Orateur
Description
The problem of hierarchy in flavour physics suggests the existence of a broken flavour symmetry. Modular symmetry is one of them but needs only one field, the modulus, which simultaneously plays the role of a flavon and Yukawa couplings are promoted to function of this modulus. Fields transformations under modular symmetry are characterized by an integer called the weight and a representation of a finite quotient group of the full modular group $SL(2,\mathbb{Z})$. It has been proven that modular symmetry can predict the masses and mixing angles of the fermionic sector of the Standard Model. Moreover, if the modulus takes special values, modular forms naturally acquire a hierarchy. This hierarchy depends on the choice of the finite quotient group and representations of the fields. We have investigated every possible choice and restrict them to a few number of representations able to naturally reproduce the hierarchies observed in the leptonic sector. Finally, we explicitly built one of these models based on the group $A_4\times\mathbb{Z}_4$ and found that with parameters of order one we can reproduce the masses and mixing angles of the leptonic sector.