  New massive spin-2 particles are predicted in theoretical extensions to the
Standard Model (SM) attempting to solve the hierarchy problem. Such theories
postulate that gravity is diluted compared to the other fundamental forces
because it can propagate in extra spatial dimensions. While such theoretical
models are of high experimental interest because they predict massive spin-2
particles ($Y_{2}$) potentially detectable by collider experiments, searches at
the Large Hadron Collider (LHC) have thus far produced no significant evidence
for their existence. This work considers a hypothetical physics scenario where
low coupling strengths between the $Y_{2}$ and quarks/gluons is the underlying
reason behind the null $Y_{2}$ search results at the LHC, which have mainly
relied on Drell-Yan and gluon-gluon fusion production mechanisms. The focus of
this paper is a feasibility study to search for $Y_{2}$ particles using vector
boson fusion (VBF) processes at the LHC. In the context of an effective field
theory approach with varying couplings $\kappa_{V}$ between $Y_{2}$ and the
weak bosons of the SM, we consider the $Y_{2}\to\gamma\gamma$ decay mode to
show that the requirement of a diphoton pair combined with two high $p_{T}$
forward jets with large dijet mass and with large separation in pseudorapidity
can significantly reduce the SM backgrounds. Assuming proton-proton collisions
at $\sqrt{s} = 13$ TeV, we present the total VBF production cross sections,
$Y_{2}$ decay widths, and $Y_{2}\to\gamma\gamma$ branching ratios as a function
of $m(Y_{2})$, considering universal and non-universal couplings to the SM
particles. The unitarity-violating phase space is described. The proposed VBF
$Y_{2}\to\gamma\gamma$ search is expected to achieve a discovery reach with
signal significance greater than 5$\sigma$ for $Y_{2}$ masses up to 4.4 TeV and
$\kappa_{V}$ couplings down to 0.5.
