Peter Uwer *) Universität Karlsruhe Financed through Heisenberg fellowship and SFB-TR09 Graduiertenkolleg “Physik an Hadronbeschleunigern”, Freiburg 07.11.07 ppttj and ppWWj at next- to-leading order in QCD collaboration with S.Dittmaier, S. Kallweit and S.W
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Peter Uwer *) Universität Karlsruhe *) Financed through Heisenberg fellowship and SFB-TR09 Graduiertenkolleg “Physik an Hadronbeschleunigern”, Freiburg.
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Peter Uwer*)
Universität Karlsruhe
*) Financed through Heisenberg fellowship and SFB-TR09
Graduiertenkolleg “Physik an Hadronbeschleunigern”, Freiburg 07.11.07
ppttj and ppWWj at next-to-leading order in QCD
Work in collaboration with S.Dittmaier, S. Kallweit and S.Weinzierl
2
Contents
1. Introduction
2. Methods
3. Results
4. Conclusion / Outlook
3
Preliminaries
Technicalities Physics
Experts Non-Experts
Outline of the main problems/issues/challenges with only brief description of methods used
4
Why do we need to go beyond the Born approximation
?
5
Residual scale dependence
Quantum corrections lead to scale dependence of the coupling constants, i.e:
Large residual scale dependence of the Born approximation
In particular, if we have high powers of s:
6
Scale dependence
For ≈ mt and a variation of a factor 2 up and down:
1 2 3 4 n
20 %
40 %
30 %
10 %
22QCD
23QCD
24QCD
In addition we have also the factorization scale...
Need loop corrections to make quantitative predictions
Born approximation gives only crude estimate!
7
Corrections are not small...
Top-quark pair production at LHC:
~30-40%
/mt
[Dawson, Ellis, Nason ’89, Beenakker et al ’89,’91,Bernreuther, Brandenburg, Si, P.U. ‘04]
Scale independent corrections are also important !
8
...and difficult to estimate
WW production via gluon fusion:
tot = no cuts, std = standard LHC cuts, bkg = Higgs search cuts
30 % enhancement due to an “NNLO” effect (s2)
[Duhrssen, Jakobs, van der Bij, Marquard 05Binoth, Ciccolini,Kauer Krämer 05,06]
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To summarize:
NLO corrections are needed because
● Large scale dependence of LO predictions…
● New channels/new kinematics in higher orders can have important impact in particular in the presence of cuts
● Impact of NLO corrections very difficult to predict without actually doing the calculation
10
Shall we calculate NLO correctionsfor everything
?
11
WW + 1 Jet ― Motivation
● For 155 GeV < mh < 185 GeV, H WW is important channel
● In mass range 130 ―190 GeV, VBF dominates over ggH
NLO corrections for VBF known [Han, Valencia, Willenbrock 92Figy, Oleari, Zeppenfeld 03,Berger,Campbell 04, …]
Signal:
Background reactions:
WW + 2 Jets, WW + 1 Jet
If only leptonic decay of W´s and 1 Jet is demanded(improved signal significance)
Higgs search:
two forward tagging jets + Higgs
NLO corrections unknown
Top of the Les Houches list 07
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t t + 1 Jet ― Motivation
Important signal process
- Top quark physics plays important role at LHC
- Large fraction of inclusive tt are due to tt+jet
- Search for anomalous couplings
- Forward-backward charge asymmetry (Tevatron)
- Top quark pair production at NNLO ?
- New physics ?
- Also important as background (H via VBF)
LHC is as top quark factory
13
Methods
14
Next-to leading order corrections
Experimentally soft and collinear partons cannot be resolved due to finite detector resolution
Real corrections have to be included
The inclusion of real corrections also solves the problemof soft and collinear singularities*)
Regularization needed dimensional regularisation
1
n
1
n
* 1
n+1
*) For hadronic initial state additional term from factorization…
*)
15
Ingredients for NLO
1
n
1
n
*
1
n+1
1
n+1
1
n
1
n
+
Many diagrams, complicated structure,
Loop integrals (scalar and tonsorial)divergent (soft and mass sing.)
Many diagrams,divergent (after phase space integ.)
Combination procedure to addvirtual and real corrections