Speaker
Description
In modular-invariant models of flavour, hierarchical fermion mass matrices may
arise solely due to the proximity of the modulus $\tau$ to a point of
residual symmetry. This mechanism does not require flavon fields
and may produce viable fermion (charged-lepton and quark)
mass hierarchies without fine-tuning. Models of lepton flavour in which
the indicated idea is realised are presented.
The problem of modulus stabilisation in the framework of the modular
symmetry approach to the flavour problem is discussed as well.
By analysing simple UV-motivated
CP-invariant potentials for the modulus $\tau$ it is shown that a class of
these potentials has (non-fine-tuned) CP-breaking minima in the vicinity
of the point of residual $Z^{\rm ST}_3$
symmetry, $\tau \simeq e^{i 2\pi/3}$. Stabilising the modulus at these
novel minima breaks spontaneously the CP symmetry and
can naturally explain the mass hierarchies of charged leptons and
possibly of quarks.
