  In the framework of the large extra dimensions (LED) model, we investigate the effects induced by the Kaluza-Klein (KK) gravitons up to the QCD next-to-leading order (NLO) on the $W$-pair production followed by a subsequential $W$-decay at the CERN LHC. We depict the regions in the $\mathcal{L}-M_{S}$ parameter space where the LED effect can and cannot be observed from the analyses of the $pp \to W^+W^- + X$ and $pp \to W^+W^- \to W^{\pm}l^{\mp}\stackrel{(-)}{\nu} + X$ processes. We find that the ability of probing the LED effects can be improved by taking the cutoffs for the invariant mass of $W$-pair and the transverse momentum of the final lepton. Our results demonstrate that the NLO QCD corrections to observables are significant, and do not show any improvement for the renormalization/factorization scale uncertainty on the QCD NLO corrected cross section, because the LO result underestimates the scale dependence. 
Revisiting the large extra dimension effects on $W$-pair production at   the LHC in NLO QCD