Graduiertenkolleg “Physik an Hadronbeschleunigern”, Freiburg 07.11.07
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Graduiertenkolleg “Physik an Hadronbeschleunigern”, Freiburg 07.11.07. pp  ttj and pp  WWj at next-to-leading order in Q C D. Peter Uwer *). Universität Karlsruhe. Work in collaboration with S.Dittmaier, S. Kallweit and S.Weinzierl. *) Financed through Heisenberg fellowship and SFB-TR09.

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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

Contents Freiburg 07.11.07

  • Introduction

  • Methods

  • Results

  • Conclusion / Outlook

Preliminaries Freiburg 07.11.07





 Outline of the main problems/issues/challenges with only brief description of methods used

Residual scale dependence
Residual scale dependence Freiburg 07.11.07

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:

Scale dependence
Scale dependence Freiburg 07.11.07

40 %

30 %

20 %

10 %












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

Corrections are not small
Corrections are not small... Freiburg 07.11.07

Top-quark pair production at LHC:

[Dawson, Ellis, Nason ’89,

Beenakker et al ’89,’91,

Bernreuther, Brandenburg, Si, P.U. ‘04]



Scale independent corrections are also important !

And difficult to estimate
...and difficult to estimate Freiburg 07.11.07

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)

To summarize
To summarize: Freiburg 07.11.07

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

Shall we calculate NLO corrections Freiburg 07.11.07

for everything


Ww 1 jet motivation
WW + 1 Jet Freiburg 07.11.07 ― Motivation

Higgs search:

  • For 155 GeV < mh < 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


two forward tagging jets + Higgs

Background reactions:

WW + 2 Jets, WW + 1 Jet

Top of the

Les Houches list 07

NLO corrections


If only leptonic decay of W´s and 1 Jet is demanded

(improved signal significance)

T t 1 jet motivation
t t + 1 Jet Freiburg 07.11.07 ― 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 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)

Methods Freiburg 07.11.07

Next to leading order corrections
Next-to leading order corrections Freiburg 07.11.07









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…

Ingredients for nlo
Ingredients for NLO Freiburg 07.11.07













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.)

How to do the cancellation in practice
How to do the cancellation in practice Freiburg 07.11.07

Consider toy example:

Phase space slicing method:


[Frixione,Kunszt,Signer ´95, Catani,Seymour ´96, Nason,Oleari 98, Phaf, Weinzierl, Catani,Dittmaier,Seymour, Trocsanyi ´02]

Subtraction method

Dipole subtraction method 1
Dipole subtraction method (1) Freiburg 07.11.07

[Frixione,Kunszt,Signer ´95, Catani,Seymour ´96, Nason,Oleari 98, Phaf, Weinzierl, Catani,Dittmaier,Seymour, Trocsanyi ´02]

How it works in practise:


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]

Dipole subtraction method 2
Dipole subtraction method (2) Freiburg 07.11.07

Universality of soft and coll. Limits!

Universal structure:

Generic form of individual dipol:

Leading-order amplitudes

Vector in color space




Color charge operators,

induce color correlation

Spin dependent part,

induces spin correlation

6 different colorstructures in LO,

36 (singular) dipoles


Dipole subtraction method implementation
Dipole subtraction method Freiburg 07.11.07 — implementation

LO – amplitude,

with colour information,

i.e. correlations

List of dipoles we

want to calculate







reduced kinematics,

“tilde momenta” + Vij,k

Dipole di

1 Freiburg 07.11.07


LO amplitudes enter in many places…

Leading order amplitudes techniques
Leading order amplitudes Freiburg 07.11.07 ― techniques

Many different methods to calculate LO amplitudes exist

(Tools: Alpgen [MLM et al], Madgraph [Maltoni, Stelzer], O’mega/Whizard [Kilian,Ohl,Reuter],…)

We used:

  • Berends-Giele recurrence relations

  • Feynman-diagramatic approach

  • Madgraph based code

Helicity bases


Speed and numerical stability

1 Freiburg 07.11.07





Virtual corrections
Virtual corrections Freiburg 07.11.07

Scalar integrals


  • Scalar integrals

  • How to derive the decomposition?

Traditional approach: Passarino-Veltman reduction

Large expressions  numerical implementation

Numerical stability and speed are important

Passarino veltman reduction
Passarino-Veltman reduction Freiburg 07.11.07

[Passarino, Veltman 79]


Reduction of tensor integrals what we did
Reduction of tensor integrals Freiburg 07.11.07 — what we did…

Four and lower-point tensor integrals:

Reduction à la Passarino-Veltman,

withspecial reductionformulae insingular regions,

 two complete independent implementations !

Five-point tensor integrals:

  • Apply4-dimensional reductionscheme, 5-point tensor integrals are reduced to 4-point tensor integrals

 No dangerous Gram determinants!


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

What about twistor inspired techniques
What about twistor inspired techniques ? Freiburg 07.11.07

  • 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

Results Freiburg 07.11.07

Tt 1 jet production
tt + 1-Jet production Freiburg 07.11.07

Sample diagrams (LO):

Partonic processes:

related by crossing

One-loop diagrams (~ 350 (100) for gg (qq)):

Most complicated 1-loop diagramspentagons of the type:

Leading order results some features
Leading-order results Freiburg 07.11.07 — some features



  • Assume top quarks as always tagged

  • To resolve additional jet demand minimum kt of 20 GeV


  • Strong scale dependence of LO result

  • No dependence on jet algorithm

  • Cross section is NOT small


Checks of the nlo calculation
Checks of the NLO calculation Freiburg 07.11.07

  • 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++

Top quark pair 1 jet production at nlo
Top-quark pair + 1 Jet Production at NLO Freiburg 07.11.07

[Dittmaier, P.U., Weinzierl PRL 98:262002,’07]



  • Scale dependence is improved

  • Sensitivity to the jet algorithm

  • Corrections are moderate in size

  • Arbitrary (IR-safe) obserables calculable

 work in progress

Forward backward charge asymmetry tevatron
Forward-backward charge asymmetry (Tevatron) Freiburg 07.11.07

[Dittmaier, P.U., Weinzierl PRL 98:262002,’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…) ?

Differential distributions
Differential distributions Freiburg 07.11.07

Preliminary *)

*) Virtual correction cross checked, real corrections underway

P t distribution of the additional jet
p Freiburg 07.11.07 Tdistribution of the additional jet



Corrections of the oder of 10-20 %,

again scale dependence is improved

Pseudo rapidity distribution
Pseudo-Rapidity distribution Freiburg 07.11.07



 Asymmetry is washed out by the NLO corrections

Top quark p t distribution
Top quark Freiburg 07.11.07 pt distribution

The K-factor is not

a constant!

 Phase space dependence, dependence on the observable


Ww 1 jet
WW + 1 Jet Freiburg 07.11.07

Leading-order – sample diagrams

Next-to-leading order – sample diagrams

Next-to-leading order – sample diagrams

Many different channels!

Checks Freiburg 07.11.07

Similar to those made in tt + 1 Jet

Main difference:

Virtual corrections were cross checked using LoopTools


Scale dependence ww 1jet
Scale dependence WW+1jet Freiburg 07.11.07

[Dittmaier, Kallweit, Uwer 07]

Cross section defined as in tt + 1 Jet

[NLO corrections have been calculated also by Ellis,Campbell, Zanderighi t0+1d]

Cut dependence
Cut dependence Freiburg 07.11.07

[Dittmaier, Kallweit, Uwer 07]

Note: shown results independent from the decay of the W´s

Conclusions Freiburg 07.11.07

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

Conclusions Freiburg 07.11.07

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

Conclusions Freiburg 07.11.07

WW + 1-Jet production at NLO:

  • Two complete independent calculations

  • Scale dependence is improved (LHC jet-veto)

  • Corrections are important

[Gudrun Heinrich ]

Outlook Freiburg 07.11.07

  • Proper definition of FB-charge asymmetry

  • Further improvements possible

  • (remove redundancy, further tuning, except. momenta,…)

  • Distributions

  • Include decay

  • Apply tools to other processes

The End Freiburg 07.11.07