NNLO+NNLL top-quark-pair cross sections

ATLAS-CMS recommended predictions for top-quark-pair cross sections using the Top++v2.0 program (M. Czakon, A. Mitov, 2013)

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Introduction

Predictions for top-quark-pair cross sections at NNLO+NNLL soft gluon resummation have been pepared using the Top++v2.0 program (M.Czakon, A. Mitov, Comput.Phys.Commun. 185 (2014) 2930) in a common ATLAS-CMS effort. The goal is to provide a common reference cross section for top-quark-pair (ttbar) production to be used by the ATLAS and CMS collaborations.

Prescription


The calculations are performed for top-quark mass (mtop) values of 172.5 GeV and 173.2 GeV. The renormalisation and factorisation scales, muR and muF, are taken as: muR = muF = mtop. The following NNLO PDF sets are used: MSTW2008NNLO, CT10 NNLO, NNPDF2.3 NNLO. The midpoint of the envelope is used for the central prediction.

  • Scale uncertainty: consider restricted scale variation (used also by Czakon, Fiedler and Mitov, arXiv:1303.6254):
    • Vary muR, muF independently by a factor of 2 while never allowing them to differ by more than a factor of 2 from each other.
    • The scale uncertainty is defined by taking the envelope of the resulting cross section values.
  • PDF+alphaS uncertainty: PDF4LHC-style treatment to provide a combined PDF+alphaS uncertainty (different approach to arXiv:1303.6254):
    • Evaluate the 68% CL PDF uncertainties for the PDF sets mentioned above at the most similar alphaS values.
    • Evaluate the 68% CL alphaS uncertainty.
    • Take the envelope of the PDF+alphaS uncertainties.
  • Mass uncertainty: assign a mtop variation of 1.0 GeV, following the latest top-quark mass combinations: mtop(Tevatron) = 173.20 +/- 0.87 GeV, mtop(LHC) = 173.29 +/- 0.95 GeV (ATLAS, CMS).


In addition, two parametrisations are provided:


More information, including comparison of this method with Czakon et al. arXiv:1303.7215 can be found in the presentation given at the open TOPLHCWG meeting on 28.11.13.

Recommendations for most analyses

Quote as total uncertainty the sum in quadrature of the scale uncertainty and the PDF+alphaS uncertainty.

For other top-quark property measurements and search analyses, the uncertainty on the top-quark mass can be added in quadrature as well.

The central values for the cross section, calculated at different sqrt(s) and for several top-quark masses are provided in the tables, together with the different uncertainties. The parametrisations of the cross section as a function of the top-quark mass and sqrt(s) are also given.

Proposed citation and list of references

For longer publications:

Proposed text and citations to refer to the calculation (example for 7 TeV and mtop = 172.5 GeV):

The ttbar cross section for pp collisions at a centre-of-mass energy of sqrt(s) = 7 TeV is sigma_ttbar= 177^{+10}_{-11}$~pb for a top quark mass of 172.5 GeV. It has been calculated at next-to-next-to leading order (NNLO) in QCD including resummation of next-to-next-to-leading logarithmic (NNLL) soft gluon terms with top++2.0 [1-7]. The PDF and alphaS uncertainties were calculated using the PDF4LHC prescription [8] with the MSTW2008 68% CL NNLO [9,10], CT10 NNLO [11,12] and NNPDF2.3 5f FFN [13] PDF sets, added in quadrature to the scale uncertainty.


[1] M.~Beneke et al., Hadronic top-quark pair production with NNLL threshold resummation , Nucl.Phys. B855 (2012) 695-741,arXiv:1109.1536 [hep-ph].
[2] M. Cacciari, et al., Top-pair production at hadron colliders with next-to-next-to-leading logarithmic soft-gluon resummation, Phys. Lett. B 710, 612 (2012), arXiv:1111.5869[hep-ph].
[3] P. Baernreuther, M. Czakon and A. Mitov, Percent Level Precision Physics at the Tevatron: First Genuine NNLO QCD Corrections to qqbar --> ttbar, Phys. Rev. Lett. 109, 132001 (2012) arXiv:1204.5201 [hep-ph].
[4] M. Czakon and A. Mitov, NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels, JHEP 1212, 054 (2012), arXiv:1207.0236 [hep-ph].
[5] M. Czakon and A. Mitov, NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction, JHEP 1301, 080 (2013), arXiv:1210.6832[hep-ph].
[6] M. Czakon, P. Fiedler, and A. Mitov, The total top quark pair production cross-section at hadron colliders through O(alphaS^4), Phys. Rev. Lett. 110 (2013) 252004, arXiv:1303.6254[hep-ph].
[7] M. Czakon and A. Mitov, Top++: a program for the calculation of the top-pair cross-section at hadron colliders, Comput.Phys.Commun. 185 (2014) 2930.
[8] M. Botje et al., The PDF4LHC Working Group interim recommendations, arXiv:1101.0538[hep-ph].
[9] A.D. Martin et al., Parton distributions for the LHC, Eur. Phys. J.C63 (2009) 189-285, arXiv: 0901.0002 [hep-ph].
[10] A.D Martin et al., Uncertainties on alphaS in global PDF analyses and implications for predicted hadronic cross sections, Eur. Phys. J.C64 (2009) 653-680, arXiv:0905.3531[hep-ph].
[11] H.-L. Lai et al., New parton distributions for collider physics, Phys. Rev. D82 (2010) 074024, arXiv:1007.2241 [hep-ph].
[12] J. Gao et al., The CT10 NNLO Global Analysis of QCD, arXiv:1302.6246 [hep-ph].
[13] R.D. Ball et al., Parton distributions with LHC data, Nucl. Phys. B867 (2013) 244-289, arXiv:1207.1303 [hep-ph].


For shorter publications or for those publications for which the predicted cross section does not play a central role:

Proposed text and citations to refer to the calculation (example for 8 TeV and mtop = 172.5 GeV):

The predicted ttbar production cross section is sigma_ttbar = 252.9 +6.4-8.6 (scale) +-11.7 (PDF + alphaS) pb as calculated with the Top++2.0 program to next-to-next-to-leading order in perturbative QCD, including soft-gluon resummation to next-to-next-to-leading-log order (see [1] and references therein), and assuming a top-quark mass mtop = 172.5 GeV. The first uncertainty comes from the independent variation of the factorisation and renormalisation scales, mF and mR, while the second one is associated to variations in the PDF and alphaS, following the PDF4LHC prescription with the MSTW2008 68% CL NNLO, CT10 NNLO and NNPDF2.3 5f FFN PDF sets (see [2] and references therein, and [3-5])".


[1] M. Czakon and A. Mitov, Top++: a program for the calculation of the top-pair cross-section at hadron colliders, Comput.Phys.Commun. 185 (2014) 2930.
[2] M. Botje et al., The PDF4LHC Working Group interim recommendations, arXiv:1101.0538[hep-ph].
[3] A.D Martin et al., Uncertainties on alphaS in global PDF analyses and implications for predicted hadronic cross sections, Eur. Phys. J.C64 (2009) 653-680, arXiv:0905.3531[hep-ph].
[4] J. Gao et al., The CT10 NNLO Global Analysis of QCD, arXiv:1302.6246 [hep-ph].
[5] R.D. Ball et al., Parton distributions with LHC data, Nucl. Phys. B867 (2013) 244-289, arXiv:1207.1303 [hep-ph].

Tables and Figures

Top-quark-pair cross sections at 7, 8, 13, and 14 TeV calculated for specific top-quark-mass values

The values in the tables are given in pb.

7 TeV
Top Mass (GeV) Central value Scale uncert. PDF+alphaS uncert. Mass uncert.
172.5 177.31 +4.56 -5.99 +9.02 -9.02 +5.44 -5.26
173.2 173.60 +4.46 -5.85 +8.85 -8.85 +5.32 -5.14
8 TeV
Top Mass (GeV) Central value Scale uncert. PDF+alphaS uncert. Mass uncert.
172.5 252.89 +6.39 -8.64 +11.67 -11.67 +7.58 -7.33
173.2 247.74 +6.26 -8.45 +11.47 -11.47 +7.41 -7.16
173.34 246.73 +6.23 -8.41 +11.43 -11.43 n/e
13 TeV
Top Mass (GeV) Central value Scale uncert. PDF+alphaS uncert. Mass uncert.
172.5 831.76 +19.77 -29.20 +35.06 -35.06 +23.18 -22.45
173.2 815.96 +19.37 -28.61 +34.38 -34.38 +22.67 -21.95
14 TeV
Top Mass (GeV) Central value Scale uncert. PDF+alphaS uncert. Mass uncert.
172.5 984.50 +23.21 -34.69 +41.31 -41.31 +27.14 -26.29
173.2 966.01 +22.68 -33.89 +40.52 -40.52 +26.54 -25.71

Parametrisations

Formula Caption
sigma_vs_mass_formula.png Parametrisation for the mass dependence of the ttbar cross section proposed by Czakon, Fiedler and Mitov, arXiv:1303.6254.
Table Caption
fit_mtop_7TeV.jpg Result of the fit to the top-quark mass dependence for the ttbar cross sections at 7 TeV. The top-quark mass is set to 172.5 GeV.
fit_mtop_8TeV.jpg Result of the fit to the top-quark mass dependence for the ttbar cross sections at 8 TeV. The top-quark mass is set to 172.5 GeV.
fit_mtop_13TeV.png Result of the fit to the top-quark mass dependence for the ttbar cross sections at 13 TeV. The top-quark mass is set to 172.5 GeV.
fit_mtop_14TeV.png Result of the fit to the top-quark mass dependence for the ttbar cross sections at 14 TeV. The top-quark mass is set to 172.5 GeV.
Formula Caption
sigma_vs_sqrts_formula.png Parametrisation for the sqrt(s) dependence of the ttbar cross section proposed by Langenfeld et al., arXiv:0907.2527.
Table Caption
fit_sqrts_mtop1725.jpg Result of the fit to the sqrt(s) dependence for the ttbar cross section. The top-quark mass is set to 172.5 GeV.
fit_sqrts_mtop1732.jpg Result of the fit to the sqrt(s) dependence for the ttbar cross section. The top-quark mass is set to 173.2 GeV.

Figures

Figure Caption
tt_xsec_7TeV.png Top-quark-pair cross-section measurements by the ATLAS and CMS collaborations at 7 TeV. The band shows the NNLO QCD calculation complemented with NNLL resummation (top++2.0). The theory band represents uncertainties due to renormalisation and factorisation scale, parton density functions and the strong coupling. The measurements and the theory calculation are quoted at mtop = 172.5 GeV. The upper part of the figure shows early LHC measurements and their combination. The lower part summarizes measurements performed after the LHC cross-section combination. Status of figure: July 2014 (ICHEP14).
tt_xsec_8TeV.png Top-quark-pair cross-section measurements by the ATLAS and CMS collaborations at 8 TeV. The band shows the NNLO QCD calculation complemented with NNLL resummation (top++2.0). The theory band represents uncertainties due to renormalisation and factorisation scale, parton density functions and the strong coupling. The measurements and the theory calculation are quoted at mtop = 172.5 GeV. Status of figure: July 2014 (ICHEP14).
tt_xsec_8TeV_wa.png Top-quark-pair cross-section measurements by the ATLAS and CMS collaborations at 8 TeV. The band shows the NNLO QCD calculation complemented with NNLL resummation (top++2.0). The theory band represents uncertainties due to renormalisation and factorisation scale, parton density functions and the strong coupling. The measurements and the theory calculation are quoted at the current World Average mtop = 173.34 GeV. Status of figure: July 2014 (ICHEP14).
tt_xsec_vsroots.png Summary of LHC and Tevatron measurements of the top-quark-pair production cross section as a function of the centre-of-mass energy compared to the NNLO QCD calculation complemented with NNLL resummation (top++2.0). The theory band represents uncertainties due to renormalisation and factorisation scale, parton density functions and the strong coupling. The measurements and the theory calculation are quoted at mtop = 172.5 GeV. Measurements made at the same centre-of-mass energy are slightly offset for clarity. Status of figure: July 2014 (ICHEP14).

-- MariaAldaya - 28 Jul 2014

Topic attachments
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PNGpng fit_mtop_14TeV.png r1 manage 135.3 K 2014-07-28 - 12:00 MariaAldaya  
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