  A new physics scenario shows that four-fermion operators of
Nambu-Jona-Lasinio (NJL) type have a strong-coupling UV fixed point, where
composite fermions $F$ (bosons $\Pi$) form as bound states of three (two) SM
elementary fermions and they couple to their constituents via effective contact
interactions at the composite scale $\Lambda \approx {\cal O} $(TeV). We
present a phenomenological study to investigate such composite particles at the
LHC by computing the production cross sections and decay widths of composite
fermions in the context of the relevant experiments at the LHC with $pp$
collisions at $\sqrt{s}={\rm 13}$ TeV and $\sqrt{s}={\rm 14}$ TeV.
Systematically examining all the different composite particles $F$ and the
signatures with which they can manifest, we found a vast spectrum of composite
particles $F$ that has not yet been explored at the LHC. Recasting the recent
CMS results of the resonant channel $pp\rightarrow e^+F \rightarrow e^+e^-
q\bar{q}'$, we find that the composite fermion mass $m_F$ below 4.25 TeV is
excluded for $\Lambda$/$m_F$ = 1. We further highlight the region of parameter
space where this specific composite particle $F$ can appear using 3 ab$^{-1}$,
expected by the High-Luminosity LHC, computing 3 and 5 $\sigma$ contour plots
of its statistical significance.
