2011 QCD and High Energy Interactions - Rencontres de Moriond ...

dσ/dp t,max [fb/GeV]
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10 3
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NLO
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NNLO
10 2
pp, 14 TeV
66 < m + -
e e < 116 GeV
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K-factor wrt LO
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NLO
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nNLO (µ dep)
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nNLO (R LS dep)
MCFM 5.7, CTEQ6M
pp, 14 TeV
anti-k t , R=0.7
p t,j1 > 200 GeV
0
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pt,j1 (GeV)
K-factor wrt LO
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MCFM 5.7, CTEQ6M
pp, 14 TeV
anti-k t , R=0.7
p t,j1 > 200 GeV
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NLO
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nNLO (µ dep)
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nNLO (RLS dep)
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HT,jets (GeV)
Figure 2: Left: Comparison of spectra of the harder lepton in the Drell-Yan process between ¯nNLO results from
LoopSim+MCFM and full NNLO results from DYNNLO. Middle and Right: Comparison of ¯nNLO/LO and
NLO/LO K-factors from MCFM+LoopSim for pt,j1 and HT,jets observables in the Z+jet process.
and 0-loops. Then, it generates all diagrams from 1-loop event with n − 1 particles in the final
state. Finally, it sorts out double counting by removing all approximate contributions obtained
from tree events that have exact counterparts generated from events with exactly 1-loop.
3 Results
We start by showing our predictions for the case of Drell-Yan process for which we can compare
to the existing exact NNLO result. 3 The process is suitable to study with LoopSim since above a
certain value of transverse momentum, one finds large NLO corrections to the lepton pt-spectra.
This gives an opportunity to use this process for validation of the method.
As shown in the left panel of Fig. 2 the spectrum of the harder lepton falls rapidly above
certain value of pt at LO. At NLO, however, it gets huge correction in this region since the
initial-state radiation can give a boost to the Z-boson, causing one of the leptons to shift to
higher pt. As seen from the figure, we find near perfect agreement between the ¯nNLO and
NNLO results. This was expected in the intermediate and high pt region but not guaranteed
a priori below the peak, where the NLO/LO K factor was not large. The uncertainty bands
in Fig. 2 come from varying the factorization and renormalization scales by factors 1/2 and 2
around the central value, which was taken to be the mass of the Z-boson. For the LoopSim
radius we used RLS = 1.
We turn now to the Z+j process. Here, we provide ¯nNLO predictions from LoopSim+MCFM 2
for the pt of the hardest jet and HT,jets. As we see in the middle plot of Fig. 2, the correction
from LO to NLO is large. The scale uncertainty is obtained again by variation of a factor of 2
around µ0 = p2 t,j1 + m2 Z . We notice that the ¯nNLO correction for this observable really makes
a difference. The scale uncertainties get significantly smaller and there is a substantial overlap
between NLO and ¯nNLO bands, suggesting convergence of this prediction. We also show the
uncertainty corresponding to varying RLS = 1 ± 0.5.
In the right plot of Fig. 2 we show the ¯nNLO correction for HT,jets distribution. Here the
situation is different from the case of pt,j1, since the NLO and ¯nNLO bands do not overlap. We
have checked by studying dijet events that the K-factor of 2 from NLO to ¯nNLO is genuine and
it comes from additional initial-state radiation, which appears at ¯nNLO. This radiation can
form a third jet, which shifts the HT,jets distribution to slightly larger values, and because the
distribution falls very steeply, one gets a non-negligible correction.
It is also interesting to see what the LoopSim method predicts for dijets events. We have used
LoopSim+NLOjet++ 4 to study the distribution of the effective mass observables HT,n, which are