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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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slide1

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
Contents
  • Introduction
  • Methods
  • Results
  • Conclusion / Outlook
preliminaries
Preliminaries

Technicalities

Physics

Non-Experts

Experts

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

residual scale dependence
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:

scale dependence
Scale dependence

40 %

30 %

20 %

10 %

1

3

2

4

n

22

QCD

23

QCD

24

QCD

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...

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 !

and difficult to estimate
...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)

to summarize
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
ww 1 jet motivation
WW + 1 Jet ― 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

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 W´s and 1 Jet is demanded

(improved signal significance)

t t 1 jet motivation
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 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)
next to leading order corrections
Next-to leading order corrections

1

1

1

n

n

n+1

*)

*

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

1

1

1

1

1

1

n

n

n

n

n+1

n+1

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

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

dipole subtraction method 1
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]

dipole subtraction method 2
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

Exampleggttgg:

dipole subtraction method implementation
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

slide20

1

n+1

LO amplitudes enter in many places…

leading order amplitudes techniques
Leading order amplitudes ― 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

Issues:

Speed and numerical stability

slide22

1

1

*

n

n

virtual corrections
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

passarino veltman reduction
Passarino-Veltman reduction

[Passarino, Veltman 79]

?

reduction of tensor integrals what we did
Reduction of tensor integrals — 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!

[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

what about twistor inspired techniques
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
tt 1 jet production
tt + 1-Jet production

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 — 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:

checks of the nlo calculation
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++

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

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

forward backward charge asymmetry tevatron
Forward-backward charge asymmetry (Tevatron)

[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

Preliminary *)

*) Virtual correction cross checked, real corrections underway

p t distribution of the additional jet
pTdistribution of the additional jet

LHC

Tevtron

Corrections of the oder of 10-20 %,

again scale dependence is improved

pseudo rapidity distribution
Pseudo-Rapidity distribution

Tevtron

LHC

 Asymmetry is washed out by the NLO corrections

top quark p t distribution
Top quark pt distribution

The K-factor is not

a constant!

 Phase space dependence, dependence on the observable

Tevtron

ww 1 jet
WW + 1 Jet

Leading-order – sample diagrams

Next-to-leading order – sample diagrams

Next-to-leading order – sample diagrams

Many different channels!

checks
Checks

Similar to those made in tt + 1 Jet

Main difference:

Virtual corrections were cross checked using LoopTools

[T.Hahn]

scale dependence ww 1jet
Scale dependence WW+1jet

[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

[Dittmaier, Kallweit, Uwer 07]

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

conclusions
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
conclusions1
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
conclusions2
Conclusions

WW + 1-Jet production at NLO:

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

[Gudrun Heinrich ]

outlook
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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