Has a Higgs-flavon with a $750$ GeV mass been detected at the LHC13?

Abstract: Higgs-flavon fields appear as a part of the Froggatt-Nielsen (FN) mechanism, which attempts to explain the hierarchy of Yukawa couplings. We explore the possibility that the 750 GeV diphoton resonance recently reported at the LHC13, could be identified with a low-scale Higgs-flavon field $H_F$ and find the region of the parameter space consistent with CMS and ATLAS data. It is found that the extra vector-like fermions of the ultraviolet completion of the FN mechanism are necessary in order to reproduce the observed signal. We consider a standard model (SM) extension that contains two Higgs doublets (a standard one and an inert one) and one complex FN singlet. The inert doublet includes a stable neutral boson, which provides a viable dark matter candidate, while the mixing of the standard doublet and the FN singlet induces flavor violation in the Higgs sector at the tree-level. Constraints on the parameters of the model are derived from the LHC Higgs data, which include the search for the lepton flavor violating decay of the SM Higgs boson $h\to \bar{\mu}\tau $. It is also found that in some region of the parameter space the model may give rise to a large branching ratio for the $H_F \to hh$ decay, of the order of 0.1, which could be searched for at the LHC.