Related papers: Modular $A_4$ Symmetry With Three-Moduli and Flavo…
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 $\tau$, and all masses and Yukawa couplings are modular forms. Similar…
In the modular symmetry approach to neutrino models, the flavour symmetry emerges as a finite subgroup $\Gamma_N$ of the modular symmetry, broken by the vacuum expectation value (VEV) of a modulus field $\tau$. If the VEV of the modulus…
We propose a non-holomorphic modular $A_4$ model under the assumption of universal couplings. In this framework, a charged lepton mass hierarchy is not created through parameter fine tuning or hierarchical Yukawa couplings, but instead is…
We study the lepton flavor models, whose flavor symmetries are finite subgroups of the modular group such as $S_3$ and $A_4$. In our models, couplings are also nontrivial representations of these groups and modular functions of the modulus.…
We consider a flavor model based on A4 modular group to account for both lepton and quark parameters (masses and mixing). The inverse seesaw mechanism is considered to produce the light neutrino masses. Lepton masses and mixing are obtained…
We propose a quark-lepton model via leptoquarks and modular $A_4$ symmetry. Since the neutrino mass is induced at one-loop level mediated by down quarks as well as leptoquarks, we have to explain lepton and quark masses and mixings with a…
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…
We study quark and lepton mass matrices with the common modulus $\tau$ in the $A_4$ modular symmetry. The viable quark mass matrices are composed of modular forms of weights $2$, $4$ and $6$. It is remarked that the modulus $\tau$ is close…
In this paper, we present a systematic investigation on simple inverse seesaw models for neutrino masses and flavor mixing based on the modular $S^{}_4$ symmetry. Two right-handed neutrinos and three extra fermion singlets are introduced to…
In this paper, we study the implications of the modular $A^{}_4$ flavor symmetry in constructing a supersymmetric minimal type-(I+II) seesaw model, in which only one right-handed neutrino and two Higgs triplets are introduced to account for…
We consider the modular symmetry associated with the compactification of extra dimensions as the flavor symmetry on lepton sector. Especially, we propose a model based on the modular $A_4$ symmetry with three right-handed neutrinos and a…
In the modular invariant flavor model of $\rm A_4$, we study the hierarchical structure of lepton/quark flavors at nearby fixed points of $\tau=i$ and $\tau=\omega$ of the modulus, which are in the fundamental domain of $\rm…
We consider a model with three right-handed neutrinos in which Yukawa coupling constants and Majorana masses are obtained by requiring the modular $A_4$ symmetry. It has been shown that the model can explain mass hierarchies and mixing…
We explore the implications of symmetries that remain unbroken at the self-dual point $\tau=i$ in modular invariant theories. Assuming that (a) the three generations of lepton doublets transform as an irreducible representation of a finite…
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…
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 Maa{\ss} modular forms of level $N$ in…
We study quark and lepton mass matrices in the $A_4$ modular symmetry towards the unification of the quark and lepton flavors. We adopt modular forms of weights $2$ and $6$ for quarks and charged leptons, while we use modular forms of…
An extension of the Standard Model with $\Gamma_2\simeq S_3$ modular flavor symmetry is presented. We consider the construction of the lepton sector, augmented by two right-handed neutrino states, in the vicinity of the fixed points $\tau =…
In this paper, we investigate lepton mass spectra, flavor mixing and CP violation with a modular $S^{}_4$ symmetry under the assumption that neutrinos are Dirac fermions. We find that the Majorana mass term can be forbidden by adjusting the…
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…