arXiv subjects

Jun-Nan Lu

Publications and source records attributed to Jun-Nan Lu.

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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 $τ$. The weighton $ϕ$ is defined as a complete singlet with unit modular weight, leading to fermion mass suppression by powers of $\tildeϕ$, 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, $q\equiv e^{i2πτ}$. 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 $\tildeϕ$ and $q$. We present two examples in detail, based on the modular group $T'$, close to the CP boundary of $τ$, which can address both fermion mass and mixing hierarchies using a weighton field.

hep-ph↗

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 Kähler 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 $m_{ββ}$ in neutrinoless double beta decay.

hep-ph↗

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.

hep-ph↗

arXiv2024

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 masses models based on the modular binary octahedral group $2O$. A comprehensive numerical analysis is performed, and we present some benchmark quark/lepton masses models in well 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.

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

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↗

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

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 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

$SO(10)$ 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↗

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

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↗