Introduction

Details on the commonly referred publications and strategies for cross section of top related channels. This page tries to collect and reflect official recommendations as much as possible. From J. M. Campbell and J. W. Huston and W. J. Stirling (2007) on the right showing cross section of various channels at Tevatron and at the LHC.

Cross Section

ttbar Cross Section

Current Strategy The NLO event generator used in the current study, MC@NLO reports 774 pb, close to the NLO value below. For the purpose of comparison with previous studies (such as [6]) , cross section used in this study is the NLO + NLL calculation of 833 pb and the normalisation of the signal is scaled up by 883/774.

There are several theoretical calculations of this channel with different features. pb ([Kidonakis03]): NLO. Scale dependency only with MRST2002. pb ([Kidonakis03]): Only the scale uncertainty is included. This is a NLO calculation that includes NNLL soft-gluon corrections. pb ([Bonciani98]): NLO + NLL (scale uncertainty only). These two are resummation calculations, but they are not necessarily improvements over NLO because while they include soft gluon emission in logs, they still are missing fixed terms that might add or subtract from the logs. Thus, they are not better in precision than the NLO calculations. Note that the NLL or NNLL additions are not real higher order K-factors but are effects of soft resummation. A K-factor would be the one-bin effect on the cross section from NNLO () calculations, as estimated by changing the renormalisation scale. Soft resummation happens in the heart of jets - and these resummations will not alter e.g. the number of jets nor the kinematics of jets in a uncontrolled way. They therefore will not affect the selection efficiencies much - all jet algorithms are infrared safe.

A helpful diagram to get a quick rough idea of branching ratio.

Reference

• ttbar at NLO+NNLL : [Kidonakis03] Next-to-next-to-leading order soft gluon corrections in top quark hadroproduction
  Author: N. Kidonakis, R. Vogt
  Ref: Phys.Rev.D68:114014,2003
• ttbar at NLO+NLL : [Bonciani98] NLL resummation of the heavy-quark hadroproduction cross section
  Author: Roberto Bonciani, Stefano Catani, Michelangelo Mangano
  Ref: Nucl Phys B 529 (1998) 424-450, CiteBase Link

Single Top Cross Section

Current Strategy While MC@NLO has finally implemented NLO event generation for single top, the current validated generator is AcerMC which is LO (t-channel is near NLO, has -1 weight). Like in ttbar, generator cross sections are scaled to NLO theoretical cross section. Details on K-factors can be found in this talk

t-channel and s-channel

t-channel and s-channel single top cross sections go down for higher top mass. And uncertainty of top mass contribute to uncertainty of the cross section, three examples are given here.

process	delta(mt)		NLO cross section (pb)	sum	ref
t-channel	±4.3 GeV	top	155.9 +7.5 -7.7	246.6 +11.8 –12.2	[Sullivan04]
		anti-top	90.7 +4.3 -4.5
s-channel	±4.0 GeV	top	6.56 +0.69 -0.63	10.65 +1.12 -1.02	[Sullivan04]
		anti-top	4.09 +0.43 0.39

You can check if the calculation is correct by adding in quadrature each contribution listed in the table below. Note the multiplication sign in the first column, the uncertainty is for each GeV error in mt.

process	x dmt (GeV)	mu/2 – 2mu	PDF	b mass	alpha_s(del_NLO)
t-channel	–0.73 % +0.78 %	±3%	+1.3 % –2.2 %	< 1%	±0.1%
s-channel	–1.97 % +2.26 %	±2%	+3.3 % -3.9 %	< 0.4%	±1.2%

Reference

• s, t-channel at NLO: [Sullivan04] Understanding single-top-quark production and jets at hadron colliders
  Author: Zack Sullivan
  Ref: Phys Rev D 70 (2004) 114012
  hep-ph/0408049 (Date: 3/8/04)
• Single Top NLO: [Cao04] Next-to-Leading Order Corrections to Single Top Quark Production and Decay at the Tevatron: 1. s-channel Process
  Authors: Q.-H. Cao, R. Schwienhorst, J. Benitez, R. Brock, C.-P. Yuan
  Ref: Phys Rev D 71, 054023 (2005)
  
• Single Top NLO: [Cao05] Next-to-Leading Order Corrections to Single Top Quark Production and Decay at the Tevatron: 2. t-channel Process
  Authors: Q.-H. Cao, R. Schwienhorst, J. Benitez, R. Brock, C.-P. Yuan
  Ref: Phys Rev D 72, 094027 (2005)
  

Reference (polarisation)

• [Chen05] General analysis of single top production and W helicity in top decay
  Authors: C.-R. Chen, C.-P. Yuan
  Ref: Phys Rev D 71, 054023 (2005)
  
• [Mahlon99] Single Top Quark Production at the LHC: Understanding Spin
  Author: Gregory Mahlon and Stephen Parke
  Ref: Phys Lett B476 (2000) 323-330
  hep-ph/9912458

Wt-channel

The latest results on Wt production at LHC is give by Campbell and Tramontano [Campbell05] who use mt=175 and 178 GeV. A previous work by [Zhu02] used mt=175 GeV.

The authors motivate the use of relatively lower factorisation scale, muF <~ (mW+mt)/4 (~ 65 GeV), and choose a scale of 50 GeV. At next-to-leading order, there is an extra b-antiquark in the diagrams and a pT veto is imposed in order to separate Wtb from ttbar where tbar is resonant (i.e. to remove ttbar contribution at NLO). For higher values of this veto, the NLO cross section is higher. The choice of low factorisation scale is not consistent with typically high value chosen for renormalization scale (of the order of Mt). The figure below shows the variation of cross section due to change in renormalization scale only. The author quotes 3% variation.

Therefore, we chose the central value of Wt cross section at mu=Mt with 3% variation on the value due to scale variation.

• pb [Campbell05]: NLO + NLL.

Reference

• Wt at NLO: [Campbell05] Next-to-leading order corrections to Wt production and decay
  Author: John Campbell, Francesco Tramontano
  Ref: Nucl Phys B 726 (2005) 109-130
• Wt at LO: [Tait99] The tW- modes of single top production
  Author: Tait, T. M. P.
  Ref: hep-ph/9909352
• Wt at LO: [Zhu02]
  S. Zhu,
  Ref: Phys. Lett. B 524, 283 (2002) [Erratum-ibid. B 537, 351 (2002)].
• Wt + X : [Belyaev00] Single top quark tW+X production at the LHC: a closer look
  Author: Belyaev, A. S. and Boos, E. E.
  Ref: hep-ph/0003260

Background Cross Section

This part is still a work in progress. The current discussion in CSC cross section note may help (here)

W+Jets

The following has selection cut of lepton Pt>=15GeV and jet Pt>=20GeV. Error is only from scale dependence only

process		NLO cross section (pb)	LO cross section (pb)	ref
W+ -> e+nu		6780 +290 -130	5670	[Campbell03]
W- -> e-nu		4830 +210 -90	3970
Z -> e+e-		915 +/- 31	803
W+j-> e+nuj		1880 +60 -50	1660
W-j-> e-nuj		1420 +/- 40	1220
Zj -> e+e-j		288 +8 -7	248
W+jj -> e+nujj		699 +0 -18	773
W-jj -> e-nujj		491 +0 -7	558
Zjj-> e+e-jj		105 +1 -5	116

Reference

• W+jj and Z+jj at NLO : [Campbell03] Next-to-leading order QCD predictions for W+2j and Z+2j production at the CERN LHC
  Author: John Campbell (Argonne), R.K. Ellis (FNAL), D. Rainwater (DESY)
  Ref: hep-ph/0308195

W+bb, W+bj

process		NLO cross section (pb)	LO cross section (pb)	ref
W+bb -> e+nubb		3.06 +0.62 -0.54	1.30 +0.21 -0.18	[Campbell03]
W-bb -> e-nubb		2.11 +0.46 -0.37	0.90 +0.14 -0.12
Zbb-> e+e-bb		2.28 +0.32 -0.29	1.80 +0.60 -0.40

Reference

• Wbb+nJets : [Mangano2001] Multijet Matrix Elements and Shower Evolution in Hadronic Collisions: Wbb + n Jets as a Case Study
  Author: L. M. Mangano and M. Moretti and R. Pittau
  hep-ph/0108069

WW, WZ, ZZ

QCD

Other Reference

Written for the Tevatron, also apply to LHC: [Sullivan05] Angular correlations in single-top-quark and Wjj production at next-to-leading order
Author: Zack Sullivan
Ref: Phys.Lett.B631:126-132,2005

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