Top quark cross sections and differential distributions

Abstract

I present results for the top quark pair total cross section and the top
quark transverse momentum distribution at Tevatron and LHC energies. I also
present results for single top quark production. All calculations include NNLO
corrections from NNLL threshold resummation.

Full text

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arXiv:1105.3481v1 [hep-ph] 17 May 2011
Top quark cross sections and differential distributions
Nikolaos Kidonakis
Kennesaw State University, Physics #1202, Kennesaw, GA 30144, USA
Abstract
I present results for the top quark pair total cross section and the top quark transverse
momentum distribution at Tevatron and LHC energies. I also present results for single
top quark production. All calculations include NNLO corrections from NNLL threshold
resummation.
TOP-ANTITOP PAIR PRODUCTION
The leading order processes for top-antitop pair production are q¯ q → t¯t (dominant at the
Tevatron) and gg → t¯t (dominant at LHC energies). The QCD corrections for top pair produc-
tion are significant and receive contributions from soft-gluon corrections which are dominant
near threshold. These soft corrections have been resummed through NNLL [1], requiring two-
loop calculations of the soft anomalous dimensions [1, 2]. Approximate NNLO differential-level
cross sections, using single-particle inclusive kinematics for partonic threshold, can be derived
from the expansion of the resummed cross section.
Figures 1 and 2 show the NNLO approximate cross section [1] together with recent data
from the corresponding experiments at the Tevatron [3, 4] and the LHC [5, 6]. The theoretical
prediction agrees well with the measured cross sections. The upper and lower curves indicate
the uncertainty from scale variation and pdf errors. It is important to note that the soft-gluon
approximation works very well not only for Tevatron but also for LHC energies because partonic
threshold is still important. There is only 1% difference between the first-order approximate
and exact corrections as shown in Fig. 3, and thus less than 1% difference between NLO
approximate and exact cross sections. For our best prediction in Figs. 1 and 2 we added the
NNLO approximate corrections to the exact NLO cross section. In all the results presented
here we have used the MSTW 2008 NNLO pdf [7].
At the Tevatron, we find that the NNLO corrections provide a 7.8% enhancement over NLO.
For a top quark mass of 173 GeV, we find
σNNLOapprox
t¯t
(mt= 173GeV, 1.96TeV) = 7.08+0.00
−0.24
+0.36
−0.27pb
where the first uncertainty is from scale variation between mt/2 and 2mtand the second is
from the MSTW NNLO pdf at 90% C.L. The NNLO approximate corrections reduce the scale
dependence greatly over a large range; the separate factorization and renormalization scale
dependence has also been calculated in [1].
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165
170
175
180
m (GeV)
5
6
7
8
9
10
σ (pb)
NNLO approx
+ - scale and pdf
CDF
D0
pp -> tt at Tevatron S1/2=1.96 TeV
Figure 1: Top-antitop pair cross section at the Tevatron.
165
170
175
180
m (GeV)
100
120
140
160
180
200
220
σ (pb)
NNLO approx
+ - scale and pdf
ATLAS
CMS
pp -> tt at LHC S1/2=7 TeV
Figure 2: Top-antitop pair cross section at the LHC.
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165
170
175
180
m (GeV)
0
10
20
30
40
50
60
70
σ (pb)
O(αs) approx corrections
O(αs) exact corrections
pp -> tt at LHC S1/2=7 TeV µ=m
qq + gg channels first-order corrections
Figure 3: Approximate and exact NLO corrections for t¯t production at the LHC.
At the LHC at 7 TeV energy, we find
σNNLOapprox
t¯t
(mt= 173GeV, 7TeV) = 163+7
−5
+9
−9pb,
which is an enhancement over NLO of 7.6%.
The top quark transverse momentum distribution at the Tevatron is shown in Fig. 4. The
pTdistribution is enhanced by the NNLO corrections but the shape is not significantly affected.
Similar results have also been obtained for the LHC [1].
In Fig. 5 we show the theoretical cross sections for t¯t production in p¯ p and pp collisions
as functions of collider energy and corresponding Tevatron [3, 4] and LHC [5, 6] data, again
noting the agreement between theory and experiment.
SINGLE TOP QUARK PRODUCTION
We continue with single top quark production and start by discussing the t-channel pro-
cesses: qb → q′t and ¯ qb → ¯ q′t. The t channel is numerically the largest at the Tevatron and the
LHC. We find for the NNLO approximate cross section [8]
σNNLOapprox,top
t−channel
(mt= 173GeV, 1.96TeV) = 1.04+0.00
−0.02± 0.06 pb,
σNNLOapprox,top
t−channel
(mt= 173GeV, 7TeV) = 41.7+1.6
−0.2± 0.8 pb.
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0
50
100
150
200
250
300
pT (GeV)
0
0.01
0.02
0.03
0.04
0.05
0.06
dσ/dpT (pb/GeV)
NLO µ=m
NLO µ=m/2, 2m
NNLO approx µ=m
NNLO approx µ=m/2, 2m
pp -> tt at Tevatron S1/2=1.96 TeV m=173 GeV
Figure 4: Top quark pT distribution at the Tevatron.
2
34
5
6
7
8
S1/2 (TeV)
1
10
100
σ (pb)
NNLO approx
CDF
D0
ATLAS
CMS
tt cross section at pp and pp colliders
Figure 5: Top-antitop pair cross sections in p¯ p (dash-dotted line) and pp (dashed line) collisions
versus collider energy.
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0
1
2
34
5
6
S1/2 (TeV)
7
89 10
11
12
1314
1
10
100
σ (pb)
NNLO approx
+ - scale and pdf
D0
CDF
CMS
ATLAS
t-channel single top + single antitop cross section
Figure 6: Single top plus single antitop t-channel cross section versus collider energy.
The NNLO approximate corrections contribute a 4% increase over NLO at the Tevatron and a
1% decrease at the LHC at 7 TeV.
For t-channel antitop production the cross section at the Tevatron is identical to that for
top production. However, at the LHC the cross section is different
σNNLOapprox,antitop
t−channel
(mt= 173GeV, 7TeV) = 22.5 ± 0.5+0.7
−0.9pb.
Figure 6 shows the combined single top plus single antitop t-channel cross section as a
function of energy together with data from the Tevatron [9, 10] and the LHC [11, 12]. Again,
the theory is consistent with the measured cross sections.
We continue with s-channel single top quark production: q¯ q′→¯bt, which is numerically
small at both Tevatron and LHC energies [13]. For top production we find
σNNLOapprox,top
s−channel
(mt= 173GeV, 1.96TeV) = 0.523+0.001
−0.005
+0.030
−0.028pb,
σNNLOapprox,top
s−channel
(mt= 173GeV, 7TeV) = 3.17 ± 0.06+0.13
−0.10pb.
The NNLO approximate corrections are an enhancement over NLO of 15% at the Tevatron and
13% at the LHC. Figure 7 shows the s-channel top cross section as a function of top quark
mass at the Tevatron. The antitop cross section at the Tevatron is the same.
For s-channel antitop production at the LHC we have
σNNLOapprox,antitop
s−channel
(mt= 173GeV, 7TeV) = 1.42 ± 0.01+0.06
−0.07pb.
5