NNLL Momentum-Space Resummation for Stop-Pair Production at the LHC

TL;DR

The paper implements NNLL momentum-space resummation for stop-pair production at the LHC by factorizing partonic cross sections into hard and soft functions in two kinematic schemes (PIM and 1PI) and solving their RGEs. It matches the resummed results to fixed-order NLO to obtain NLO+NNLL predictions for the total cross section, then averages the two kinematic schemes to estimate scheme uncertainties. The study demonstrates reduced scale dependence and perturbative uncertainties relative to NLO/NLL and finds good agreement with approximate NNLO results, reinforcing the robustness of the approach and its applicability to other colored SUSY-particle processes.

Abstract

If supersymmetry near the TeV scale is realized in Nature, the pair production of scalar top squarks is expected to be observable at the Large Hadron Collider. Recently, effective field-theory methods were employed to obtain approximate predictions for the cross section for this process, which include soft-gluon emission effects up to next-to-next-to-leading order (NNLO) in perturbation theory. In this work we employ the same techniques to resum soft-gluon emission effects to all orders in perturbation theory and with next-to-next-to-logarithmic (NNLL) accuracy. We analyze the effects of NNLL resummation on the stop-pair production cross section by obtaining NLO+NNLL predictions in pair invariant mass and one-particle inclusive kinematics. We compare the results of these calculations to the approximate NNLO predictions for the cross sections.

Figures (6)

• Figure 1: Dependence of the default value $\mu_{0,s}$ for the soft scale (in units of $m_{\tilde{t}_1}$) on the top-squark mass, for PIM (green line) and 1PI kinematics (orange line) kinematics. The plot refers to the LHC operating at a center-of-mass energy of $\sqrt{S}=8$ TeV.
• Figure 2: Comparison between 1PI and PIM predictions and the residual perturbative uncertainty (brown band) of the averaged prediction (see text for further explanation).
• Figure 3: Dependence of the cross section on the factorization scale (first row), hard matching scale (second row), and soft matching scale (third row). The plots in the left panels refer to the LHC at $\sqrt{S}=8$ TeV, while the right panels refer to 14 TeV. The reference scales for the factorization and hard scales are chosen equal to their default values $\mu_{0,f}$ and $\mu_{0,h}$. The reference soft scale, $\bar{\mu}_{0,s}$ is set to $250$ GeV for both collider energies and both kinematics. The three scales are varied in the range $[1/3 \mu_{0,i},3 \mu_{0,i}]$. In order to study the scale dependence of the cross section, the NLL corrections are evaluated using CT10NLO PDFs while the NNLL (non-matched to NLO) corrections are evaluated using CT10NNLO PDFs.
• Figure 4: Comparison of the relative size of the approximate NNLO and NLO+NNLL corrections with respect to the NLO cross section. The plots span the mass range $m_{\tilde{t}_1} \in [500,2000]$ GeV. The left and right panels refer to the LHC operating at $\sqrt{S} = 8$ TeV and $\sqrt{S} = 14$ TeV, respectively.
• Figure 5: Mass scans with CT10 PDFs for the LHC with $\sqrt{S}=8$ TeV (first row) and $\sqrt{S}=14$ TeV (second row). The bands represent the perturbative scale uncertainties at NLO and NLO+NNLL. The left panels show a detail of the mass range 500—800 GeV. All of the SUSY parameters other than $m_{\tilde{t}_1}$ are fixed at the values of the benchmark point 40.2.5AbdusSalam:2011fc. The plots are obtained by employing CT10NNLO PDFs Lai:2010vvGao:2013xoa.