1 / 39

Next-to-Leading Order Corrections in Particle Production at LHC

Explore the importance of NLO corrections in particle production at the LHC. Detailed methods, challenges, and results addressed in this workshop presentation from October 2007 in Berlin.

vondaw
Download Presentation

Next-to-Leading Order Corrections in Particle Production at LHC

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related