Phenomenology of QCD threshold resummation for gluino pair production at NNLL

TL;DR

This work assesses NNLL threshold resummation for gluino-pair production at the LHC, comparing Mellin-space results with exact NLO and NNLO_approx, and providing momentum-space inputs and implementation details. It shows that soft resummation tends to keep the hadronic cross section close to the fixed NLO value, with only modest enhancements relative to NNLO_approx after PDF convolution. The analysis highlights scale choices, color decompositions, and the handling of Coulomb and soft contributions, emphasizing that PDF and α_s uncertainties dominate the theoretical error. The results inform SUSY exclusion limits and establish groundwork for incorporating Coulomb resummation in momentum-space approaches, while noting intrinsic ambiguities in threshold resummation that persist across formalisms.

Abstract

We examine the impact of threshold resummation for the inclusive hadronic production cross section of gluino pairs at next-to-next-to-leading-logarithmic accuracy, compared to the exact next-to-leading-order cross section and the next-to-next-to-leading-order approximation. Here, we apply formulas derived recently in the classical Mellin-space formalism. Moreover, we give the analytic input for the alternative momentum-space formalism and discuss the crucial points of the numeric implementation. We find that soft resummation keeps the hadronic cross section close to the fixed next-to-leading-order result.

Figures (3)

• Figure 1: Partonic cross section for gluon fusion versus the energy above the production threshold normalized to the gluino pair mass. The renormalization and factorization scales have been set to $\mu=m_{\widetilde{g}}=800\,\mathrm{GeV}$. We plot the NNLO approximation which is exact up to NLO, and the NNLO threshold limit $\text{NNLO}_{\rm th}$ which contains only threshold-enhanced contributions and NLO constants. Moreover, we show the NNLL resummed cross section and its expansion in $\alpha_s$ up to second order, NNLL(2), as well as the resummed partonic cross section matched onto the NNLO approximation. First panel: Coulomb corrections are included at fixed order in the resummation formula. Second panel: Coulomb corrections are neglected during resummation but kept in the NNLO approximation.
• Figure 2: Comparison of the resummed partonic cross section to the exact NLO result and the NNLO approximation. The scale is varied within the interval $\mu\in[m_{\widetilde{g}}/2,2m_{\widetilde{g}}]$ around $\mu=m_{\widetilde{g}}=800\,\mathrm{GeV}$.
• Figure 3: Inclusive hadronic cross section versus the squared cms energy. The error bars refer only to scale variation. Left panel: Fixed order for $m_{\widetilde{g}}=800\,\mathrm{GeV}$ and $m_{\widetilde{g}}=1\,\mathrm{TeV}$. Right panel: NNLO approximation and soft NNLL resummation matched onto the latter.