Threshold Improved QCD Corrections for Stop-Antistop production at Hadron colliders

TL;DR

The paper tackles the problem of predicting the total hadronic cross section for stop-anti-stop production at hadron colliders with high precision. It develops NNLO threshold corrections and approximated NNLO Coulomb corrections using soft-gluon resummation in Mellin space up to $NNLL$, including the exact scale dependence and analytic expressions for the NNLO scaling functions. The results, convolved with MSTW2008 NNLO PDFs, provide explicit cross sections and $K$-factors for the Tevatron and LHC, showing enhancements of roughly $10$–$20\%$ over $NLO$ and improved scale stability. These refined predictions strengthen stop mass exclusion limits and illustrate the practical impact of high-order QCD corrections for SUSY searches at hadron colliders.

Abstract

I present improved predictions for the total hadronic cross section of stop-antistop production at hadron colliders including next-to-next-to-leading-order threshold corrections and approximated Coulomb corrections. The results are based on soft corrections, which are logarithmically enhanced near threshold. I present analytic formulas for the NNLO scaling functions at threshold and explicit numbers for the total hadronic cross sections for the Tevatron and the LHC. Finally I discuss the systematic error, the scale uncertainty and the PDF error of the hadronic cross section.

Figures (6)

• Figure 1: LO production of a $\tilde{t}_i\,\tilde{t}_i^{\ast}$ pair via $gg$ annihilation (diagrams a-d) and $q \bar{q}$ annihilation (diagram e).
• Figure 2: Scaling functions $f^{(ij)}_{q \bar{q}}$ with $i = 0,1,2$ and $j\le i$. The masses are $m_{\tilde{t}_{1}}=300\,\,\mathrm{GeV}$, $m_{\tilde{q}} = 400\,\,\mathrm{GeV}$, $m_{\tilde{t}_{2}}=480\,\,\mathrm{GeV}$$m_{\tilde{g}} = 500\,\,\mathrm{GeV}$.
• Figure 3: Total hadronic cross section at LO, NLO, and NNLO$_{\text{approx}}$ at the LHC 7$\,\mathrm{TeV}$ (first row) and 14$\,\mathrm{TeV}$ (second row) and the Tevatron (1.96$\,\mathrm{TeV}$, third row). The right column shows the corresponding $K$ factors. The PDF set used is MSTW2008 NNLO Martin:2009iq.
• Figure 4: Left hand side: Theoretical uncertainty of the total hadronic cross section at the LHC (14$\,\mathrm{TeV}$) at LO (upper figure, blue band), NLO (central figure, green band), NNLO$_{\text{approx}}$ (lower figure, purple line). At NNLO$_{\text{approx}}$, the theoretical uncertainty has shrunk to a small band. Right hand side: Scale dependence of the total hadronic cross section for the example point $m_{\tilde{t}_{1}} = 300\,\mathrm{GeV}$, $m_{\tilde{q}} = 400\,\,\mathrm{GeV}$, $m_{\tilde{t}_{2}}=480\,\,\mathrm{GeV}$, $m_{\tilde{g}} = 500\,\,\mathrm{GeV}$. The vertical bars indicate the total scale variation in the range $[m_{\tilde{t}_{{}}}/2,2\*m_{\tilde{t}_{{}}}]$.
• Figure 5: Contour lines of the total hadronic NLO (left) and NNLO (right) cross section from the independent variation of the renormalisation and factorisation scale $\mu_r$ and $\mu_f$ for LHC, $14\,\mathrm{TeV}$, with PDF set MSTW2008 NNLO Martin:2009iq for the example point with $m_{\tilde{t}_{{}}}=300\,\mathrm{GeV}$. The dot in the middle of the figure indicates the cross section for $\mu_r=\mu_f=m_{\tilde{t}_{{}}}$, and the range corresponds to $\mu_f,\mu_r \in [m_{\tilde{t}_{{}}}/2,2m_{\tilde{t}_{{}}}]$.