  We present three loop soft-plus-virtual (SV) corrections to the spin-2
production at the Large Hadron Collider (LHC). For this calculation, we make
use of the recently computed quark and gluon three loop form factors for the
spin-2 production, the universal soft-collinear coefficients as well as the
mass factorization kernels. The SV coefficients are presented up to
next-to-next-to-next-to leading order (N$^3$LO). We also use these coefficients
at three loops to compute the resummed prediction for inclusive cross-section
to next-to-next-to-next-to leading logarithmic accuracy (N$^3$LL) matched to
next-to-next-to leading order (NNLO). We use the standard technique to derive
the Mellin N-dependent coefficients and also the N-independent coefficients to
achieve the resummation using the minimal prescription matching procedure.
Considering the spin-2 propagator in the large extra dimensional (ADD) model,
we also study the numerical impact of these three-loop SV corrections as well
as the resummed predictions on the di-lepton invariant mass distribution at the
13 TeV LHC. We find that the conventional scale uncertainties in the
NNLO+N$^3$LL resummed results substantially get reduced to as low as 2\% in the
high invariant mass region. We also estimate the PDF uncertainties in our
predictions that will be useful in the experimental searches for large extra
dimensions.
