Related papers: Multiple modular symmetries as the origin of flavo…
In this paper, we have realized the left-right symmetric model with modular symmetry. We have used $\Gamma$(3) modular group which is isomorphic to non-abelian discrete symmetry group $A_4$. The advantage of using modular symmetry is the…
The neutrino oscillation data are well explained by the tri-bimaximal pattern. Recently a paper appeared showing that also the bimaximal pattern could be a very good starting point in order to describe the lepton mixing. In this paper I…
Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is…
We study the modular symmetric standard-model effective field theory. We employ the stringy Ansatz on coupling structure that 4-point couplings $y^{(4)}$ of matter fields are written by a product of 3-point couplings $y^{(3)}$ of matter…
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…
Strongly coupled supersymmetric theories can give rise to composite quarks and leptons at low energy. We show that the internal structure of these particles can explain the origin of three generations and provide a qualitative understanding…
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 study classes of models which are based on some discrete family symmetry which is completely broken such that the observed neutrino flavour symmetry emerges indirectly as an accidental symmetry. For such "indirect" models we discuss the…
We study a symmetry breaking of residual flavor symmetries realized at fixed points of the moduli space. In the supersymmetric modular invariant theories, a small departure of the modulus from fixed points is required to realize fermion…
Present data prefer a large but non-maximal 2-3 mixing in the lepton sector. We argue that this value, in connection with $\sin\theta_{13}\simeq 0.15$, is the generic outcome of minimal flavour structures. We present a few different…
The observed pattern of lepton flavor mixing and CP violation strongly indicates the possible existence of a simple flavor symmetry in the neutrino sector -- the effective Majorana neutrino mass term keeps invariant when the three…
We present a see-saw $A_4$ model for Tri-Bimaximal mixing which is based on a very economical flavour symmetry and field content and still possesses all the good features of $A_4$ models. In particular the charged lepton mass hierarchies…
In this paper, we incorporate the modular $S^{}_4$ flavor symmetry into the supersymmetric version of the minimal type-I seesaw model, in which only two right-handed neutrino singlets are introduced to account for tiny Majorana neutrino…
We study the flavor structure of the lepton and baryon number--conserving dimension-6 operators in the Standard Model effective field theory (SMEFT). Building on the work of [1], we define several well-motivated flavor symmetries and…
Discrete flavor symmetries provide a promising approach to understand the flavor sector of the standard model of particle physics. Top-down (TD) explanations from string theory reveal two different types of such flavor symmetries:…
Modular invariance has recently paved new promising directions in flavor model building. Motivated by this development, we present in this work the first implementation of the $S_3$ modular symmetry within the Pati-Salam unification…
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 perform an exhaustive analysis of all possible breaking patterns arising from $S_4\rtimes H_{CP}$ in a new {\it tri-direct CP approach} to the minimal seesaw model with two right-handed neutrinos, and construct a realistic flavour model…
We present a supersymmetric $T_{13}$ model for the tri-bimaximal neutrino mixing, and the complete flavor group is $T_{13}\times Z_{4}\times Z_2$. At leading order, the residual symmetry of the charged lepton sector is $Z_3$, and the…
Group theoretical arguments seem to indicate the discrete symmetry S4 as the minimal flavour symmetry compatible with tribimaximal neutrino mixing. We prove in a model independent way that indeed S4 can realize exact tribimaximal mixing…