Flavour bounds on the flavon of a minimal and a non-minimal $${\mathcal {Z}}_2 \times {\mathcal {Z}}_N$$ Z 2 × Z N symmetry

Abstract

Abstract We investigate flavour bounds on the $${\mathcal {Z}}_2 \times {\mathcal {Z}}_5$$ Z 2 × Z 5 and $${\mathcal {Z}}_2 \times {\mathcal {Z}}_9$$ Z 2 × Z 9 flavour symmetries. These flavour symmetries are a minimal and a non-minimal forms of the $${\mathcal {Z}}_2 \times {\mathcal {Z}}_N$$ Z 2 × Z N flavour symmetry, that can provide a simple set-up for the Froggatt–Nielsen mechanism. The $${\mathcal {Z}}_2 \times {\mathcal {Z}}_5$$ Z 2 × Z 5 and $${\mathcal {Z}}_2 \times {\mathcal {Z}}_9$$ Z 2 × Z 9 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 $${\mathcal {Z}}_2 \times {\mathcal {Z}}_5$$ Z 2 × Z 5 and $${\mathcal {Z}}_2 \times {\mathcal {Z}}_9$$ Z 2 × Z 9 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 $${\mathcal {Z}}_2 \times {\mathcal {Z}}_5$$ Z 2 × Z 5 symmetry come from the $$D^0 - {{\bar{D}}}^0$$ D 0 - D ¯ 0 mixing. The bounds on the $${\mathcal {Z}}_2 \times {\mathcal {Z}}_9$$ Z 2 × Z 9 flavour symmetry are stronger than that of the minimal $${\mathcal {Z}}_2 \times {\mathcal {Z}}_5$$ Z 2 × Z 5 symmetry. The ratio $$R_{\mu \mu }$$ R μ μ 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.