arXiv subjects

Bu-Yao Qu

Publications and source records attributed to Bu-Yao Qu.

9 recordsLinked to original sources

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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arXiv2025

Non-holomorphic modular flavor symmetry and odd weight polyharmonic Maaß form

We extend the framework of non-holomorphic modular flavor symmetry to include the odd weight polyharmonic Maaß forms. The integer weight polyharmonic Maaß forms of level $N$ can be arranged into multipltets of the homogeneous finite modular group $Γ'_N$. We propose to construct the integer weight, including weight one, non-holomorphic polyharmonic Maaß forms from the non-holomorphic Eisenstein series. The previous results of even weight polyharmonic Maaß 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 $Γ'_3\cong T'$ 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

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 $Y_ν$, right-handed neutrino mass matrix $M_R$ and the light neutrino mass matrix $M_ν$ 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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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

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.

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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.

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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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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.

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