Related papers: Modular flavor symmetric models

Flavor symmetry plays a crucial role in the standard model of particle physics but its origin is still unknown. We develop a new method (based on outer automorphisms of the Narain space group) to determine flavor symmetries within…

We present a flavor model with the $S_3$ modular invariance in the framework of SU(5) GUT. The $S_3$ modular forms of weights $2$ and $4$ give the quark and lepton mass matrices with a common complex parameter, the modulus $\tau$. The GUT…

The observed pattern of fermion masses and mixing is an outstanding puzzle in particle physics, generally known as the flavor problem. Over the years, guided by precision neutrino oscillation data, discrete flavor symmetries have often been…

We propose models in which the hierarchical structures of the masses and mixing in both quark and lepton sectors are explained by the $S_4^\prime$ modular flavor symmetry near the fixed point $\tau \sim i\infty$. The model provides the…

Most of the free parameters in the Standard Model (SM) -- a quantum field theory which has successfully elucidated the behaviors of strong, weak and electromagnetic interactions of all the known fundamental particles, come from the lepton…

We discussed the scenario that a discrete flavor group combined with CP symmetry is broken to $Z_2\times CP$ in both neutrino and charged lepton sectors. All lepton mixing angles and CP violation phases are predicted to depend on two free…

Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate the yet phenomenologically unexplored binary dihedral group 2D_3. After building the vector-valued modular forms in the…

Flavour symmetries are fundamental tools in the search for an explanation to the flavour puzzle: fermion mass hierarchies, the neutrino mass ordering, the differences between the mixing matrices in the quark and lepton sector, can all find…

We analyse the possibility of describing quark masses, mixing and CP violation in $S'_4$ modular flavour models without flavons. We focus on the case where the closeness of the modulus to the point of residual $\mathbb{Z}^{ST}_3$ symmetry…

The formalism of non-holomorphic modular flavor symmetry is developed, and the Yukawa couplings are level $N$ polyharmonic Maa{\ss} forms satisfying the Laplacian condition. We find that the integer (even) weight polyharmonic Maa{\ss} forms…

Modular flavor symmetries provide us with a new, promising approach to the flavor problem. However, in their original formulation the kinetic terms of the standard model fields do not have a preferred form, thus introducing additional…

We propose a mass matrix model that gives a unified description of quark and lepton with the same texture form based on a flavor 2 <-> 3 symmetry. The model is in contrast with the conventional picture that the mass matrix forms in the…

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…

One of the major challenges of particle physics has been to gain an in-depth understanding of the role of quark flavor and measurements and theoretical interpretations of their results have advanced tremendously: apart from masses and…

We briefly review some recent developments in theoretical models of fermion masses, mixings and CP violation with discrete non-Abelian symmetries. Then, we explain the main ideas of a recently proposed Minimal S_3 Invariant Extension of the…

In a class of neutrino mass models with modular flavor symmetries, it has been observed that CP symmetry is preserved at the fixed point (or stabilizer) of the modulus parameter $\tau = {\rm i}$, whereas significant CP violation emerges…

Supersymmetric theories supplemented by an underlying flavor-symmetry $\mathcal{G}_f$ provide a rich playground for model building aimed at explaining the flavor structure of the Standard Model. In the case where supersymmetry breaking is…

To explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor…

Behind the observed pattern of lepton flavor mixing is a partial or approximate mu-tau flavor symmetry --- a milestone on our road to the true origin of neutrino masses and flavor structures. In this review article we first describe the…

We propose a method to explore the flavor structure of quarks and leptons with reinforcement learning. As a concrete model, we utilize a basic value-based algorithm for models with $U(1)$ flavor symmetry. By training neural networks on the…