Peter Uwer *)

1. Workshop on massive particle production at the LHC —— October, 2007, Berlin Production of heavy particles and jets 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. Introduction ? Why do we need next-to-leading order corrections • LO predictions give in many cases only rough estimate Large uncertainty due to residual scale dependence as a consequence of uncalculated higher orders • 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

5. The master equation for the LHC ! LHC is a discovery machine LHC physics = Standard Model + New Physics New Physics = LHC physics - Standard Model

6. 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 [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)

7. 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)

8. Methods

9. Next-to leading order corrections 1 1 n n * 1 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

10. 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

11. 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]

12. 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:

13. 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

14. Leading order amplitudes ― techniques Many different methods to calculate LO amplitudes exist We used: • Berends-Giele recurrence relations • Feynman-diagramatic approach • Madgraph based code Helicity bases Issues: Speed and numerical stability

15. 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

16. 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

17. 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

18. Results

19. 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:

20. 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:

21. 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++

22. 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

23. 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…) ?

24. Differential distributions Preliminary *) *) Virtual correction cross checked, real corrections underway

25. pTdistribution of the additional jet LHC Tevtron Corrections of the oder of 10-20 %, again scale dependence is improved

26. Pseudo-Rapidity distribution Tevtron LHC  Asymmetry is washed out by the NLO corrections

27. Top quark pt distribution The K-factor is not a constant!  Phase space dependence, dependence on the observable Tevtron

28. WW + 1 Jet Leading-order – sample diagrams Next-to-leading order – sample diagrams Next-to-leading order – sample diagrams Many different channels!

29. Checks Similar to those made in tt + 1 Jet Main difference: Virtual corrections were cross checked using LoopTools [T.Hahn]

30. 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, and Binoth, Guillet, Karg, Sanguinetti]

31. Cut dependence [Dittmaier, Kallweit, Uwer 07] Note: shown results independent from the decay of the W´s

32. 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

33. 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

34. Conclusions WW + 1-Jet production at NLO: • Two complete independent calculations • Scale dependence is improved (LHC jet-veto) • Corrections are important  [Gudrun Heinrich ]

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

36. The End

37. Numerical precisision Process with light quarks (Berends-Giele recursion)

38. Rapidity versus Pseudo-Rapidity Tevtron Tevtron

39. Introduction — Top quark pair production + 1 Jet Higgs searches at LHC The WBF process WW is important over a wideHiggs mass range Important backgrounds: [Atlas `03] [Alves, Eboli, Plehn, Rainwater ’04]  Precise predictions for pp tt + jet are necessary