  Searches for new low-mass matter and mediator particles have actively been
pursued at fixed target experiments and at $e^+e^-$ colliders. It is
challenging at the CERN LHC, but they have been searched for in Higgs boson
decays and in $B$ meson decays by the ATLAS and CMS Collaborations, as well as
in a low transverse momentum phenomena from forward scattering processes (e.g.,
FASER). We propose a search for a new scalar particle in association with a
heavy vector-like quark. We consider the scenario in which the top quark ($t$)
couples to a light scalar $\phi^\prime$ and a heavy vector-like top quark $T$.
We examine single and pair production of $T$ in $pp$ collisions, resulting in a
final state with a top quark that decays purely hadronically, a $T$ which
decays semileptonically ($T$ $\rightarrow$ $W$ + $b$ $\rightarrow$ $\ell$ $\nu$
$b$), and a $\phi^\prime$ that is very boosted and decays to a pair of
collimated photons which can be identified as a merged photon system. The
proposed search is expected to achieve a discovery reach with signal
significance greater than 5$\sigma$ (3$\sigma$) for $m(T)$ as large as 1.8 (2)
TeV and $m(\phi^\prime)$ as small as 1 MeV, assuming an integrated luminosity
of 3000 fb$^{-1}$. This search can expand the reach of $T$, and demonstrates
that the LHC can probe low-mass, MeV-scale particles.
