  The detection of a single Higgs boson at the Large Hadron Collider (LHC) has
allowed one to probe some properties of it, including the Yukawa and gauge
couplings. However, in order to probe the Higgs potential, one has to rely on
new production mechanisms, such as Higgs pair production. In this paper, we
show that such a channel is also sensitive to the production and decay of a
so-called `Flavon' field ($H_F$), a new scalar state that arises in models that
attempt to explain the hierarchy of the Standard Model (SM) fermion masses. Our
analysis also focuses on the other decay channels involving the Flavon
particle, specifically the decay of the Flavon to a pair of $Z$ bosons ($H_F
\to Z Z$) and the concurrent production of a top quark and charm quark ($H_F\to
tc$), having one or more leptons in the final states. In particular, we show
that, with 3000 fb$^{-1}$ of accumulated data at 14 TeV (the Run 3 stage) of
the LHC an heavy Flavon $H_F$ with mass $M_{H_F} \simeq 2m_t $ can be explored
with $3\sigma -5\sigma $ significance through these channels.
