  Studying SU(3) gauge theories with increasing number of light fermions is
relevant both for understanding the strong dynamics of QCD and for constructing
strongly interacting extensions of the Standard Model (e.g. UV completions of
composite Higgs models). In order to contrast these many-flavors strongly
interacting theories with QCD, we study the flavor-singlet spectrum as an
interesting probe. In fact, some composite Higgs models require the Higgs boson
to be the lightest flavor-singlet scalar in the spectrum of a strongly
interacting new sector with a well defined hierarchy with the rest of the
states. Moreover, introducing many light flavors at fixed number of colors can
influence the dynamics of the lightest flavor-singlet pseudoscalar. We present
the on-going study of these flavor-singlet channels using multiple
interpolating operators on high-statistics ensembles generated by the LatKMI
collaboration and we compare results with available data obtained by the
Lattice Strong Dynamics collaboration. For the theory with 8 flavors, the two
collaborations have generated configurations that complement each others with
the aim to tackle the massless limit using the largest possible volumes.
