arXiv subjects

Gui-Jun Ding

Publications and source records attributed to Gui-Jun Ding.

At least 19 recordsLinked to original sources

arXiv2026

Non-holomorphic $S^{\prime}_{4}$ modular symmetry for leptons and leptogenesis

We perform a comprehensive and systematic investigation of lepton models based on the non-holomorphic $S^{\prime}_{4}$ modular symmetry, by using level 4 polyharmonic Maa{\ss} forms spanning integer weights from $-4$ to $6$. The light neutrino masses are generated by the type-I seesaw mechanism with two right-handed neutrinos, no flavon fields other than the modulus $\tau$ is introduced, and the generalized CP symmetry is not imposed. An exhaustive numerical analysis yields 36 viable models with only four real couplings besides the modulus $\tau$ when neutrino masses are normal ordering. They are classified into three categories, each containing twelve models which yield quite similar predictions for lepton observables and are distinguished by the assignment of $E^c_1$. Furthermore, we perform a detailed numerical analysis for one representative model from each category. These representative models are found to yield very sharp predictions for neutrino masses and mixing parameters, and they are distinguished by the predictions for the atmospheric mixing angle $\theta_{23}$, the Dirac CP phase $\delta_{CP}$ and the Majorana CP phase $\alpha_{21}$. Furthermore, we find that only two of these three representative models accommodate successful thermal leptogenesis in the unflavored regime, reproducing the observed baryon asymmetry with the identical parameter values that satisfy neutrino oscillation data. In these models, the real part of the modulus $\tau$ is the unique source of CP violation in both lepton mixing and leptogenesis.

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arXiv2026

Two-zero textures of the Majorana neutrino mass matrix from $\mathbb{Z}_3$ gauging of $\mathbb{Z}_N$ non-invertible symmetry

Texture-zero ansatze offer an economical description of neutrino masses, with current data allowing only seven inequivalent two-zero Majorana textures in the charged-lepton mass basis. We investigate how such textures can arise from non-invertible symmetries realized through $\mathbb{Z}_3$ gauging of $\mathbb{Z}_N$. In contrast to $\mathbb{Z}_2$ gauging, which necessarily induces diagonal neutrino mass terms via the Weinberg operator, $\mathbb{Z}_3$ gauging admits complex representations and allows a richer class of neutrino mass textures. If the light neutrino mass is described by the Weinberg operator, we find that the textures $\mathbf{A}_{1,2}$, $\mathbf{B}_{3,4}$, and $\mathbf{C}$ can be realized from the $\mathbb{Z}_{3}$ gauging of $\mathbb{Z}_{13}$ symmetry, while all the seven phenomenologically viable two-zero textures can emerge from $\mathbb{Z}_{3}$ gauging of $\mathbb{Z}_{19}$ symmetry without requiring supersymmetry. When the neutrino mass is generated by the type-I seesaw mechanism, the structure of the non-invertible symmetry is more restrictive, yielding only texture $\mathbf{C}$ for $N\neq7$. These results demonstrate the strong predictive power of non-invertible symmetries for neutrino mass textures. Furthermore, the more general $\mathbb{Z}_{n}$ gauging of the $\mathbb{Z}_{N}$ symmetry with $n>3$ is analyzed, which results in novel fusion rules.

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arXiv2026

Systematical decomposition of dimension-11 short-range neutrinoless double beta decay operators

Neutrinoless double beta decay ($0\nu\beta\beta$) may receive sizable contributions from short-range physics beyond the Standard Model. We present a systematical classification of all tree-level ultraviolet completions of the dimension-11 short-range $0\nu\beta\beta$ decay operators, renormalizable scenarios with scalar and fermion mediators are considered. We identify eight distinct topologies and twenty-eight viable diagrams, from which all consistent UV completions are generated by imposing Standard Model gauge invariance. All these models involve a total of 61 new fields beyond the Standard Model and they typically feature fractionally charged fermions and exotic bosons such as dileptons, diquarks, and leptoquarks. We further study a representative model without colored mediators and analyze its implications for the $0\nu\beta\beta$ decay half-life and light neutrino masses. We find that current and future $0\nu\beta\beta$ decay experiments impose stringent constraints. Our systematic decomposition provides a general framework for exploring exotic short-range contributions to $0\nu\beta\beta$ decay in future experiments.

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arXiv2026

New modular fixed point models and their phenomenological implications for JUNO, T2HK and DUNE

We perform a general analysis of minimal modular fixed point models based on two right-handed neutrinos (2RHNs) and three modular fixed points, and find that the only viable possibilities are based on modular $S_4'$ and $A_5$ symmetry. Such models are highly predictive, with neutrino masses and the lepton mixing mixing matrix being fixed by three real parameters, as in the Littlest Seesaw Models. We perform an exhaustive scan over all possible models in this class and find many viable fixed points and modular form alignments, after confronting them with the latest neutrino oscillation global fits. The resulting models have the new feature that the two Dirac columns take more general forms than traditional Littlest Seesaw models, resulting in new sum rule relations between the solar and reactor angles, beyond those associated with TM1 (where the first column of the tri-bimaximal mixing matrix is preserved), which are compared to present and future projected JUNO results. We also compare the predictions of these models for the atmospheric angle and CP violating phase to current global fits and future T2HK and DUNE sensitivities.

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arXiv2025

$Sp(4,\mathbb{Z})$ modular inflation

We investigate inflation models governed by the Siegel modular group $Sp(4,\mathbb{Z})$. The $Sp(4,\mathbb{Z})$ group extends the $SL(2,\mathbb{Z})$ framework from one modulus to three moduli while preserving the hyperbolic geometry of the K\"ahler potential, allowing for the construction of cosmological $\alpha$-attractor models. In this context, we use genus $g=2$ absolute invariants to construct inflationary potentials within specific subspaces of the Siegel moduli space. These models are driven by the imaginary components of the moduli $\tau$ and naturally yield plateau-like potentials consistent with Planck 2018 observations in large field limit. We employ two-dimensional complex subspaces to realize E-model and T-model like two-field inflation scenarios. We explore the subspace of complex dimension one to construct a modified polynomial $\alpha$-attractor model, which can accommodate the larger spectral index $n_s$ favored by recent ACT and SPT data, particularly in the larger $N$ regime.

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arXiv2025

Discrete flavour and CP symmetries in light of JUNO and neutrino global fit

Working within the reference three-neutrino mixing framework, we confront the lepton mixing predictions derived using non-Abelian discrete flavour and CP symmetries with the first JUNO data on the solar neutrino mixing parameters $\sin^2\theta_{12}$ and with the results of the latest global neutrino data analysis. We focus on symmetry breaking patterns for which the lepton PMNS mixing matrix depends only on one or two free real parameters. Performing a comprehensive statistical analysis in each of the considered cases, we report the best fit values, the $3\sigma$ C.L. allowed ranges and the $\chi^2$-distributions of the lepton mixing observables - the three mixing angles and the three CP-violation phases. We find that the JUNO measurements can disfavour or rule out a number of the mixing patterns associated with specific types of breaking of the discrete flavour and CP symmetries. The synergy of JUNO, DUNE and T2HK data can provide an exhaustive test of the considered approach to lepton mixing based on non-Abelian discrete lepton flavour symmetries combined with the CP symmetry.

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arXiv2025

Zooming in on `bi-large' neutrino mixing with the first JUNO results

The leptonic mixing matrix is examined within bi-large mixing patterns and confronted with the latest results announced by the Jiangmen Underground Neutrino Observatory (JUNO). We analyze the viability of bi large mixing schemes and assess JUNO's ability to test neutrino mixing and discriminate among different bi-large mixing patterns, some of which are strongly disfavored when compared with neutrino oscillation global-fit results. Specific octant and CP predictions emerge. Finally, we comment on the implications of JUNO's findings for neutrinoless double beta decay.

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arXiv2025

Texture-zeros in minimal seesaw from non-invertible symmetry fusion rules

The $Z_2$ gauging of $Z_N$ symmetry can enforce certain elements of the fermion Yukawa couplings to vanish. We have performed a systematical study of texture zero patterns of lepton mass matrices in the minimal seesaw model, and we present all the possible patterns of the charged lepton Yukawa coupling $Y_E$, neutrino Yukawa coupling $Y_{\nu}$, right-handed neutrino mass matrix $M_R$ and the light neutrino mass matrix $M_{\nu}$ which can be derived from the $Z_2$ gauging of $Z_N$ symmetry. The realization of the textures with the maximum number of zeros and the second maximum number of zeros from non-invertible symmetry is studied, and the phenomenological implications in neutrino oscillation are discussed.

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arXiv2025

Lepton models from non-holomorphic $A^{\prime}_{5}$ modular flavor symmetry

In the framework of non-holomorphic modular invariance approach, we have systematically constructed all minimal lepton models based on the non-holomorphic $A^{\prime}_{5}$ modular symmetry from a bottom-up approach. In these models, the Yukawa couplings are described by polyharmonic Maa{\ss} forms of integer weights at level $N=5$. Under the assumption of Majorana neutrinos, both the Weinberg operator and the type-I seesaw mechanism are considered for neutrino mass generation. All minimal models are found to be based on generalized CP (gCP) symmetry, and each of them depends on five real dimensionless parameters and two overall scales. Through comprehensive numerical scanning, we obtain 6 (4) phenomenologically viable Weinberg operator models and 94 (76) phenomenologically viable seesaw models for normal (inverted) ordering neutrino masses. For each viable model, we present predictions for key neutrino properties, such as lepton masses, CP violation phases, mixing angles, effective Majorana mass for neutrinoless double beta decay and the kinematical mass in beta decay. Furthermore, we provide detailed numerical analysis for two representative models to illustrate our results.

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arXiv2025

Non-holomorphic modular flavor symmetry and odd weight polyharmonic Maa{\ss} form

We extend the framework of non-holomorphic modular flavor symmetry to include the odd weight polyharmonic Maa{\ss} forms. The integer weight polyharmonic Maa{\ss} forms of level $N$ can be arranged into multipltets of the homogeneous finite modular group $\Gamma'_N$. We propose to construct the integer weight, including weight one, non-holomorphic polyharmonic Maa{\ss} forms from the non-holomorphic Eisenstein series. The previous results of even weight polyharmonic Maa{\ss} forms are reproduced. We apply this formalism to address the flavor structure of the standard model. An example lepton model based on the modular group $\Gamma'_3\cong T'$ is constructed, where neutrino masses are generated via type-I seesaw mechanism with two right-handed neutrinos. This model can accommodate the experimental data for both normal and inverted neutrino mass orderings. We further extend this model to include quarks, so that the masses and mixing parameters of both quark and lepton sectors can be successfully described in terms of only thirteen real free parameters. It is the modular invariant model with the smallest number of free parameters so far, only normal ordering neutrino mass is viable after including quarks, and the correlations among the input parameters and flavor observables are analyzed.

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arXiv2025

Modular Symmetry with Weighton

We systematically develop the weighton mechanism for natural quark and charged lepton mass hierarchies in the framework of modular symmetry with a single modulus field $\tau$. The weighton $\phi$ is defined as a complete singlet with unit modular weight, leading to fermion mass suppression by powers of $\tilde{\phi}$, which is the vacuum expectation value of the field scaled by a flavour cut-off. Further mass and mixing angle suppression comes from powers of the small parameter, $q\equiv e^{i2\pi \tau}$. Assuming some fields transform as triplets under the finite modular symmetry, with general assignments for the other fields, we perform a complete analysis for the levels $N=3, 4, 5$, expressing fermion masses and mixings in terms of powers of the small parameters $\tilde{\phi}$ and $q$. We present two examples in detail, based on the modular group $T'$, close to the CP boundary of $\tau$, which can address both fermion mass and mixing hierarchies using a weighton field.

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arXiv2024

Modular invariant inflation and reheating

We use modular symmetry as an organizing principle that attempts to simultaneously address the lepton flavor puzzle, inflation, and post-inflationary reheating. We demonstrate this approach using the finite modular group $A_4$ in the lepton sector. In our model, neutrino masses are generated via the Type-I see-saw mechanism, with modular symmetry dictating the form of the Yukawa couplings and right-handed neutrino masses. The modular field also drives inflation, providing an excellent fit to recent Cosmic Microwave Background (CMB) observations. The corresponding prediction for the tensor-to-scalar ratio is very small, $r \sim \mathcal{O}(10^{-7})$, while the prediction for the running of the spectral index, $\alpha \sim -\mathcal{O}(10^{-3})$, could be tested in the near future. An appealing feature of the setup is that the inflaton-matter interactions required for reheating naturally arise from the expansion of relevant modular forms. Although the corresponding inflaton decay rates are suppressed by the Planck scale, the reheating temperature can still be high enough to ensure successful Big Bang nucleosynthesis. The same couplings responsible for reheating can also contribute to generating baryon asymmetry of the Universe through non-thermal leptogenesis. However, the contribution is negligibly small in the current inflationary setup.

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arXiv2024

Non-holomorphic modular $A_{5}$ symmetry for lepton masses and mixing

We perform a comprehensive bottom-up study of all the simplest lepton models based on non-holomorphic $A_{5}$ modular flavor symmetry, in which neutrinos are assumed to be Majorana particles and their masses are generated by the Weinberg operator or the type I seesaw mechanism. In the case that the generalized CP (gCP) symmetry is not considered, we find that 21 Weinberg operator models and 174 seesaw models can accommodate the experimental data in lepton sector, and all of them depend on six dimensionless free parameters and two overall scales. If gCP symmetry compatible with $A_{5}$ modular symmetry is imposed, one more free parameter would be reduced. Then only 4 of the 21 Weinberg operator models and 100 of the 174 seesaw models agree with the experimental data on lepton masses and mixing parameters. Furthermore, we perform a detailed numerical analysis for two example models for illustration.

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arXiv2024

Interplay and Correlations Between Quark and Lepton Observables in Modular Symmetry Models

In a predictive modular invariant theory of flavour there should exist correlations between the quark and lepton observables. So far these observables have been analyzed separately, making it impossible to investigate their interconnections. We perform for the first time a joint analysis of quark and lepton observables (22 altogether) in a modular flavour model. The model is based on $2O$ flavour symmetry and, within its class, it is characterized by the minimal number of free parameters (14 real constants). The joint analysis shows that the model is in good agreement with the experimental data for normal neutrino mass ordering, while predicting the leptonic Dirac CP-violating (CPV) phase ($\delta_{CP}$), the two Majorana CPV phases ($\eta_1$, $\eta_2$), the lightest neutrino mass ($m_1$) and the effective neutrino masses probed by beta and neutrinoless double beta decay ($m_\beta$ and $m_{\beta\beta}$). A detailed comparison of the separate (lepton-only and quark-only) and combined (lepton and quark) fit results shows differences in best-fit values and jointly allowed regions, that reflect a nontrivial interplay between quark and lepton observables in the model. Most importantly, our analysis highlights the existence of significant correlations between various pairs of such observables. For instance, the ratio of the strange and bottom quark masses, $r_{sb}$, is strongly negatively correlated with each of the three lepton mixing angles and with $\delta_{CP}$, $m_1$, $m_\beta$ and $m_{\beta\beta}$, while being positively correlated with $\eta_1$ and $\eta_2$. These findings, that are missed in separate analyses of quark and lepton flavour sectors, fall within ranges that can be tested by current and future experiments.

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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.

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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.

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arXiv2024

Minimal eclectic flavor group $Q_{8}\rtimes S_3$ and neutrino mixing

We perform a comprehensive analysis of the minimal eclectic flavor group $Q_{8}\rtimes S_3$ which is isomorphic to $GL(2,3)$, and all its irreducible representations are induced from the irreducible representations of $Q_{8}$ and $S_{3}$. The consistency conditions between EFG and generalized CP (gCP) symmetry are revisited, and we find the gCP symmetry compatible with the minimal EFG $Q_{8}\rtimes S_3$. The most general forms of K\"ahler potential and superpotential based on $Q_{8}\rtimes S_3$ are discussed, and the corresponding fermion mass matrices are presented. A concrete lepton model invariant under $Q_{8}\rtimes S_3$ 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 $m_{\beta\beta}$ in neutrinoless double beta decay.

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arXiv2024

Modular Invariant Slow Roll Inflation

We propose new classes of inflation models based on the modular symmetry, where the modulus field $\tau$ 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 $10^{-4}$.

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