Peter Uwer

Funded through DFG/SFB-TR09 and Helmholtz Alliance „Physics at the Terascale“

DIS 2009 —— Madrid, April 26th -30th 2009

Work done in collaboration with S.Dittmaier and S.Weinzierl

Hadronic top quark pair production in association with a hard jet atnext-to-leading order QCD

2

Contents

1. Motivation

2. Total cross sections

3. Distributions

4. Conclusion / Outlook

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Why is top quark physics interesting ?

Top quark is the heaviest elementary fermion discovered so far

● Top mass close to the scale of electroweak symmetry breaking

special role in EWSB?

Is the unnatural natural Yukawa coupling natural ?

● Is the top quark still point like ?

Top quark plays special role in many extensions of the SM

I.e.:Technicolor or Topcolor models octet resonances decaying into top-quark pairs

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Why is top quark physics interesting ?

Are the quantum numbers as predicted by the SM ?

In the SM top quark couplings highly constrained by gauge structure

Measure the couplings / quantum numbers as precisely as possible

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Important measurements

● tt cross section

● W-Polarization in top decay

● ttH cross section

● ttZ cross section

● Single top production

● Spin correlations

● tt+Jet(s) production

● tt cross section Measurement of the electric charge

Search for anomalous couplings, important background

Weak decay of a `free’ quark, bound on the top width and Vtb, search for anomalous couplings

Direct measurement of the CKM matrix element Vtb, top polarization, search for

anomalous Wtb couplings

Measurement of the Yukawa coupling

Precise determination of top mass, consistency checks with theo. predictions, search for new physics in the tt invariant

mass spectrum

Test of the V-A structure in top decay

Measurement of the Z couplings

A lot of progress recently

Possible deviations: Different production mechanism due to heavy SUSY partner? Decay into charged Higgs in multi Higgs generalization of the SM? Behaviour of long. pol. W from t decay? And many others…

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Why is tt+1 Jet production important ?

● Search for anomalous top-gluon couplings

● Large fraction of inclusive tt are due to tt+jet

● Measurement of the electric charge from the related process

● Ingredient for top cross section at NNLO accuracy

● Important background for higgs discovery via VBF recent progress

“Technical importance”:

Important benchmark process for one-loop calculations for the LHC

Ideal test ground for developing and testing of new

methods for one-loop calculations

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tt+1 Jet cross section — definition

Production of a top-quark pair together with an additional jet

● Assume top-quarks as always tagged● Define additional jet resolution criteria to resolve light jet

Minimal pT of the additional jet, excludes soft configurations and dangerous collinear configurations

cross section is IR safe

Jet = partonPossible recombination of two partons to one jet

Ellis-Soper jet algorithm

LO:NLO:

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Leading-order results — some features

Observable: ● Assume top quarks as always tagged

● To render cross section finite ask for additonal jet with minimum pt.

Note:● Strong scale dependence of LO result

● No dependence on jet algorithm (parton=jet!)

● Cross section is NOT small

LHCTevatron

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Top-quark pair + 1 Jet Production at NLO[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

Tevtron LHC

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What can we learn with respect to NNLO ?

NLO corrections to tt+1-jet are part of the NNLO correctionsto inclusive top-quark pair production

Corrections are small for mt

Exact NNLO behavior close to threshold derived recently should provide good approximation to complete NNLO

!

[Moch, P.U, ‘08]

Resummed results in NNLL accuracy also available

MRST2006 NNLO

(including 2-loop Coulomb corrections and exact scale dependence)

Extension of earlier work by [Bonciani, Catani, Mangano, Nason ’98]

Update: see U. Langenfelds talk,Tuesday, 11:15, Heavy Flavours

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Forward-backward charge asymmetry (Tevatron)

● Numerics more involved due to cancellations● Large corrections, LO asymmetry almost washed out● Scale dependence gets worse in NLO● Refined definition (larger cut, different jet algorithm…) ?

Effect appears already in top quark pair production

[Kühn, Rodrigo]

[Dittmaier, PU, Weinzierl PRL 98:262002, ’07]

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Forward-backward charge asymmetry

central value uncertaintynum. intgration

shift towards =2m,m/2

● cross section receives moderate corrections● scale dependence largely reduced● large corrections to the asymmetry

no conclusive picture yet

Tevatron

General picture to large extend independent of pTcut

[Dittmaier,PU,Weinzierl 08]

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Differential distributions

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Pseudo-Rapidity distribution

Tevatron

Again: charge asymmetry is washed out by the corrections

[Dittmaier, P.U., Weinzierl, arXiv:0810.0452]

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pT distribution of the additional jet

Corrections of the order of 10-20 %,again scale dependence is improved

LHCTevatron

[Dittmaier, P.U., Weinzierl,arXiv:0810.0452]

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Top quark pt distribution

The K-factor is nota constant!

Phase space dependence, dependence on the observable

LHC

[Dittmaier, P.U., Weinzierl, arXiv:0810.0452]

Bin-dependent scale?

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Conclusions

● Many interesting measurements possible at LHC and

Tevatron

● A lot of progress as far as theory is concerned

Top quark physics:

Top quark pair + 1-Jet production at NLO:

● Non-trivial calculation

● Two complete independent calculations

● Methods used work very well

● Cross section corrections are under control

● Further investigations for the FB-charge

asymmetry necessary (Tevatron)

● Distributions receive only moderate corrections

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Outlook

● Finer binning for Tevatron

● Different scale choice

● Root-ntuple? [J.Huston]

● Proper definition of FB-charge asymmetry

● Top decay

● Combination with parton shower à la MC@NLO, POWHEG

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The End

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Top-quark pair production in NNLO — ingredients

∫+*

x2Re ∫+2

∫2

∫+*

x2Re +2

∫

∫ x2Re*

+

+ …

Leading-order, Born approximation

Next-to-leading order(NLO)

Next-to-next-to-leading order (NNLO)

n-legs

(n+1)-legs, real corrections

+ ∫2

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Motivation: One loop calculations for LHC

„State of the art“:

23 reactions at the border of what is feasible with current techniques*)

High demand for one-loop calculations for the LHC:

[Gudrun Heinrich ]

Nice overview of currentStatus in G.Heinrich‘s opening talk at Les Houches ´07

*) Only very vew 24 calculation available so far [Denner, Dittmaier, Roth, Wieders 05], [Bredenstein,Denner,Dittmaier, Pozzorini 08] many uncalculated 23 processes...

(qq)

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Parton luminosities

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Next-to-leading order corrections

Every piece is individually divergent,only in the combination a finite result is obtained

Standard procedure:

Dipole subtraction method

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

We need: 1. Virtual corrections2. Real corrections3. Subtractions

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Virtual corrections – Traditional approach

Number of 1-loop diagrams ~ 350 (100) for

Most complicated 1-loop diagrams pentagons of the type:

Algebraic decomposition of amplitudes:color, i.e.

standard matrix

elements, i.e.

Partonic processes:

related by crossing

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Bottleneck of one-loop corrections

Tensor integrals:

Fast and numerically stable evaluation is difficult

Large cancellation for exceptional phase space points,Integral basis degenerates

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Reduction of tensor integrals — what we did…

Reduction à la Passarino-Veltman,with special reduction formulae in singular regions, two complete independent implementations !

Five-point tensor integrals:

Four and lower-point tensor integrals:

● Apply 4-dimensional reduction scheme, 5-point tensor

integrals are reduced to 4-point tensor integrals

Based on the fact that in 4 dimension 5-point integrals can be reduced to 4 point integrals

No dangerous Gram determinants!

[Melrose ´65, v. Neerven, Vermaseren 84]

[Denner, Dittmaier 02]

● Reduction à la Giele and Glover[Davydychev 01,Duplancic, Nizic 03,

Giele, Glover 04]

Use integration-by-parts identities to reduce loop-integrals, inspired from multi-loop calculations

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Real corrections

Numerical evaluation of the amplitude in the helicity bases

Treatment of soft and collinear singularities à la Catani and Seymour

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

Methods: ● Feynman diagramatic approach● Berends-Giele recurrence relations● Madgraph

in all single-unresolved regionsWith:

Many tools available: Alpgen, Madgraph, O’mega, Sherpa

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Subtraction

Two independent libraries to calculate the dipoles

Note: there are many of them (i.e. 36 for ggttgg)

Main issue: Speed !Significant amount of computing power goes into dipoles!