NLL soft and Coulomb resummation for squark and gluino production at the LHC

TL;DR

The paper advances precise predictions for squark and gluino production at the LHC by performing NLL resummation of threshold soft-gluon and Coulomb corrections, extended to stop-antistop in a P-wave channel. Using a momentum-space SCET/pNRQCD framework, it combines hard, soft, and Coulomb functions with bound-state effects and matches to NLO to yield cross sections with reduced theoretical uncertainties to roughly 10%. Results show significant enhancements over NLO (typically 15–30%, and larger for some gluino-rich channels), with substantial contributions from bound-state physics, particularly below threshold. The study provides benchmark-based predictions and grid files for 7–14 TeV runs and demonstrates consistency with Mellin-space approaches, while outlining potential NNLL extensions and finite-width refinements as future work.

Abstract

We present predictions of the total cross sections for pair production of squarks and gluinos at the LHC, including the stop-antistop production process. Our calculation supplements full fixed-order NLO predictions with resummation of threshold logarithms and Coulomb singularities at next-to-leading logarithmic (NLL) accuracy, including bound-state effects. The numerical effect of higher-order Coulomb terms can be as big or larger than that of soft-gluon corrections. For a selection of benchmark points accessible with data from the 2010-2012 LHC runs, resummation leads to an enhancement of the total inclusive squark and gluino production cross section in the 15-30 % range. For individual production processes of gluinos, the corrections can be much larger. The theoretical uncertainty in the prediction of the hard-scattering cross sections is typically reduced to the 10 % level.

Figures (16)

• Figure 1: Ratio of the LO production cross sections for the processes \ref{['eq:processes']} to the total Born production rate of coloured sparticles, $\sigma_{\text{SUSY}}$, for the LHC with $\sqrt s=7$ TeV. Left: Mass dependence for a fixed mass ratio $m_{\tilde{q}}=m_{\tilde{g}}=M$. Right: Dependence on the ratio $m_{\tilde{g}}/m_{\tilde{q}}$ for a fixed average mass $(m_{\tilde{q}}+m_{\tilde{g}})/2=1.2$ TeV.
• Figure 2: NLO $K$-factor for the processes \ref{['eq:processes']} at the LHC with $\sqrt s=7$ TeV. Left: Mass dependence for a fixed mass ratio $m_{\tilde{q}}=m_{\tilde{g}}=M$. Right: Dependence on the ratio $m_{\tilde{g}}/m_{\tilde{q}}$ for a fixed average mass $(m_{\tilde{q}}+m_{\tilde{g}})/2=1.2$ TeV.
• Figure 3: Ratio of the singular NLO contributions obtained from \ref{['eq:NLOapprox']} to the exact NLO corrections for the LHC with $\sqrt s=7$ TeV. Left: Mass dependence for a fixed mass-ratio $m_{\tilde{q}}=m_{\tilde{g}}=M$. Right: Dependence on the ratio $m_{\tilde{g}}/m_{\tilde{q}}$ for a fixed average mass ($m_{\tilde{q}}+m_{\tilde{g}})/2=1.2$ TeV.
• Figure 4: Tree-level diagram topologies contributing to $q_k \bar{q}_l \rightarrow \tilde{q}_i \bar{\tilde{q}}_j$.
• Figure 5: Left: NLO $K$-factor for stop-pair production at $\sqrt{s}=7\,$TeV as a function of the stop mass. Right: ratio of the singular NLO contributions obtained from Eqs. (\ref{['eq:NLOapprox']}) and (\ref{['eq:NLOapprox-P']}) to the full NLO cross section for $PP \rightarrow \tilde{t}_1 \bar{\tilde{t}}_1$.