1. 1 Production of heavy particles and high energetic jets at hadron colliders Peter Uwer *) CERN (PH-TH) and Uni Karlsruhe (TTP) DPG Tagung Dortmund, 29/03/2006 *) Heisenberg Fellow, Deutsche Forschungsgemeinschaft (DFG)

2. 2 Contents: ● Introduction ● Theoretical framework ● Top quark physics at the LHC ● New developments and open questions ● Conclusions

3. 3 Why are we interested in the production of heavy particles and high energetic jets ● Measurement possible due to distinctive signature ● pQCD gives good theoretical prediction ? ? Signals we are looking for i.e. Higgs boson, top quark, Explore physics at the TeV scale Experimentally and theoretically accessible: ! ! Interest in Higgs and top about obvious, what about W, Z?

4. 4 ● appear often as major backgrounds ● Well known, may be used: ● to callibrate the detectors ● for commissioning ● as luminosity monitor W, Z are also important In addition:

5. 5 Measurement of the parton luminosity from W cross section: [Dittmar, Pauss, Zürcher 97] Rapidity distribution distinguishes between different pdf’s  Can be used to measure parton luminosity

6. 6 Top quarks are of particular importance: Although discovered already 10 years ago, not all the quantum numbers have been measured yet ● Top quark plays special role in many extensions of the Standard Model ● Top quark is also an important background, in particular for the Higgs search Precise measurements necessary to establish the top quark in the Standard Model

7. 7 Theoretical framework: QCD improved parton model Final state X ij

8. 8 [Frank Krauss]  talks by S. Gieseke t121.1 and F. Krauss t121.2 this afternoon

9. 9 Parton distribution function (pdf) ● Non-perturbative objects ● Universal, do not depend on the specific process ● Scale dependence predicted by QCD: (DGLAP) Evolution kernels known at NNLO accuracy [Moch,Vermaseren,Vogt ’04] [Dokshitzer,Gribov,Lipatov,Altarelli,Parisi]

10. 10 hard scattering cross section calculable in pQFT ● In most cases LO gives a poor approximation ● The more the final state becomes exclusive the more difficult becomes the calculation of higher orders ● Important processes should be known at least at NLO accuracy ● Theory in good shape for 2  1 processes

11. 11 Important examples: Total cross section: ● Drell-Yan ● Higgs boson production via gluon fusion Differential distributions: ● Electroweak gauge boson rapididity distribution ● Fully diff. Higgs boson production at NNLO [Harlander, Kilgore 02, Hamberg, vNeerven, Matsuura 91] [Harlander, Kilgore 02, Anastasiou, Melnikov 02, Ravindran, Smith, vNeerven 03] [Anastasiou, Dixon, Melnikov, Petriello 03] [Anastasiou, Melnikov, Petriello 05] Known at NNLO accuracy !

12. 12 Bin-integrated Higgs boson rapidity distribution at the LHC: [Anastasiou, Melnikov, Petriello 05] NNLO corrections stabilize perturbative expansion

13. 13 For more complicated final states only NLO results are available 2-jet production is only known at NLO ● Required 2-loop amplitudes are known since 2001 ● Combination with real corrections has not yet been done General problem: Algorithm needed for the systematic treatment of soft and collinear singularities at NNLO QCD In particular:

14. 14 Generic structure of NNLO corrections ∫ ∫ ∫ + + every contribution contains soft- or collinear divergencies procedure needed to cancel divergencies between different terms Several algorithms proposed recently See also talk by G. Heinrich t121.3 this afternoon Heinrich 03,05,06, Anastasiou, Melnikov, Petriello ’04, Weinzierl ‘03, Gehrmann-de Ridder,Gehrmann,Glover ‘04,’05, Frixione, Grazzini ’05, del Duca, Somogyi, Trocsanyi ‘06 x * 2Re * x 2

15. 15 What about NLO corrections General algorithms exist to treat collinear and soft singularities 2  2 reactions well studied Only limited results are available for 2  3 reactions in particular if massive particles are involved Important examples: pp  3 Jets, pp  ttH, pp  Zjj 2  4 results only for e + e -  4f EW ? ? ! ! [Denner, Dittmaier, Roth, Wieders ‘05]

16. 16 Top quark physics at hadron colliders

17. 17 Why is top quark physics interesting / important ● Not very well studied so far ! ● Top quark mass is an important parameter in electroweak precision measurements ● In many extensions of the standard model top quark plays special role ● Top quark might be sensitive to new physics (rare decays?) ● Important background ? ?

18. 18 Important task for the LHC: Measure the quantum numbers and parameters of the top quark! Important observables: ● tt cross section ● W-Polarization in top decay ● ttH cross section ● Single top production ● Spin correlations ● tt+Jet(s) production ● tt  cross section Precise determination of top mass, consistency checks with theo. predictions, search for new physics in the tt invariant mass spectrum Measurement of the electric charge Test of the V-A structure in top decay Measurement of the Yukawa coupling 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 V tb, search for anomalous couplings Search for anomalous couplings, important background ( )

19. 19 Top quark pair production Single top quark production Quark-Antiquark annihilation Gluon fusion NLO corrections known! [Dawson, Ellis, Nason ’89, Beenakker et al ’89,’91, Bernreuther, Brandenburg, P.U., Si 04] One-loop corrections also known! [Tait ´00, Belayev 01, Harris ´02, Cao et al 04, Campbell et al 04, Frixione, Laenen, Motylinski, Webber ‘05] Main production mechanism at hadron colliders:

20. 20 LHC is a top factory: Measurements will in general not be restricted by statistics! Top quark physics can be done „from the first day“ on! Current status Tevatron: 350/pb analysed, 1/fb on tape LHC: ~8,000,000 tt pairs per year, ~1 pair / sec

21. 21 Is the top quark just another heavy quark?

22. 22 Top quark extremely short lived: Top quark decays essentially as a quasi free quark Top quark is the only quark with this property, all the lighter quarks hadronize before they decay Unique possibility to study a quasi free quark  Spin of the top quark is a good observable, can be studied due to the parity violating decay t  Wb [Bigi, Dokshitzer, Khoze, Kühn, Zerwas ´86] NO!

23. 23 Spin correlations: Polarization versus correlations Due to parity invariance of QCD, top’s produced in qq  tt and gg  tt are essentially unpolarized *) But: Spins of top quark and antiquark are correlated *) absorptive parts at the one-loop level induce a small polarization (~1%) transverse to the scattering plane [Bernreuther,Brandenburg 93, Mahlon, Parke 96, Stelzer,Willenbrock 96, Bernreuther, Brandenburg, Si, P.U. 04] [Dharmaratna, Goldstein ‘96, Bernreuther,Brandenburg, P.U. ‘96] Quantum mechanics: close to threshold:  Spins are parallel or anti-parallel close to threshold

24. 24 Why are spin correlations interesting? ● Test of the top quark spin ● Search for new physics ● i.e. CP violating interactions, Higgs with undefined parity, properties of s-channel resonance ● Test of the idea that top decays as a quasi free quark ● precise test of the production and decay mechanism ● Affect the angular distributions of the decay products ● important for event selection

25. 25 Spin correlations: Observables… Observables of the form have simple interpretation: where ↑/↓ denote spin up/down with respect to a,b as quantization axis To measure C,D study double differential distributions. Also interesting:

26. 26 Measurement of the top quark polarization How can we measure the “spin” of the top quark? Basic ingredients: ● Top quark decays before hadronization ● Parity violating decay t  Wb The top quark polarization can be studied through the angular distribution of the decay products! QCD NLO corrections known! [Czarnecki, Jezabek, Kühn 91, Brandenburg, Si, P.U. ‘02]

27. 27 Spin correlations: LO Standard Model predictions Double differential distribution: Size of C depends on the “quantization axis”: Tevatron LHC Spin correlations can be very large!  R =  F =m t =175 GeV, CTEQ6L

28. 28 In general very complicated task: Approximation: ● double pole approximation ● calculate only factorizable contributions NLO corrections calculable: Spin correlation: NLO corrections Scale dep.:Tevatron: LHC: LHC Tevatron [Bernreuther, Brandenburg, Si, P.U. 03,04]  R =  F =m t =175 GeV,  s (  =m t )=0.1074, CTEQ6.1M

29. 29 A realistic analysis… [ATLAS collaboration, P. Pralavorio, F.Hubaut, E.Monnier ‘05] no correlationwith correlation Very difficult analysis, dominated by systematic uncertainties parton level after reconstruction

30. 30 Atlas Simulation [Hubaut, Monnier, Pralavorio,Smolek,Simak 05] 4-5 % accuracy !  double differential distribution  single differential distribution Current accuracy at the Tevatron: ~15-20% (opening angle distribution) Precise measurements possible at the LHC!

31. 31 Nice side effect of the spin correlations studies: Precise measurement of the W-polarization possible using tt events [Pralavario, Hubaut, Monnier ‘05] Using the same tt events as in the previous analysis: Simulated data sample corresponds to one year at low luminosity. Tevatron:

32. 32 Are only QCD corrections important? At high energies enhancement of electroweak corrections possible due to the presence of large Sudakov logarithms Missing cancellation of logarithmic corrections between real and virtual corrections  Weak corrections need to be taken into account ! For top quark pair production this has been done recently [Kühn, Penin, Smirnov ‘00] [Beenakker, Denner, Hollik, Mertig, Sack, Wackeroth ’93, Bernreuther, Fücker, Si ‘05, Kühn, Scharf, P.U. 05, Moretti, Nolten, Ross ‘06]

33. 33 As far as theoretical predictions for top quark physics are concerned (SM!) : Theory is in good shape This is not the case for other important reactions relevant for the LHC physics program

34. 34 Les Houches workshop, “Physics at TeV colliders”

35. 35 Why are NLO corrections difficult Basic problem of loop calculations: Obtain a finite result in a finite amount of time Origin of the problem lies in the reduction of tensor integrals to scalar loop integrals In addition: huge expressions for processes with 5 and more legs ? ? ?  Semi numerical methods

36. 36 Recent progress: new reduction methods ● Semi-numerical approach inspired from 2-loop calculations, recursion relations ● Improved / modified Passarino-Veltman reduction [Denner, Dittmaier ‘05] [Giele, Glover ‘04] ● Multi dimensional contour deformation [Binoth, Ciccolini, Heinrich 05] Dedicated algorithms to avoid numerical instabilities due to vanishing Gram determinants

37. 37 What about twistor space? ● leading-order: Yield compact analytical expressions, but numerically Berends-Giele recursion still faster ● next-to-leading order Much progress for N=4, N=1 Supersym. Yang-Mills, for QCD work in progress “In the past year, much progress has occurred, although much more remains to be done, to apply these ideas to problems in collider physics.” [Bern, Bjerrum-Bohr, Dunbar, Ita ‘06]

38. 38 Conclusion / Outlook ● The production of heavy particles plays a central role at Tevatron and LHC ● QCD corrections are important ● For key processes NNLO is known ( 2  1 ) ● NNLO for 2  2 processes: work in progress ● Precise predictions are available for top quark physics  precise measurements possible ● For many important reactions even NLO is still missing  more effort needed