  Experiments at the LHC may yet discover a dijet resonance indicative of
Beyond the Standard Model (BSM) physics. In this case, the question becomes:
what BSM theories are consistent with the unexpected resonance? One possibility
would be a spin-2 object called the colorphilic graviton--a spin-2
color-singlet particle which couples exclusively to the quark and gluon
stress-energy tensors. We assess the possibility of this state's discovery in
the dijet channel as an s-channel resonance, and report the regions of
parameter space where colorphilic gravitons have not yet been excluded by
LHC-13 data but still may be discovered in the dijet channel at LHC-14 for
integrated luminosities of 0.3, 1, and 3 ab$^{-1}$. We then delineate which of
those regions remain accessible to future collider searches, once one accounts
for applicability of the narrow-width approximation, detector mass resolution,
and self-consistency according to tree-level partial-wave unitarity. We
discover that--despite the strong constraints unitarity imposes on collider
searches--the colorphilic graviton remains potentially discoverable in the LHC
dijet channel. A means of investigation would be to apply the color
discriminant variable (CDV), a dimensionless combination of quantities
(cross-section, decay width, and invariant mass) that can be quickly measured
after the discovery of a dijet resonance. Previous publications have
demonstrated the CDV's utility when applied to theories containing Z',
colorons, excited quarks, and diquarks. We extend this analysis to the
colorphilic graviton by applying the CDV to the appropriate region of parameter
space. We conclude that resolvable, discoverable dijet resonances consistent
with colorphilic gravitons span a narrower range of masses than those
consistent with leptophobic Z' models, and can be distinguished from those
originating from coloron, excited quark, and diquark models.
