Resummed inclusive cross-section in Randall-Sundrum model at NNLO+NNLL

Abstract

The complete next-to-next-to leading order (NNLO) QCD correction has been studied to the di-lepton invariant mass distribution within the Randall-Sundrum (RS) framework. In addition, the soft-virtual (SV) cross-section at next-to-next-to-next-to leading order (N3LO) as well as threshold resummation to next-to-next-to leading logarithms (NNLL) level have been presented. The analytical coefficient for SV production has been obtained up to three loops very recently along with the process-dependent coefficients needed to perform resummation up to NNLL. These coefficients are universal for any universal spin-2 model where spin-2 particle couples to the Standard Model (SM) particles with equal strength. We use these coefficients in predicting N3LO SV results as well as matched NNLO+NNLL results for invariant mass distribution for Drell-Yan (DY) production in RS model. We performed a detailed phenomenological analysis and present our results in terms of mass dependent K-factors for the 13 TeV centre-of-mass energy at the Large Hadron Collider (LHC) for the search of such RS Kaluza-Klein (KK) resonances. The NNLO cross-section adds about 21% correction to the next-to-leading order (NLO) results. We found that the SV correction at the N3LO order decreases the cross-section by 0.7% near the first KK resonance (M1 = 1500 GeV) whereas the resummed result shows an increment over NNLO by 7% of LO. We performed a detailed analysis including scale variation and parton distribution function (PDF) variations. These new results provide an opportunity to stringently constrain the parameters of the model in particular in the search of heavy spin-2 resonances at the LHC.

Precision QCD phenomenology of exotic spin-2 search at the LHC

“…Here we observe that for (k q , k g ) = (1.0, 0.1) at low Q = M G values, the NLO K-factors K 1 can be as high as 3 while the corresponding K-factors for the universal case are about 1.5 [45]. Because k q is much larger than k g , at LO one can expect dominant contributions from Drell-Yan like process while the Higgs-like process is suppressed because of smaller coupling k g .…”

“…For the results presented just in figure 1, we use NNLO PDF at all orders. We observe that even at the resonance region, the cross section depends on the choice of k q and k g , which is not the case for the RS model where the height of the peak is independent of the corresponding coupling c 0 [45]. This particular nature can be understood from the parton level Born cross sections, eq.…”

“…At the LHC energies where the parton fluxes are large, the threshold logarithms can give sizeable contribution and through resummation these lead to better perturbative convergence as well as theoretical uncertainties for various processes [20,22,24,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Recently the effect of these large threshold logarithms has been studied in ADD and RS models [44,45] and better perturbative results have been predicted at N 3 LL(NNLL) accuracies. In view of this, we systematically include the threshold resummation effects in DY production for non-universal spin-2 model and present a detailed phenomenological results up to NNLL accuracy.…”

Resummed inclusive cross-section in ADD model at N3LL

“…The analytical results obtained in this article will also be useful to predict the resummed result for models with curved space-time dimension e.g. Randall-Sundrum scenario which however we leave for the future study [141].…”

Resummed Drell-Yan cross-section at N3LL

“…Moreover, it has been very well established that the resummed contributions give a sizable contributions to the cross-section. In fact many SM fixed order calculations have been improved with the corresponding resummed results, for example, the inclusive scalar Higgs production in gluon fusion [6,19,[23][24][25] (see also [26] for renormalisation group improved prediction) as well as in bottom quark annihilation [27], deep inelastic scattering [28,29], DY production [6,19,30], pseudo-scalar Higgs production [31][32][33], spin-2 production [34,35] etc. Threshold resummation not only improves the inclusive fixed order results but also differential observables like rapidity [21,[36][37][38][39] and in the context of LHC precision measurements, it is important to include these corrections and they are shown to improve the fixed order results.…”