  Besides the Higgs particle discovered in 2012, with mass 125 GeV, recent LHC
data show tentative signals for new resonances in diboson as well as diphoton
searches at high center-of-mass energies (2 TeV and 750 GeV, respectively). If
these signals are confirmed (or other new resonances are discovered at the TeV
scale), the large hierarchies between masses of new bosons require a dynamical
explanation. Motivated by these tentative signals of new physics, we
investigate the theoretical possibility that large hierarchies in the masses of
glueballs could arise dynamically in new strongly-coupled gauge theories
extending the standard model of particle physics. We study lattice data on
non-Abelian gauge theories in the (near-)conformal regime as well as a simple
toy model in the context of gauge/gravity dualities. We focus our attention on
the ratio $R$ between the mass of the lightest spin-2 and spin-0 resonances,
that for technical reasons is a particularly convenient and clean observable to
study. For models in which (non-perturbative) large anomalous dimensions arise
dynamically, we show indications that this mass ratio can be large, with $R>5$.
Moreover, our results suggest that $R$ might be related to universal properties
of the IR fixed point. Our findings provide an interesting step towards
understanding large mass ratios in the non-perturbative regime of quantum field
theories with (near) IR conformal behaviour.
