NLO single-top channel cross sections

ATLAS-CMS recommended predictions for single-top cross sections using the Hathor v2.1 program

Introduction

The goal is to provide a common inclusive reference cross section for single-top to be used by the ATLAS and CMS collaborations. Until the newly available t channel NNLO prediction and its uncertainties are fully expressed and available for the parameter values of choice, this reference cross section is obtained with automated NLO tools which guarantee flexible and easily configurable settings in order to be in accordance with configurations used for Monte Carlo samples and agreed-on parameter values. Predictions for the t channel cross sections at NLO in QCD have been pepared using the Hathor v2.1 program (P. Kant et al., arXiv:1406.4403 and M. Aliev et al., arXiv:1007.1327) in a common ATLAS-CMS effort. The same applies to the s channel, while the approx. NNLO predictions of Kidonakis are the reference for Wt.

Prescription and common assumptions

For all the calculations, a top quark mass of 172.5 GeV is used. Also the renormalization and factorization scales are set to this value.

t and s channel

  • Scale uncertainty:
    • Vary muR, muF independently up and down 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.
    • For deriving the scale uncertainty, the MSTW2008 NLO PDF is used.
  • PDF+alphaS uncertainty: PDF4LHC style treatment to provide a combined PDF+alphaS uncertainty:
    • Evaluate the 68% CL PDF uncertainties for the PDF sets MSTW2008NLO, CT10 NLO, NNPDF2.3 NLO. The alphaS(mZ) values corresponding to the best fit of the respective PDF set are used. In this case, this is alphaS=0.118 for CT10 NLO, alphaS=0.12018 for MSTW2008 NLO and alphaS=0.119 for NNPDF2.3 NLO
    • Evaluate the 68% CL alphaS uncertainty.
    • Take the envelope of the PDF+alphaS uncertainties.
    • The midpoint of the envelope is used for the central prediction.
  • Mass uncertainty: assign a top-mass variation of 1.0 GeV (Caution: not a part of the total uncertainty to be used in cross section measurements analyses, but quoted here for completeness. For other properties measurements or Vtb extraction you might need to take the mass uncertainty into account.)
  • Beam energy uncertainty:
    • For the computation of the impact of the beam energy uncertainty on the cross-section the sqrt(s) dependence parametrisation given below is used.
    • The uncertainty is given by dsigma/dsqrt(s)*0.1%*sqrt(s). The relative energy uncertainty per beam is 0.1% (Phys. Rev. Accel. Beams 20, 081003). Since both beams are assumed to be 100% correlated, the relative energy uncertainty of the pp centre-of-mass system stays the same.
    • Caution: this uncertainty is not part of the total uncertainty used in cross-section measurements, but quoted here for completeness. For other property measurements however (eg. Vtb extraction), you might want to take the beam energy uncertainty into account.

The non-diagonal CKM matrix is taken from J. Beringer et al. (Particle Data Group), Phys. Rev. D86, 010001 (2012).

Wt channel

  • Scale uncertainty:
    • The procedure is the same as for t and s channel, but the MSTW2008 NNLO PDF is used.
  • PDF uncertainty:
    • The error sets of MSTW2008 NNLO corresponding to the 90% CL eigenvectors are used to obtain the PDF uncertainty.

Recommendations for application and citation in most analyses

Application

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

Citation

Proposed text and citations refer to the calculation for 8 TeV:

The predicted t channel single-top cross section for pp collisions at a centre-of-mass energy of $\sqrt{s}=8$\,TeV is $\sigma_{\text{t}}= 54.9^{+2.3}_{-1.9}$\,pb for the top quark and $\sigma_{\bar{\text{t}}}=29.7^{+1.7}_{-1.5}$\,pb the anti-top quark, respectively. It is calculated for a top quark mass of 172.5\,GeV at next-to-leading order (NLO) in QCD with Hathor v2.1 [1,2]. The PDF and alphaS uncertainties are calculated using the PDF4LHC prescription [3] with the MSTW2008 68% CL NLO [4,5], CT10 NLO [6] and NNPDF2.3 [7] PDF sets, added in quadrature to the scale uncertainty.


[1] M. Aliev et al., HATHOR - HAdronic Top and Heavy quarks crOss section calculatoR, arXiv:1007.1327 [hep-ph].
[2] P. Kant et al., HATHOR for single top-quark production: Updated predictions and uncertainty estimates for single top-quark production in hadronic collisions, arXiv:1406.4403 [hep-ph].
[3] M. Botje et al., The PDF4LHC Working Group interim recommendations, arXiv:1101.0538 [hep-ph].
[4] A.D. Martin et al., Parton distributions for the LHC, Eur. Phys. J.C63 (2009) 189-285, arXiv: 0901.0002 [hep-ph].
[5] 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].
[6] H.-L. Lai et al., New parton distributions for collider physics, Phys. Rev. D82 (2010) 074024, arXiv:1007.2241 [hep-ph].
[7] R.D. Ball et al., Parton distributions with LHC data, Nucl. Phys. B867 (2013) 244-289, arXiv:1207.1303 [hep-ph].

Predictions at 7, 8, 13, and 14 TeV for top quark, anti-top quark and the combined case

Single-top t channel cross sections

The renormalisation and factorisation scales, muR and muF, are taken as: muR = muF = mtop = 172.5 GeV.

The values in the tables are given in pb.

7 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 41.80 +1.24 -0.82 +1.28 -1.28 +1.78 -1.52 +0.42 -0.42 ±0.09
anti-top 22.02 +0.67 -0.43 +1.08 -1.08 +1.27 -1.16 +0.24 -0.23 ±0.05
top + anti-top 63.89 +1.92 -1.25 +2.19 -2.19 +2.91 -2.52 +0.65 -0.65 ±0.14
8 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 54.87 +1.64 -1.09 +1.60 -1.60 +2.29 -1.94 +0.52 -0.52 ±0.11
anti-top 29.74 +0.92 -0.59 +1.39 -1.39 +1.67 -1.51 +0.30 -0.30 ±0.07
top + anti-top 84.69 +2.56 -1.68 +2.76 -2.76 +3.76 -3.23 +0.82 -0.82 ±0.18
13 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 136.02 +4.09 -2.92 +3.52 -3.52 +5.40 -4.57 +1.11 -1.11 ±0.24
anti-top 80.95 +2.53 -1.71 +3.18 -3.18 +4.06 -3.61 +0.71 -0.70 ±0.16
top + anti-top 216.99 +6.62 -4.64 +6.16 -6.16 +9.04 -7.71 +1.81 -1.81 ±0.39
14 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 154.76 +4.66 -3.39 +3.96 -3.96 +6.12 -5.21 +1.23 -1.24 ±0.27
anti-top 93.28 +2.92 -2.01 +3.58 -3.58 +4.62 -4.11 +0.80 -0.79 ±0.17
top + anti-top 248.09 +7.58 -5.40 +6.98 -6.98 +10.30 -8.82 +2.03 -2.03 ±0.44

Single-top Wt channel cross sections

Taken from: N.Kidonakis: NNLO approximate calculations, mtop = 172.5 GeV, MSTW2008 NNLO PDF set, PDF uncertainties evaluated using the set's 90% CL uncertainty. See also: http://arxiv.org/abs/1005.4451 and http://arxiv.org/abs/1311.0283.

7 TeV
Mode Central value Scale uncert. PDF uncert.
top + antitop 15.74 +0.40 -0.40 +1.10 -1.14
8 TeV
Mode Central value Scale uncert. PDF uncert.
top + antitop 22.37 +0.60 -0.60 +1.40 -1.40
13 TeV
Mode Central value Scale uncert. PDF uncert.
top + antitop 71.7 +1.80 -1.80 +3.40 -3.40
14 TeV
Mode Central value Scale uncert. PDF uncert.
top + antitop 84.4 +2.0 -2.0 +3.00 -4.80

Top and antitop equally contribute to the total cross section.

Caution: The table below is obtained with Hathor. It is still preliminary. Stick to Kidonakis numbers above for the moment (as of Jun 16, 2015).

The renormalisation and factorisation scales, muR and muF, are taken as: muR = muF = 65 GeV. Overlap at NLO with ttbar is removed by a cut on the b quark of pt > 60 GeV.

The values in the tables are given in pb.

7 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 6.59 +0.26 -0.28 +0.63 -0.63 +0.68 -0.69 +0.71 -0.92  
anti-top 6.59 +0.26 -0.28 +0.63 -0.63 +0.68 -0.69 +0.71 -0.92  
top + anti-top 13.18 +0.52 -0.56 +1.26 -1.26 +1.36 -1.38 +1.41 -1.84 ±0.04
8 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 9.39 +0.39 -0.41 +0.85 -0.85 +0.93 -0.94 +1.02 -1.32  
anti-top 9.38 +0.39 -0.41 +0.85 -0.85 +0.93 -0.94 +1.02 -1.32  
top + anti-top 18.77 +0.77 -0.82 +1.70 -1.70 +1.86 -1.88 +2.05 -2.65 ±0.06
13 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 30.11 +1.51 -1.81 +2.29 -2.29 +2.75 -2.92 +3.46 -4.31  
anti-top 30.09 +1.51 -1.81 +2.29 -2.29 +2.75 -2.92 +3.46 -4.31  
top + anti-top 60.20 +3.03 -3.62 +4.59 -4.59 +5.50 -5.85 +6.92 -8.63 ±0.16
14 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 35.45 +1.84 -2.23 +2.64 -2.64 +3.22 -3.46 +4.09 -5.08  
anti-top 35.43 +1.85 -2.23 +2.64 -2.64 +3.22 -3.45 +4.09 -5.08  
top + anti-top 70.89 +3.69 -4.45 +5.28 -5.28 +6.44 -6.91 +8.19 -10.16 ±0.18

Single-top s channel cross sections

The renormalisation and factorisation scales, muR and muF, are taken as: muR = muF = mtop = 172.5 GeV.

The values in the tables are given in pb.

7 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 2.76 +0.08 -0.07 +0.08 -0.08 +0.11 -0.10 +0.06 -0.06 <±0.01
anti-top 1.52 +0.04 -0.04 +0.07 -0.07 +0.08 -0.08 +0.04 -0.04 <±0.01
top + anti-top 4.29 +0.12 -0.10 +0.14 -0.14 +0.19 -0.17 +0.10 -0.10 ±0.01
8 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 3.34 +0.09 -0.08 +0.09 -0.09 +0.13 -0.12 +0.07 -0.07 <±0.01
anti-top 1.90 +0.05 -0.04 +0.08 -0.08 +0.10 -0.09 +0.05 -0.04 <±0.01
top + anti-top 5.24 +0.15 -0.12 +0.16 -0.16 +0.22 -0.20 +0.12 -0.12 ±0.01
13 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 6.35 +0.18 -0.15 +0.14 -0.14 +0.23 -0.20 +0.14 -0.13 ±0.01
anti-top 3.97 +0.11 -0.09 +0.15 -0.15 +0.19 -0.17 +0.09 -0.09 ±0.01
top + anti-top 10.32 +0.29 -0.24 +0.27 -0.27 +0.40 -0.36 +0.23 -0.22 ±0.01
14 TeV
Mode Central value Scale uncert. PDF+alphaS uncert. Total uncert. Mass uncert. Ebeam uncert.
top 6.98 +0.20 -0.16 +0.15 -0.15 +0.25 -0.22 +0.15 -0.14 ±0.01
anti-top 4.42 +0.13 -0.10 +0.16 -0.16 +0.20 -0.19 +0.10 -0.10 ±0.01
top + anti-top 11.39 +0.32 -0.26 +0.29 -0.29 +0.43 -0.39 +0.25 -0.24 ±0.02

Mass dependence parametrisation

Description

Formula Caption
sigma_vs_mass_formula.png Parametrisation for the mass dependence as proposed by Czakon, Fiedler and Mitov, arXiv:1303.6254 for the ttbar cross-section. The reference mass is 172.5GeV for all cases. NB: the cross-sections of all three channels decrease with an increasing top quark mass.

Single-top t channel

7 TeV
PDF Mode σref [pb] a1 a2
MSTW2008nlo68cl top 42.4069 2.312 1.118
anti-top 22.4868 2.208 0.9125
CT10nlo top 41.1551 2.304 1.103
anti-top 21.3727 2.21 0.9196
NNPDF23_nlo_as_0119 top 42.5328 2.317 1.127
anti-top 22.7307 2.223 0.9406
8 TeV
PDF Mode σref [pb] a1 a2
MSTW2008nlo68cl top 55.6097 2.393 1.285
anti-top 30.3693 2.293 1.083
CT10nlo top 54.0592 2.384 1.269
anti-top 28.8910 2.293 1.086
NNPDF23_nlo_as_0119 top 55.7427 2.399 1.298
anti-top 30.6611 2.308 1.113
13 TeV
PDF Mode σref [pb] a1 a2
MSTW2008nlo68cl top 137.6009 2.635 1.81
anti-top 82.6669 2.55 1.621
CT10nlo top 134.5398 2.627 1.792
anti-top 78.9935 2.546 1.614
NNPDF23_nlo_as_0119 top 137.4581 2.645 1.831
anti-top 83.0066 2.567 1.657
14 TeV
PDF Mode σref [pb] a1 a2
MSTW2008nlo68cl top 156.5287 2.667 1.879
anti-top 95.2744 2.584 1.694
CT10nlo top 153.1715 2.658 1.861
anti-top 91.1114 2.579 1.685
NNPDF23_nlo_as_0119 top 156.2639 2.677 1.901
anti-top 95.5775 2.6 1.729

Single-top Wt

Evaluated at NLO+NNLL for top+antitop with the MSTW2008 NNLO PDF set.

7 TeV
σref [pb] a1 a2
15.74 +0.926 -0.693
8 TeV
σref [pb] a1 a2
22.37 +1.031 -0.568
13 TeV
σref [pb] a1 a2
71.7 +1.326 -0.390
14 TeV
σref [pb] a1 a2
84.4 +1.368 -0.326

Single-top s channel

7 TeV
PDF Mode σref [pb] a1 a2
MSTW2008nlo68cl top 2.7832 0.1933 -0.2303
anti-top 1.5569 -0.06379 -0.174
CT10nlo top 2.7608 0.1705 -0.2286
anti-top 1.4942 -0.08015 -0.157
NNPDF23_nlo_as_0119 top 2.7797 0.1815 -0.2286
anti-top 1.5567 -0.04914 -0.1695
8 TeV
PDF Mode σref [pb] a1 a2
MSTW2008nlo68cl top 3.3551 0.251 -0.2197
anti-top 1.9362 0.0118 -0.1848
CT10nlo top 3.3368 0.231 -0.2195
anti-top 1.8623 -0.004674 -0.1684
NNPDF23_nlo_as_0119 top 3.3562 0.2433 -0.2214
anti-top 1.9335 0.02653 -0.1781
13 TeV
PDF Mode σref [pb] a1 a2
MSTW2008nlo68cl top 6.3546 0.4156 -0.1942
anti-top 4.0367 0.2322 -0.2001
CT10nlo top 6.3622 0.4034 -0.1925
anti-top 3.9139 0.2158 -0.1893
NNPDF23_nlo_as_0119 top 6.3651 0.4211 -0.1931
anti-top 4.0138 0.2466 -0.1909
14 TeV
PDF Mode σref [pb] a1 a2
MSTW2008nlo68cl top 6.9735 0.4365 -0.1909
anti-top 4.4860 0.2602 -0.2002
CT10nlo top 6.9870 0.425 -0.189
anti-top 4.3546 0.2439 -0.1897
NNPDF23_nlo_as_0119 top 6.9830 0.4435 -0.1891
anti-top 4.4577 0.2748 -0.1915

Centre-of-mass energy dependence parametrisation

Description

Formula Caption
sigma_vs_sqrts_formula.png Parametrisation for the sqrt(s) dependence of hadronic inclusive cross sections proposed by Langenfeld et al., arXiv:0907.2527 (the same as used for the ttbar cross-sections). All cross-sections used for the determination of the fit parameters are computed in the same way as the values above, ie. with a top-quark mass of 172.5GeV, the renormalization and factorization scales at this mass and the PDF4LHC prescription used to obtain the central values for the cross-sections w.r.t. to the PDF uncertainty.

Single-top t channel

Mode a0 a1 a2 a3 a4 a5 a6
top -4.27835 -8.43962 1.41417 1.62397 1.68152 -0.9851 0.196224
anti-top -1.69805 -1.82585 0.615003 0.173748 0.487396 -0.221678 -0.0842429
top + anti-top -5.98384 -10.3253 2.03362 1.76595 2.16635 -1.21191 0.109592

Single-top s channel

Mode a0 a1 a2 a3 a4 a5 a6
top 0.570909 0.236798 0.0157799 -0.0379118 -0.128326 -0.000835639 -0.000792388
anti-top 0.000590081 -0.179753 0.0353671 0.107203 0.0363796 -0.0331826 0.0135265
top + anti-top 0.558759 0.138934 0.0453426 0.105009 -0.0854976 -0.031082 0.0118111

Single-top Wt

Mode a0 a1 a2 a3 a4 a5 a6
top + anti-top -2.13668 0.582265 0.398919 -0.467872 0.221054 0.12196 -0.196817

Useful links

  • Version of current Hathor-release (v2.1-beta used for the numbers above)
  • An extenstive comparison between Hathor and MCFM in single-top is provided here

-- BenediktMaier, OliverMariaKind - Oct 2014 - Sep 2015

Topic attachments
I Attachment History Action Size Date Who Comment
PNGpng sigma_vs_mass_formula.png r1 manage 14.2 K 2015-09-12 - 22:48 OliverMariaKind sigma vs. mass formula
PNGpng sigma_vs_sqrts_formula.png r1 manage 12.8 K 2016-05-29 - 14:20 OliverMariaKind cross-section vs. centre-of-mass energy parametrisation
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Topic revision: r34 - 2017-09-19 - CarlosEscobar
 
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