arXiv subjects

Gui-Jun Ding

Publications and source records attributed to Gui-Jun Ding.

At least 37 records · Page 2Linked to original sources

arXiv2024

Modular Invariant Slow Roll Inflation

We propose new classes of inflation models based on the modular symmetry, where the modulus field $τ$ serves as the inflaton. We establish a connection between modular inflation and modular stabilization, wherein the modulus field rolls towards a fixed point along the boundary of the fundamental domain. We find the modular symmetry strongly constrain the possible shape of the potential and identify some parameter space where the inflation predictions agree with cosmic microwave background observations. The tensor-to-scalar ratio is predicted to be smaller than $10^{-6}$ in our models, while the running of spectral index is of the order of $10^{-4}$.

hep-ph↗

arXiv2024

Non-holomorphic Modular $S_4$ Lepton Flavour Models

In the formalism of the non-supersymmetric modular invariance approach to the flavour problem the elements of the Yukawa coupling and fermion mass matrices are expressed in terms of polyharmonic Maaß modular forms of level $N$ in addition to the standard modula forms of the same level and a small number of constant parameters. Non-trivial polyharmonic Maaß forms exist for zero, negative and positive integer modular weights. Employing the finite modula group $S_4$ as a flavour symmetry group and assuming that the three left-handed lepton doublets furnish a triplet irreducible representation of $S_4$, we construct all possible 7- and 8-parameter lepton flavour models in which the neutrino masses are generated either by the Weinberg effective operator or by the type I seesaw mechanism. We identify the phenomenologically viable models and obtain predictions for each of these models for the neutrino mass ordering, the absolute neutrino mass scale, the Dirac and Majorana CP-violation phases and, correspondingly, for the sum of neutrino masses and the neutrinoless double beta decay effective Majorana mass. We comment on how these models can be tested and conclude that they are all falsifiable. Detailed analyses are presented in the case of three representative benchmark lepton flavour scenarios.

hep-ph↗

arXiv2024

Non-holomorphic modular flavor symmetry

The formalism of non-holomorphic modular flavor symmetry is developed, and the Yukawa couplings are level $N$ polyharmonic Maaß forms satisfying the Laplacian condition. We find that the integer (even) weight polyharmonic Maaß forms of level $N$ can be decomposed into multiplets of the finite modular group $Γ'_N$ ($Γ_N$). The original modular invariance approach is extended by the presence of negative weight polyharmonic Maaß forms. The non-holomorphic modular flavor symmetry can be consistently combined with the generalized CP symmetry. We present three example models for lepton sector based on the $Γ_3\cong A_4$ modular symmetry, the charged lepton masses and the neutrino oscillation data can be accommodated very well, and the predictions for the leptonic CP violation phases and the effective Majorana neutrino mass are studied.

hep-ph↗

arXiv2024

Pati-Salam models with $A_4$ modular symmetry

The flavor structure of quarks and leptons and quark-lepton unification are studied in the framework of Pati-Salam models with $A_4$ modular symmetry. The three generations of the left-handed and right-handed fermions are assigned to be triplet or singlets of $A_4$. 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 $A_4$ 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.

hep-ph↗

arXiv2024

Eclectic flavor group $Δ(27)\rtimes S_3$ and lepton model building

We have performed a systematical study of the eclectic flavor group $Δ(27)\rtimes S_3$ which is the extension of the traditional flavor symmetry $Δ(27)$ by the finite modular symmetry $S_3$. Consistency between $Δ(27)$ and $S_3$ requires that the eight nontrivial singlet representations of $Δ(27)$ should be arranged into four reducible doublets. The modular transformation matrices are determined for various $Δ(27)$ multiplets, and the CP-like symmetry compatible with $Δ(27)\rtimes S_3$ are discussed. We study the general form of the Kähler potential and superpotential invariant under $Δ(27)\rtimes S_3$, and the corresponding fermion mass matrices are presented. We propose a bottom-up model for lepton masses and mixing based on $Δ(27)\rtimes S_{3}$, a numerical analysis is performed and the experimental data can be accommodated.

hep-ph↗

arXiv2024

Universal predictions of Siegel modular invariant theories near the fixed points

We analyze a general class of locally supersymmetric, CP and modular invariant models of lepton masses depending on two complex moduli taking values in the vicinity of a fixed point, where the theory enjoys a residual symmetry under a finite group. Like in models that depend on a single modulus, we find that all physical quantities exhibit a universal scaling with the distance from the fixed point. There is no dependence on the level of the construction, the weights of matter multiplets and their representations, with the only restriction that electroweak lepton doublets transform as irreducible triplets of the finite modular group. Also the form of the kinetic terms, which here are assumed to be neither minimal nor flavor blind, is irrelevant to the outcome. The result is remarkably simple and the whole class of examined theories gives rise to five independent patterns of neutrino mass matrices. Only in one of them, the predicted scaling agrees with the observed neutrino mass ratios and lepton mixing angles, exactly as in single modulus theories living close to $τ=i$.

hep-ph↗

arXiv2023

Neutrino Mass and Mixing with Modular Symmetry

This is a review article about neutrino mass and mixing and flavour model building strategies based on modular symmetry. After an introduction to neutrino mass and lepton mixing, we then turn to the main subject of this review, namely a pedagogical introduction to modular symmetry as a candidate for family symmetry, from the bottom-up point of view. After an informal introduction to modular symmetry, we introduce the modular group, and discuss its fixed points and residual symmetry, assuming supersymmetry throughout. We then introduce finite modular groups of level $N$ and modular forms with integer or rational modular weights, corresponding to simple geometric groups or their double or metaplectic covers, including the most general finite modular groups and vector-valued modular forms, with detailed results for $N=2, 3, 4, 5$. The interplay between modular symmetry and generalized CP symmetry is discussed, deriving CP transformations on matter multiplets and modular forms, highlighting the CP fixed points and their implications. In general, compactification of extra dimensions generally leads to a number of moduli, and modular invariance with factorizable and non-factorizable multiple moduli based on symplectic modular invariance and automorphic forms is reviewed. Modular strategies for understanding fermion mass hierarchies are discussed, including the weighton mechanism, small deviations from fixed points, and texture zeroes. Then examples of modular models are discussed based on single modulus $A_4$ models, a minimal $S'_4$ model of leptons (and quarks), and a multiple moduli model based on three $S_4$ groups capable of reproducing the Littlest Seesaw model. We then extend the discussion to include Grand Unified Theories (GUTs) based on modular (flipped) $SU(5)$ and $SO(10)$. Finally we discuss top-down approaches, including eclectic flavour symmetry and moduli stabilisation.

hep-ph↗

arXiv2023

General Heavy WIMP Nucleon Elastic Scattering

Heavy WIMP (weakly-interacting-massive-particle) effective field theory is used to compute the WIMP-nucleon scattering rate for general heavy electroweak multiplets through order $m_W/M$, where $m_W$ and $M$ denote the electroweak and WIMP mass scales. The lightest neutral component of such an electroweak multiplet is a candidate dark matter particle, either elementary or composite. Existing computations for certain representations of electroweak $\mathrm{SU(2)}_W\times \mathrm{U(1)}_Y$ reveal a cancellation of amplitudes from different effective operators at leading and subleading orders in $1/M$, yielding small cross sections that are below current dark matter direct detection experimental sensitivities. We extend those computations and consider all low-spin (spin-0, spin-1/2, spin-1, spin-3/2) heavy electroweak multiplets with arbitrary $\mathrm{SU(2)}_W\times \mathrm{U(1)}_Y$ representations and provide benchmark cross section results for dark matter direct detection experiments. For most self-conjugate TeV WIMPs with isospin $\le 3$, the cross sections are below current experimental limits but within reach of next-generation experiments. An exception is the case of pure electroweak doublet, where WIMPs are hidden below the neutrino floor.

hep-ph↗

arXiv2023

Systematic study of one-loop realizations of $d=7$ long-range $0νββ$ decay operators

We study the systematical one-loop decomposition of the dimension-7 long-range $0νββ$ decay operators. We find that there are 3 genuine one-loop topologies and 8 diagrams. The procedure to determine the SM quantum number assignments for both internal and external fields is presented. The Majorana neutrino mass in long-range $0νββ$ models is discussed. We also present a one-loop $0νββ$ decay model which produces Majorana neutrino mass at three-loop level. The phenomenological predictions for light neutrino mass and $0νββ$ decay half-life time including both mass mechanism and long-range contribution are studied.

hep-ph↗

arXiv2023

Neutrino Mass and Mixing Models with Eclectic Flavor Symmetry $Δ(27) \rtimes T'$

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 with generalised (g)CP, we perform a comprehensive bottom-up study of eclectic flavor symmetry models based on $Ω(1)\cong Δ(27)\rtimes T^\prime$, consisting of the flavor symmetry $Δ(27)$ in a semi-direct product with the modular symmetry $T^\prime$. The modular transformations of different $Δ(27)$ multiplets are given by solving the consistency condition. The eight nontrivial singlets of $Δ(27)$ 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 $θ_{23}$ and Dirac CP phase $δ_{CP}$ are obtained in the first model. After considering the compatible gCP symmetry and the assumption of $\Re τ=0$ 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 $π$.

hep-ph↗

arXiv2022

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 $Γ_{3}'\cong T'$ 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 doble 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).

hep-ph↗

arXiv2022

A minimal modular invariant neutrino model

We present a neutrino mass model based on modular symmetry with the fewest input parameters to date, which successfully accounts for the 12 lepton masses and mixing parameters through 6 real free parameters including the modulus. The neutrino masses are predicted to be normal ordering, the atmospheric angle $θ_{23}$ is quite close to maximal value and the Dirac CP phase $δ_{CP}$ is about $1.34π$. We also study the soft supersymmetry breaking terms due to the modulus $F$-term in this minimal model, which are constrained to be the non-holomorphic modular forms. The radiative lepton flavor violation process $μ\to eγ$ is discussed.

hep-ph↗

arXiv2022

Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry

We study the prediction for leptogenesis in two renormalizable supersymmetric $SO(10)\times A_4$ modular models in which the neutrino mass is dominantly generated by the type I seesaw mechanism. The evolution of the lepton asymmetries are described in terms of the three-flavored density matrix equations for three heavy Majorana neutrinos, where both vanishing initial condition and thermal initial condition of the right-handed neutrinos are considered. We also present an analytical approximation based on the Boltzmann equations. We find regions of parameter space compatible with the measured fermion masses and mixing parameters as well as the baryon asymmetry of the Universe. The predictions for the light neutrino masses, the effective mass in neutrinoless doble beta decay and the leptonic CP violation phases are discussed.

hep-ph↗

arXiv2021

Modular flavor symmetry and vector-valued modular forms

We revisit the modular flavor symmetry from a more general perspective. The scalar modular forms of principal congruence subgroups are extended to the vector-valued modular forms, then we have more possible finite modular groups including $Γ_N$ and $Γ'_N$ as the flavor symmetry. The theory of vector-valued modular forms provide a method of differential equation to construct the modular multiplets, and it also reveals the simple structure of the modular invariant mass models. We review the theory of vector-valued modular forms and give general results for the lower dimensional vector-valued modular forms. The general finite modular groups are listed up to order 72. We apply the formalism to construct two new lepton mass models based on the finite modular groups $A_4\times Z_2$ and $GL(2,3)$.

hep-ph↗

arXiv2021

Decomposition of $d=9$ short-range $0νββ$ decay operators at one-loop level

We perform a systematical study of the dimension-9 short-range $0νββ$ decay operators at one-loop level. There are only six genuine topologies which generate eight diagrams, and the recipe to identify the possible one-loop realizations of the $0νββ$ decay operators is sketched. Certain hypercharge assignments are excluded by the absence of tree-level diagrams in a genuine one-loop model. The mediators of each decomposition can generate Majorana neutrino masses which are discussed up to two-loop level. We present an example of $0νββ$ decay model in which the neutrino masses are generated at two-loop level, and the short-range contribution can be comparable with the mass mechanism in some region of parameter space.

hep-ph↗

arXiv2021

Modular symmetry origin of texture zeros and quark lepton unification

The even weight modular forms of level $N$ can be arranged into the common irreducible representations of the inhomogeneous finite modular group $Γ_N$ and the homogeneous finite modular group $Γ'_N$ which is the double covering of $Γ_N$, and the odd weight modular forms of level $N$ transform in the new representations of $Γ'_N$. We find that the above structure of modular forms can naturally generate texture zeros of the fermion mass matrices if we properly assign the representations and weights of the matter fields under the modular group. We perform a comprehensive analysis for the $Γ'_3\cong T'$ modular symmetry. The three generations of left-handed quarks are assumed to transform as a doublet and a singlet of $T'$, we find six possible texture zeros structures of quark mass matrix up to row and column permutations. We present five benchmark quark models which can produce very good fit to the experimental data. These quark models are further extended to include lepton sector, the resulting models can give a unified description of both quark and lepton masses and flavor mixing simultaneously although they contain less number of free parameters than the observables.

hep-ph↗

arXiv2021

Modular $S_4\times SU(5)$ GUT

Modular symmetry offers the possibility to provide an origin of discrete flavour symmetry and to break it along particular symmetry preserving directions without introducing flavons or driving fields. It is also possible to use a weighton field to account for charged fermion mass hierarchies rather than a Froggatt-Nielsen mechanism. Such an approach can be applied to flavoured Grand Unified Theories (GUTs) which can be greatly simplified using modular forms. As an example, we consider a modular version of a previously proposed $S_4\times SU(5)$ GUT, with Gatto-Sartori-Tonin and Georgi-Jarlskog relations, in which all flavons and driving fields are removed, with their effect replaced by modular forms with moduli assumed to be at various fixed points, rendering the theory much simpler. In the neutrino sector there are two right-handed neutrinos constituting a Littlest Seesaw model satisfying Constrained Sequential Dominance (CSD) where the two columns of the Dirac neutrino mass matrix are proportional to $(0,1, -1)$ and $(1, n, 2-n)$ respectively, and $n=1+\sqrt{6}\approx 3.45$ is prescribed by the modular symmetry, with predictions subject to charged lepton mixing corrections. We perform a numerical analysis, showing quark and lepton mass and mixing correlations around the best fit points.

hep-ph↗

arXiv2021

$SO(10)$ models with $A_4$ modular symmetry

We combine $SO(10)$ 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. We focus on the case where the three fermion families in the 16 dimensional spinor representation form a triplet of $Γ_3\simeq A_4$, with a Higgs sector comprising a single Higgs multiplet $H$ in the ${\mathbf{10}}$ fundamental representation and one Higgs field $\overlineΔ$ in the ${\mathbf{\overline{126}}}$ for the minimal models, plus and one Higgs field $Σ$ in the ${\mathbf{120}}$ for the non-minimal models, all with specified modular weights. The neutrino masses are generated by the type-I and/or type II seesaw mechanisms and results are presented for each model following an intensive numerical analysis where we have optimized the free parameters of the models in order to match the experimental data. For the phenomenologically successful models, we present the best fit results in numerical tabular form as well as showing the most interesting graphical correlations between parameters, including leptonic CP phases and neutrinoless double beta decay, which have yet to be measured, leading to definite predictions for each of the models.

hep-ph↗