Flavour bounds on the flavon of a minimal and a non-minimal Z2× ZN symmetry

Abstract

We investigate flavour bounds on the Z2× Z5 and Z2× Z9 flavour symmetries. These flavour symmetries are a minimal and a non-minimal forms of the Z2× ZN flavour symmetry, that can provide a simple set-up for the Froggatt–Nielsen mechanism. The Z2× Z5 and Z2× Z9 flavour symmetries are capable of explaining the fermionic masses and mixing pattern of the standard model including that of the neutrinos. The bounds on the parameter space of the flavon field of the Z2× Z5 and Z2× Z9 flavour symmetries are derived using the current quark and lepton flavour physics data and future projected sensitivities of quark and lepton flavour effects. The strongest bounds on the flavon of the Z2× Z5 symmetry come from the D- D¯ mixing. The bounds on the Z2× Z9 flavour symmetry are stronger than that of the minimal Z2× Z5 symmetry. The ratio Rμμ provides rather robust bounds on the flavon parameters in the future phase-I and phase-II of the LHCb by leaving only a very small region in the allowed parameter space of the models.