Abstract
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 (N3LOsv). 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 (N3LL) matched to N3LOsv. 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 N3LOsv +N3LL 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.
Highlights
Higgs rapidity is known to N3LO accuracy in gluon fusion [15, 16]
We find that the conventional scale uncertainties in the N3LOsv+N3LL resummed results substantially get reduced to as low as 2% in the high invariant mass region
The conventional 7-point scale uncertainties of about 8% at NNLO in the high invariant mass region get reduced to about 5% at three-loop level
Summary
The hadronic cross-section for standard DY production at the hadron collider is given by, dσP1P2 dQ τ, Q2. The partonic cross-section gets contribution from virtual photon and Z boson as in the standard DY process in SM, in addition, it gets contribution from spin-2 mediator (G) decaying to leptons. Notice that the signal and background completely get separated from each other in the cross-section after performing the phase-space integration for invariant mass distribution. This gives opportunity to calculate the SM and ADD contributions completely separately and there is no interference term between them. In case of ADD model, the pre-factor has the following form, FA(0D) D. The SV cross-section for spin-2 production is known to two loops in [100] after the subsequent calculation of the two loop form factors [101]. In the two sections we improve this accuracy by first calculating the SV cross-section at the three loops and we resum large threshold logarithms up to N3LL accuracy and matched with existing NNLO fixed order result
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