Peter Uwer

1
Graduiertenkolleg Physik an Hadronbeschleunigern
, Freiburg 07.11.07
pp?ttj and pp?WWj at next-to-leading order in QCD
Peter Uwer)
Universität Karlsruhe
Work in collaboration with S.Dittmaier, S.
Kallweit and S.Weinzierl
) Financed through Heisenberg fellowship and
SFB-TR09
2
Contents

• Introduction
• Methods
• Results
• Conclusion / Outlook

3
Preliminaries
Technicalities
Physics
Non-Experts
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 as
6
Scale dependence
For m mt and a variation of a factor 2 up and
down
In addition we have also the factorization
scale...
Born approximation gives only crude estimate!
? Need loop corrections to make quantitative
predictions
7
Corrections are not small...
Top-quark pair production at LHC
Dawson, Ellis, Nason 89, Beenakker et al
89,91, Bernreuther, Brandenburg, Si, P.U. 04
30-40
m/mt
Scale independent corrections are also important !
8
...and difficult to estimate
WW production via gluon fusion
Duhrssen, Jakobs, van der Bij, Marquard
05Binoth, Ciccolini,Kauer Krämer 05,06
tot no cuts, std standard LHC cuts, bkg
Higgs search cuts
30 enhancement due to an NNLO effect (as2)
9
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 corrections for everything
?
11
WW 1 Jet ? Motivation
Higgs search

• For 155 GeV lt mh lt 185 GeV, H ? WW is important
  channel
• In mass range 130 ?190 GeV, VBF dominates over
  gg?H

Han, Valencia, Willenbrock 92 Figy, Oleari,
Zeppenfeld 03, Berger,Campbell 04,
NLO corrections for VBF known
Signal
two forward tagging jets Higgs
Background reactions
WW 2 Jets, WW 1 Jet
Top of the Les Houches list 07
NLO corrections unknown
If only leptonic decay of Ws and 1 Jet is
demanded (?improved signal significance)
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t t 1 Jet ? Motivation
LHC is as top quark factory

• Important signal process
• Top quark physics plays important role at LHC
• Large fraction of inclusive tt are due to ttjet
• Search for anomalous couplings
• Forward-backward charge asymmetry (Tevatron)
• Top quark pair production at NNLO ?
• New physics ?
• Also important as background (H via VBF)

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
problem of soft and collinear singularities)
? Regularization needed ? dimensional
regularisation
) For hadronic initial state additional term
from factorization
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Ingredients for NLO
Many diagrams, complicated structure, Loop
integrals (scalar and tonsorial) divergent (soft
and mass sing.)

Combination procedure to add virtual and real
corrections

Many diagrams, divergent (after phase space
integ.)
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How to do the cancellation in practice
Consider toy example
Phase space slicing method
Giele,Glover,Kosower
Frixione,Kunszt,Signer 95, Catani,Seymour 96,
Nason,Oleari 98, Phaf, Weinzierl,
Catani,Dittmaier,Seymour, Trocsanyi 02
Subtraction method
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Dipole subtraction method (1)
Frixione,Kunszt,Signer 95, Catani,Seymour 96,
Nason,Oleari 98, Phaf, Weinzierl,
Catani,Dittmaier,Seymour, Trocsanyi 02
How it works in practise
Requirements
in all single-unresolved regions
Due to universality of soft and collinear
factorization, general algorithms to construct
subtractions exist
Recently NNLO algorithm
Daleo, Gehrmann, Gehrmann-de Ridder, Glover,
Heinrich, Maitre
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Dipole subtraction method (2)
Universality of soft and coll. Limits!
Universal structure
Generic form of individual dipol
Leading-order amplitudes Vector in color space
universal
!
!
Color charge operators, induce color correlation
Spin dependent part, induces spin correlation
6 different colorstructures in LO, 36 (singular)
dipoles
Example gg?ttgg
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Dipole subtraction method implementation
LO amplitude, with colour information, i.e.
correlations
List of dipoles we want to calculate
2
1
3
4
5
0
reduced kinematics, tilde momenta Vij,k
Dipole di
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LO amplitudes enter in many places
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Leading order amplitudes ? techniques
Many different methods to calculate LO amplitudes
exist
(Tools Alpgen MLM et al, Madgraph Maltoni,
Stelzer, Omega/Whizard Kilian,Ohl,Reuter,)
We used

• Berends-Giele recurrence relations
• Feynman-diagramatic approach
• Madgraph based code

Helicity bases
Issues
Speed and numerical stability
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(No Transcript)
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Virtual corrections
Scalar integrals
Issues

• Scalar integrals
• How to derive the decomposition?

Traditional approach Passarino-Veltman reduction
Large expressions ? numerical implementation
Numerical stability and speed are important
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Passarino-Veltman reduction
Passarino, Veltman 79
?
25
Reduction of tensor integrals what we did
Four and lower-point tensor integrals
Reduction à la Passarino-Veltman, with special
reduction formulae in singular regions, ? two
complete independent implementations !
Five-point tensor integrals

• Apply 4-dimensional reduction scheme, 5-point
  tensor integrals are reduced to 4-point tensor
  integrals

? No dangerous Gram determinants!
Denner, Dittmaier 02
Based on the fact that in 4 dimension 5-point
integrals can be reduced to 4 point integrals
Melrose 65, v. Neerven, Vermaseren 84

• Reduction à la Giele and Glover

Duplancic, Nizic 03, Giele, Glover 04
Use integration-by-parts identities to reduce
loop-integrals
nice feature algorithm provides diagnostics and
rescue system
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What about twistor inspired techniques ?

• For tree amplitudes no advantage compared to
  Berends-Giele like techniques (numerical
  solution!)
• In one-loop many open questions
• Spurious poles
• exceptional momentum configurations
• speed

My opinion

• For tree amplitudes tune Berends-Giele for
  stability and speed taking into account the CPU
  architecture of the LHC periode x86_64
• For one-loop amplitudes have a look at cut
  inspired methods

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Results
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tt 1-Jet production
Sample diagrams (LO)
Partonic processes
related by crossing
One-loop diagrams ( 350 (100) for gg (qq))
Most complicated 1-loop diagrams pentagons of the
type
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Leading-order results some features
LHC
Tevatron

• Assume top quarks as always tagged
• To resolve additional jet demand minimum kt of
  20 GeV

Observable

• Strong scale dependence of LO result
• No dependence on jet algorithm
• Cross section is NOT small

Note
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Checks of the NLO calculation

• Leading-order amplitudes checked with Madgraph
• Subtractions checked in singular regions
• Structure of UV singularities checked
• Structure of IR singularities checked

Most important

• Two complete independent programs using a
  complete different tool chain and different
  algorithms, complete numerics done twice !

Feynarts 1.0 Mathematica Fortran77
Virtual corrections
QGraf Form3 C,C
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Top-quark pair 1 Jet Production at NLO
Dittmaier, P.U., Weinzierl PRL 98262002, 07
Tevtron
LHC

• Scale dependence is improved
• Sensitivity to the jet algorithm
• Corrections are moderate in size
• Arbitrary (IR-safe) obserables calculable

? work in progress
32
Forward-backward charge asymmetry (Tevatron)
Dittmaier, P.U., Weinzierl PRL 98262002, 07
Effect appears already in top quark pair
production
Kühn, Rodrigo

• Numerics more involved due to cancellations, easy
  to improve
• Large corrections, LO asymmetry almost washed out
• Refined definition (larger cut, different jet
  algorithm) ?

33
Differential distributions
Preliminary )
) Virtual correction cross checked, real
corrections underway
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pT distribution of the additional jet
LHC
Tevtron
Corrections of the oder of 10-20 , again scale
dependence is improved
35
Pseudo-Rapidity distribution
Tevtron
LHC
? Asymmetry is washed out by the NLO corrections
36
Top quark pt distribution
The K-factor is not a constant!
? Phase space dependence, dependence on the
observable
Tevtron
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WW 1 Jet
Leading-order sample diagrams
Next-to-leading order sample diagrams
Next-to-leading order sample diagrams
Many different channels!
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Checks
Similar to those made in tt 1 Jet
Main difference
Virtual corrections were cross checked using
LoopTools
T.Hahn
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Scale dependence WW1jet
Dittmaier, Kallweit, Uwer 07
Cross section defined as in tt 1 Jet
NLO corrections have been calculated also by
Ellis,Campbell, Zanderighi t01d
40
Cut dependence
Dittmaier, Kallweit, Uwer 07
Note shown results independent from the decay of
the Ws
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Conclusions
General lesson

• NLO calculations are important for the success of
  LHC
• After more than 30 years (QCD) they are still
  difficult
• Active field, many new methods proposed recently!
• Many new results

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Conclusions
Top quark pair 1-Jet production at NLO

• Two complete independent calculations
• Methods used work very well
• Cross section corrections are under control
• Further investigations for the FB-charge
  asymmetry necessary (Tevatron)
• Preliminary results for distributions

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Conclusions
WW 1-Jet production at NLO

• Two complete independent calculations
• Scale dependence is improved (?LHC jet-veto)
• Corrections are important

?
Gudrun Heinrich
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Outlook

• Proper definition of FB-charge asymmetry
• Further improvements possible
• (remove redundancy, further tuning, except.
  momenta,)
• Distributions
• Include decay
• Apply tools to other processes

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The End