Resummed inclusive cross-section in ADD model at N3LL

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 ((NLOsv)-L-3). 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 ((NLL)-L-3) matched to (NLOsv)-L-3. 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 (NLOsv)-L-3 +(NLL)-L-3 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.