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Peter Uwer

DIS 2009 —— Madrid, April 26 th -30 th 2009. Hadronic top quark pair production in association with a hard jet at next-to-leading order Q C D. Peter Uwer. Work done in collaboration with S.Dittmaier and S.Weinzierl.

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Peter Uwer

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  1. DIS 2009 —— Madrid, April 26th -30th 2009 Hadronic top quark pair production in association with a hard jet at next-to-leading order QCD Peter Uwer Work done in collaboration with S.Dittmaier and S.Weinzierl Funded through DFG/SFB-TR09 and Helmholtz Alliance „Physics at the Terascale“

  2. Contents • Motivation • Total cross sections • Distributions • Conclusion / Outlook

  3. 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

  4. Why is top quark physics interesting ? In the SM top quark couplings highly constrained by gauge structure Are the quantum numbers as predicted by the SM ?  Measure the couplings / quantum numbers as precisely as possible

  5. Important measurements Precise determination of top mass, consistency checks with theo. predictions, search for new physics in the tt invariant mass spectrum  tt cross section W-Polarization in top decay ttH cross section ttZ cross section Single top production Spin correlations tt+Jet(s) production ttg cross section  Test of the V-A structure in top decay  Measurement of the Yukawa coupling   Measurement of the Z couplings Direct measurement of the CKM matrix element Vtb, top polarization, search for anomalous Wtb couplings   Weak decay of a `free’ quark, bound on the top width and Vtb, search for anomalous couplings  Search for anomalous couplings, important background Measurement of the electric charge 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…

  6. 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

  7. 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 LO: Jet = parton Possible recombination of two partons to one jet NLO:  Ellis-Soper jet algorithm

  8. Leading-order results — some features LHC Tevatron Assume top quarks as always tagged To render cross section finite ask for additonal jet with minimum pt. Observable: Strong scale dependence of LO result No dependence on jet algorithm (parton=jet!) Cross section is NOT small Note:

  9. 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

  10. What can we learn with respect to NNLO ? NLO corrections to tt+1-jet are part of the NNLO corrections to inclusive top-quark pair production ! Corrections are small for m  mt Exact NNLO behavior close to threshold derived recently should provide good approximation to complete NNLO (including 2-loop Coulomb corrections and exact scale dependence) [Moch, P.U, ‘08] MRST2006 NNLO Update: see U. Langenfelds talk, Tuesday, 11:15, Heavy Flavours Resummed results in NNLL accuracy also available Extension of earlier work by [Bonciani, Catani, Mangano, Nason ’98]

  11. Forward-backward charge asymmetry (Tevatron) [Dittmaier, PU, Weinzierl PRL 98:262002,’07] Effect appears already in top quark pair production [Kühn, Rodrigo] 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…) ?

  12. Forward-backward charge asymmetry Tevatron [Dittmaier,PU,Weinzierl 08] uncertainty num. intgration shift towards m=2m,m/2 central value cross section receives moderate corrections scale dependence largely reduced large corrections to the asymmetry General picture to large extend independent of pTcut  no conclusive picture yet

  13. Differential distributions

  14. Pseudo-Rapidity distribution [Dittmaier, P.U., Weinzierl, arXiv:0810.0452] Tevatron Again: charge asymmetry is washed out by the corrections

  15. pTdistribution of the additional jet LHC Tevatron [Dittmaier, P.U., Weinzierl, arXiv:0810.0452] Corrections of the order of 10-20 %, again scale dependence is improved

  16. Top quark pt distribution [Dittmaier, P.U., Weinzierl, arXiv:0810.0452] The K-factor is not a constant! LHC  Phase space dependence, dependence on the observable Bin-dependent scale?

  17. Conclusions Top quark physics: Many interesting measurements possible at LHC and Tevatron A lot of progress as far as theory is concerned 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

  18. 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

  19. The End

  20. Top-quark pair production in NNLO — ingredients ∫ ∫ * 2 ∫ * + + x 2Re x 2Re 2 ∫ + 2 ∫ Leading-order, Born approximation n-legs ∫ ∫ * 2 + + Next-to-leading order (NLO) 2Re x (n+1)-legs, real corrections + Next-to- next-to-leading order (NNLO) + …

  21. Motivation: One loop calculations for LHC „State of the art“: 23 reactions at the border of what is feasible with current techniques*) High demand for one-loop calculations for the LHC:   (qq)  Nice overview of current Status in G.Heinrich‘s opening talk at Les Houches ´07 [Gudrun Heinrich ] *) Only very vew 24 calculation available so far [Denner, Dittmaier, Roth, Wieders 05], [Bredenstein,Denner,Dittmaier, Pozzorini 08] many uncalculated 23 processes...

  22. Parton luminosities

  23. Next-to-leading order corrections Every piece is individually divergent, only in the combination a finite result is obtained Standard procedure: [Frixione,Kunszt,Signer ´95, Catani,Seymour ´96, Nason,Oleari 98, Phaf, Weinzierl, Catani,Dittmaier,Seymour, Trocsanyi ´02] Dipole subtraction method We need: Virtual corrections Real corrections Subtractions

  24. Virtual corrections – Traditional approach Partonic processes: related by crossing Number of 1-loop diagrams ~ 350 (100) for Most complicated 1-loop diagramspentagons of the type: Algebraic decomposition of amplitudes: color, i.e. standard matrix elements, i.e.

  25. Bottleneck of one-loop corrections Tensor integrals: Large cancellation for exceptional phase space points, Integral basis degenerates Fast and numerically stable evaluation is difficult

  26. 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] [Davydychev 01,Duplancic, Nizic 03, Giele, Glover 04] Reduction à la Giele and Glover Use integration-by-parts identities to reduce loop-integrals, inspired from multi-loop calculations

  27. Real corrections Numerical evaluation of the amplitude in the helicity bases Feynman diagramatic approach Berends-Giele recurrence relations Madgraph Methods: Many tools available: Alpgen, Madgraph, O’mega, Sherpa 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] With: in all single-unresolved regions

  28. Subtraction Note: there are many of them (i.e. 36 for ggttgg) Two independent libraries to calculate the dipoles Significant amount of computing power goes into dipoles! Speed ! Main issue:

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