NNLL resummation for squark and gluino production at the LHC

TL;DR

This article develops NNLL soft-gluon resummation for squark and gluino production at the LHC using a Mellin-moment approach, incorporating both one-loop hard matching and second-order Coulomb corrections, and matches to NNLO threshold approximations. It analyzes 8 TeV proton-proton collisions with masses up to 2.5 TeV for all four SUSY-QCD production channels, revealing substantial cross-section enhancements over previous NLO and NNLO_Approx results. Scale uncertainties are generally reduced with NNLL, though gluino-pair production exhibits residual scale sensitivity due to Coulomb and higher-log effects and incomplete two-loop matching. The findings highlight the importance of soft-gluon logarithms and Coulomb corrections in high-mass SUSY production and outline future work to complete two-loop matching and Coulomb resummation, as well as extension to higher collider energies.

Abstract

We perform the resummation of soft-gluon emissions for squark and gluino production at next- to-next-to-leading-logarithmic (NNLL) accuracy. We include also the one-loop hard matching coefficients as well as Coulomb corrections to second order, using Mellin-moment methods. We study the characteristics of this resummation in detail for a centre-of-mass (CM) energy of 8 TeV at the LHC, and for squark and gluino masses up to 2.5 TeV. We find significant enhancing effects for all four processes of squark- and gluino-pair production. Scale dependence is generally reduced compared to NLL resummation, except for gluino-pair production where we find a moderate enhancement.

Figures (6)

• Figure 1: The NNLL matched cross section for the four processes of pair production of squarks and gluinos, including the theoretical error band for the NNLO approximation. The error band includes the 68% C.L. pdf and $\alpha_{\rm s}$ errors, added quadratically, and the scale uncertainty varied in the range $m_{av}/2 \leq \mu \leq 2m_{av}$, added linearly to the combined pdf and $\alpha_{\rm s}$ error. The energy is that of the LHC at 8 TeV. The squark and gluino masses have been taken equal and the common renormalisation and factorisation scale has been set equal to the average mass of the two particles produced. For comparison, we also show the scale and total uncertainty of the NLO+NLL prediction.
• Figure 2: The NNLL matched cross section for the sum of the four processes of pair production of squarks and gluinos, including the theoretical error band for the NNLO approximation. The error band includes the 68% C.L. pdf and $\alpha_{\rm s}$ errors, added quadratically, and the scale uncertainty varied in the range $m_{av}/2 \leq \mu \leq 2m_{av}$, added linearly to the combined pdf and $\alpha_{\rm s}$ error. The energy is that of the LHC at 8 TeV. The squark and gluino masses have been taken equal and the common renormalisation and factorisation scale has been set equal to the average mass of the two particles produced. For comparison, we also show the scale and total uncertainty of the NLO+NLL prediction.
• Figure 3: The $K_X$-factor for the NNLL matched, NLO+NLL and $\rm NNLO_{Approx}$ predictions for different SUSY-QCD processes at the LHC with $\sqrt S=8$ TeV. The squark and gluino masses have been taken equal and the common renormalisation and factorisation scale has been set equal to the average mass of the two particles produced.
• Figure 4: The $K_X$-factor for the NNLL matched and NLO+NLL predictions for different values of $r=m_{{\tilde{g}}}/m_{{\tilde{q}}}=0.5,1,2$ for the four pair-production processes of squarks and gluinos at the LHC with $\sqrt S=8$ TeV. The common renormalisation and factorisation scale has been set equal to the average mass of the two particles produced.
• Figure 5: Scale dependence of the LO, NLO, NLO+NLL and NNLL matched cross sections for the four different SUSY-QCD processes at the LHC with $\sqrt S=8$ TeV. The squark and gluino masses have been taken equal to 1.2 TeV.