to explain quark masses and CKM mixing matrix, the minimal viable quark model is found to contain 10 free real parameters. Finally, we give two predictive quark-lepton unification models which use only 16 real free parameters to explain the flavor patterns of both quarks and leptons.

hep-ph↗

arXiv2020

Predictions from warped flavordynamics based on the $T'$ family group

We propose a realistic theory of fermion masses and mixings using a five-dimensional warped scenario where all fermions propagate in the bulk and the Higgs field is localized on the IR brane. The assumed $T'$ flavor symmetry is broken on the branes by flavon fields, providing a consistent scenario where fermion mass hierarchies arise from adequate choices of the bulk mass parameters, while quark and lepton mixing angles are restricted by the family symmetry. Neutrino mass splittings, mixing parameters and the Dirac CP phase all arise from the type-I seesaw mechanism and are tightly correlated, leading to predictions for the neutrino oscillation parameters, as well as expected \znbb decay rates within reach of upcoming experiments. The scheme also provides a good global description of flavor observables in the quark sector.

hep-ph↗

arXiv2020

Automorphic Forms and Fermion Masses

We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups $Γ$, that allow the presence of several moduli and make connection with the theory of automorphic forms. Moduli span a coset space $G/K$, where $G$ is a Lie group and $K$ is a compact subgroup of $G$, modded out by $Γ$. For a general choice of $G$, $K$, $Γ$ and a generic matter content, we explicitly construct a minimal Kähler potential and a general superpotential, for both rigid and local $N=1$ supersymmetric theories. We also specialize our construction to the case $G=Sp(2g,R)$, $K=U(g)$ and $Γ=Sp(2g,Z)$, whose automorphic forms are Siegel modular forms. We show how our general theory can be consistently restricted to multi-dimensional regions of the moduli space enjoying residual symmetries. After choosing $g=2$, we present several examples of models for lepton and quark masses where Yukawa couplings are Siegel modular forms of level 2.

hep-th↗

arXiv2020

Trimaximal neutrino mixing from scotogenic $A_4$ family symmetry

We propose a flavour theory of leptons implementing an $A_4$ family symmetry. Our scheme provides a simple way to derive trimaximal neutrino mixing from first principles, leading to simple and testable predictions for neutrino mixing and CP violation. Dark matter mediates neutrino mass generation, as in the simplest scotogenic model.

hep-ph↗

arXiv2020

Half-integral weight modular forms and application to neutrino mass models

We generalize the modular invariance approach to include the half-integral weight modular forms. Accordingly the modular group should be extended to its metaplectic covering group for consistency. We introduce the well-defined half-integral weight modular forms for congruence subgroup $Γ(4N)$ and show that they can be decomposed into the irreducible multiplets of finite metaplectic group $\widetildeΓ_{4N}$. We construct concrete expressions of the half-integral/integral modular forms for $Γ(4)$ up to weight 6 and arrange them into the irreducible representations of $\widetildeΓ_4$. We present three typical models with $\widetildeΓ_4$ modular symmetry for neutrino masses and mixing, and the phenomenological predictions of each model are analyzed numerically.

hep-ph↗

arXiv2020

Modular Invariant Models of Leptons at Level 7

We consider for the first time level 7 modular invariant flavour models where the lepton mixing originates from the breaking of modular symmetry and couplings responsible for lepton masses are modular forms. The latter are decomposed into irreducible multiplets of the finite modular group $Γ_7$, which is isomorphic to $PSL(2,Z_{7})$, the projective special linear group of two dimensional matrices over the finite Galois field of seven elements, containing 168 elements, sometimes written as $PSL_2(7)$ or $Σ(168)$. At weight 2, there are 26 linearly independent modular forms, organised into a triplet, a septet and two octets of $Γ_7$. A full list of modular forms up to weight 8 are provided. Assuming the absence of flavons, the simplest modular-invariant models based on $Γ_7$ are constructed, in which neutrinos gain masses via either the Weinberg operator or the type-I seesaw mechanism, and their predictions compared to experiment.

hep-ph↗

arXiv2020

A New Littlest Seesaw Model

We propose and discuss a new Littlest Seesaw model, realised in the tri-direct CP approach, in which the couplings of the two right-handed neutrinos to the lepton doublets are proportional to $(0,-1,1)$ and $(1,5/2,-1/2)$ respectively with the relative phase $η=-π/2$. This model can give an excellent description of lepton flavour mixing, including an atmospheric neutrino mixing angle in the second octant, in terms of only two input parameters. We show that the observed baryon asymmetry can be generated for the lightest right-handed neutrino mass $M_{1}=1.176\times 10^{11}$ GeV in SM and $M_{1}=3.992\times 10^{10}$ GeV in MSSM with $\tanβ=5$. We construct an explicit Littlest Seesaw model based on the flavour symmetry $S_4\times Z_4\times Z_9$ in which the desired alignments and the phase $η=-π/2$ are achieved.

hep-ph↗

arXiv2020

Testing Moduli and Flavon Dynamics with Neutrino Oscillations

We study scalar Non-Standard Neutrino Interactions (NSI) induced by moduli or flavon exchange between electrons and neutrinos. In a region with non-vanishing electron number density, they are known to determine a shift of the neutrino mass matrix. We review and extend the relevant formalism, and we update the existing limits on electron and neutrino scalar couplings. We explore the observability of scalar NSI in models of lepton masses based on flavour symmetries. We analyze models where the scalar couplings are constrained either by abelian symmetries or by modular invariance. We highlight regions of the parameter space where observable effects can occur.

hep-ph↗

arXiv2019

Confronting Tri-direct CP-symmetry models to neutrino oscillation experiments

Tri-direct CP symmetry is an economical neutrino model building paradigm, and it allows to describe neutrino masses, mixing angles and CP violation phases in terms of four free parameters. Viability of a class of tri-direct CP models is examined with a comprehensive simulation of current and future neutrino oscillation experiments. Two benchmark models as well as the full parameter space are carefully scanned, and the parameter degeneracy problem is observed from the constraint of one group of neutrino oscillation experiments. Complementary roles from the accelerator neutrino experiments (e.g., T2HK and DUNE) and reactor neutrino experiments (e.g., JUNO) are crucial to break the degeneracy and nail down fundamental neutrino mixing parameters of the underlying theory.

hep-ph↗

arXiv2019

Modular $A_4$ Symmetry Models of Neutrinos and Charged Leptons

We present a comprehensive analysis of neutrino mass and lepton mixing in theories with $A_4$ modular symmetry, where the only flavon field is the single modulus field $τ$, and all masses and Yukawa couplings are modular forms. Similar to previous analyses, we discuss all the simplest neutrino sectors arising from both the Weinberg operator and the type I seesaw mechanism, with lepton doublets and right-handed neutrinos assumed to be triplets of $A_4$. Unlike previous analyses, we allow right-handed charged leptons to transform as all combinations of $\mathbf{1}$, $\mathbf{1}'$ and $\mathbf{1}''$ representations of $A_4$, using the simplest different modular weights to break the degeneracy, leading to ten different charged lepton Yukawa matrices, instead of the usual one. This implies ten different Weinberg models and thirty different type I seesaw models, which we analyse in detail. We find that fourteen models for both NO and IO neutrino mass ordering can accommodate the data, as compared to one in previous analyses, providing many new possibilities.

hep-ph↗

arXiv2019

Status and prospects of `bi-large' leptonic mixing

Bi-large patterns for the leptonic mixing matrix are confronted with current neutrino oscillation data. We analyse the status of these patterns and determine, through realistic simulations, the potential of upcoming long-baseline experiment DUNE in testing bi-large \emph{ansatze} and discriminating amongst them.

hep-ph↗

arXiv2019

Neutrino Masses and Mixing from Double Covering of Finite Modular Groups

We extend the even weight modular forms of modular invariant approach to general integral weight modular forms. We find that the modular forms of integral weights and level $N$ can be arranged into irreducible representations of the homogeneous finite modular group $Γ'_N$ which is the double covering of $Γ_N$. The lowest weight 1 modular forms of level 3 are constructed in terms of Dedekind eta-function, and they transform as a doublet of $Γ'_3 \cong T'$. The modular forms of weights 2, 3, 4, 5 and 6 are presented. We build a model of lepton masses and mixing based on $T'$ modular symmetry.

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