Has a Higgs-flavon with a 750 GeV mass been detected at the LHC13?
Higgs-flavon fields appear as part of the Froggart-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 HF. We work within an extension of the standard model (SM) 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→μ¯τ. We also identify the viable parameter space that can reproduce the profile of the 750 GeV diphoton signal; in particular, the heavy fermions from the ultraviolet completion of the FN mechanism must play an important role to reproduce the large width of the signal. In addition, we find that the model predicts a large branching ratio for the HF→hh decay, of the order of 0.1, which should be searched for at the LHC13 to test this model.