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Extended scalar and fermion sectors offer new opportunities for generatingthe observed strong hierarchies in the fermion mass and mixing patterns of theStandard Model (SM). In this work, we elaborate on the prospects of aparticular extension of the Inert Higgs doublet model where the SM hierarchiesare generated sequentially by radiative virtual corrections in a fullyrenormalisable way, i.e. without adding any non-renormalisable Yukawa terms orsoft-breaking operators to the scalar potential. Our model has a potential toexplain the recently observed $R_{K}$ and $R_{K^{\ast }}$ anomalies, thanks tothe non universal $U_{1X}$ assignments of the fermionic fields that yield nonuniversal $Z^{\prime}$ couplings to fermions. We explicitly demonstrate thepower of this model for generating the realistic quark, lepton and neutrinomass spectra. In particular, we show that due to the presence of bothcontinuous and discrete family symmetries in the considered framework, the topquark acquires a tree-level mass, lighter quarks and leptons get their massesat one- and two-loop order, while neutrino masses are generated at three-looplevel. The minimal field content, particle spectra and scalar potential of thismodel are discussed in detail.

Sequentially loop-generated quark and lepton mass hierarchies in an extended Inert Higgs Doublet model