Phenomenology tools for the LHC

1. introduction and overview • HO corrections • PDFs  LHC benchmarks • MC tools • more speculative pQCD applications • summary Phenomenology tools for the LHC apologies for omitting many topics of interest! James Stirling Cambridge University

3. 1 introduction and overview

4. phenomenology at hadron colliders • Our goal is to make accurate predictions for • event rates (cross sections and distributions) • event shapes (content and structure) • QCD is at the heart of everything – electroweak effects are generally under control • In many cases, perturbative QCD can be used to achieve high precision • But in other contexts our understanding of the non-perturbativeQCD effects is still quite primitive, and we have to resort to models

5. ^  phenomenologytools event simulation (parton showers + tuned UE) MCs, interfaced with LO or NLO hard scattering MEs jet algorithms perturbation theory: LO, NLO, NNLO, … supplemented by resummedNnLL improvements, EW corrections, … parton distribution functions all underpinned by the QCD factorization theorem for hard-scattering (short-distance) inclusive processes

6. 2 higher-order perturbative QCD corrections

7. physical variable(s) process dependent coefficients depending on P general structure of a QCD perturbation series • choose a renormalisation scheme (e.g. MSbar) • calculate cross section to some order (e.g. NLO) • noted/d=0“to all orders”, but in practice d(N+n)/d= O((N+n)SN+n+1)  as many orders as possible! • can try to help convergence by using a “physical scale choice”, ~ P, e.g. = MZor = ETjet • what if there is a wide range of P’s in the process, e.g. W + n jets? – see later renormalisation scale

8. how precise? ? • LO for generic PS Monte Carlos, tree-level MEs • NLO for NLO-MCs and many parton-level signal and background processes • in principle, less sensitivity to unphysical renormalisation and factorisation scales, μR and μF • parton merging to give structure in jets • more types of incoming partons • more reliable pdfs • better description of final state kinematics • NNLO for a limited number of ‘precision observables’ (W, Z, DY, H, …) + E/W corrections, resummed HO terms etc… NLO NLO NNLO NLO NNLO

9. recent developments at NLO • traditional methods based on Feynman diagrams, then reduction to known (scalar box, triangle, bubble and tadpole) integrals • … and new methods based on unitarity and on-shell recursion: assemble loop-diagrams from individual tree-level diagrams • basic idea: Bern, Dixon, Kosower 1993 • cuts with respect to on-shell complex loop momenta: Cachazo, Britto, Feng 2004 • tensor reduction scheme: Ossola, Pittau, Papadopoulos 2006 • integrating the OPP procedure with unitarity: Ellis, Giele, Kunszt 2008 • D-dimensional unitarity: Giele, Kunszt, Melnikov 2008 • … • … and the appearance of automated programmes for one-loop, multi-leg amplitudes, either based on • traditional or numerical Feynman approaches (Golem, …) • unitarity/recursion (BlackHat, CutTools, Rocket, …)

10. some recent NLO results…* • pp  W+3j [Rocket: Ellis, Melnikov & Zanderighi] [unitarity] • pp  W+3j [BlackHat: Berger et al] [unitarity] • pp  tt bb [Bredenstein et al] [traditional] • pp  tt bb [HELAC-NLO: Bevilacqua et al] [unitarity] • pp  qq  4b [Golem: Binoth et al] [traditional] • pp  tt+2j [HELAC-NLO: Bevilacqua et al] [unitarity] • pp  Z+3j [BlackHat: Berger et al] [unitarity] • pp  W+4j [BlackHat: Berger et al, partial] [unitarity] • … • with earlier results onV,H + 2 jets, VV,tt + 1 jet, VVV, ttH, ttZ, … • In contrast, for NNLO we still only have inclusive *,W,Z,H with rapidity distributions and decays (although much progress on top,single jet, …) *relevant for LHC

11. Top at Tevatron Bottom at LHC K. Ellis K. Ellis reason: new processes open up at NLO!

12. However... in complicated processes like W + n jets, there are often many ‘reasonable’ choices of scales: ‘blended’ scales like HT can seamlessly take account of different kinematical configurations: Berger et al., arXiv:0907.1984

13. the impact of NNLO: W,Z Anastasiou, Dixon, Melnikov, Petriello, 2004 • only scale variation uncertainty shown • central values calculated for a fixed set pdfs with a fixed value of S(MZ2)

14. the impact of NNLO: Higgs Harlander,Kilgore Anastasiou, Melnikov Ravindran, Smith, van Neerven … • the NNLO band is about 10%, or 15% if R and F varied independently

15. SM Higgs: Tevatron exclusion limits ? cross section theory uncertainty

16. 3 parton distribution functions

17. X x1P x2P proton proton SUSY, Higgs, W,Z, … DGLAP evolution * pdfs @ LHC • most SM and new physics sample pdfs in a region of x where they are already well known • current pdf uncertainties provide the benchmark for whether LHC can add new information • low-mass forward production (e.g. b quarks, Drell-Yan) might provide new information on small-x partons

18. the pdf industry • many groups now extracting pdfs from ‘global’ data analyses (MSTW, CTEQ, NNPDF, HERAPDF, AKBM, GJR, …) • broad agreement, but differences due to • choice of data sets (including cuts and corrections) • treatment of data errors • treatment of heavy quarks (s,c,b) • order of perturbation theory • parameterisation at Q0 • theoretical assumptions (if any) about: • flavour symmetries • x→0,1 behaviour • … • definition of pdf uncertainties

19. recent global or quasi-global pdf fits

20. Note: • each set comes with its own unique S(MZ2) value (and uncertainty), correlated with the pdfs • CT10, HERAPDF, NNPDF2.1 use recent combined HERA data • NNPDF2.5(NNLO) soon

21. MSTW = Martin, S, Thorne, Watt

22. 4 LHC benchmark cross sections the following luminosity and cross section plots are from Graeme Watt: these and many more available at projects.hepforge.org/mstwpdf/pdf4lhc

23. parton luminosity* comparisons positivity constraint on input gluon Run 1 vs. Run 2 Tevatron jet data No Tevatron jet data or FT-DIS data in fit ZM-VFNS momentum sum rule *

24. benchmark W,Z cross sections New CMS 36pb-1 result (CMS-PAS-EWK-10-005): R± = 1.421 ± 0.006(stat) ± 0.014(syst) ± 0.030(th) from extrapolation to full acceptance; better to calculate and compare for experimental acceptance G. Watt, 2011

25. Wl rapidity asymmetry • very sensitive to pdfs • complex interplay of uV, dV, Sea, V ± A decay • 7 TeV data! l± W

27. SM Higgs and top cross sections … differences from both pdfsANDS ! G. Watt, 2011

28. 5 MC Tools* *For a recent review, see Peter Richardson, ‘Challenging the Standard Model’ IoP Half-Day meeting, indico.cern.ch/conferenceDisplay.py?ovw=True&confId=112764

29. Monte Carlo Event Generators • programs that simulates particle physics events with the same probability as they occur in nature • widely used for signal and background estimates • examples are PYTHIA, HERWIG, SHERPA , ... • the simulation comprises different phases: • start by simulating a hard scattering process (LO, NLO) • this is followed by the simulation of (soft and collinear) QCD radiation using a parton shower algorithm • non-perturbative models are then used to simulate the hadronization of the quarks and gluons into the observed hadrons and the underlying event • a) and b) well grounded theoretically, c) requires a model to be tuned to data: • parameters relating to the final-state parton shower and hadronization are tuned to LEP data • parameters relating to initial-state parton showers and multiple parton-parton interactions are tuned to data (e.g. UA5, Tevatron) – extrapolation to LHC?!

30. PYTHIA tunes to ATLAS 7 TeV MinBias data “PYTHIA AMBT1 and HERWIG+JIMMY AUET1 tunes from ATLAS give a good description of ATLAS soft QCD physics without severely compromising Tevatron agreement.” A. Buckley for ATLAS, Knoxville, November 2010

31. interfacing NnLO and parton showers + Benefits of both: NnLOcorrect overall rate, hard scattering kinematics, reduced scale dep. PScomplete event picture, correct treatment of collinear logs to all orders • MC@NLO(Frixione, Webber, et al ): large range of processes available, integrated withHerwig FORTRAN and Herwig++ programs • POWHEG (Nason): fewer processes, either standalone (Alioli, Nason, Oleari, Re) or integrated with Herwig++ (Hamilton, Richardson, Tully) or SHERPA (Hoeche, Krauss, Schonherr, Siegert)

32. (hadron collider) processes in MC@NLO from the MC@NLO 4.0 manual

33. HW++ vs. POWHEG vs. MC@NLO vs. MCFM Herwig++ 2.5 Release Note (S. Gieseke et al) arXiv:1102.1672 [hep-ph] Tevatron Z0Z0 LHC W+W- POWHEG vs. ATLAS jet data • S. Alioli et al, arXiv:1012.3380 [hep-ph]

34. Jet algorithms {phi}  {jk}  {partons} • Snowmass accord (1990) • simple to implement in experimental analyses as well as theory calculations • defined at any order in pQCD and yields finite results for rates at any order • yields a cross-section relatively insensitive to hadronisation • two main types • CONES: latest implementation SISCONE (Salam, Soyez, 2007) • SUCCESSIVE RECOMBINATION: Jade ... kT... anti-kT(Cacciari, Salam, Soyez 2008) • anti-kT: hard stuff clusters with nearest neighbour, privilege collinear divergence over soft divergence; gives cone-like jets without using cones! Gavin Salam, “Towards Jetography” (2009)

35. Finally, a straightforward, robust, widely-accepted algorithm for jet studies at LHC that satisfies Snowmass accord ...

36. 6 finally, there are interesting processes where our theoretical understanding is much less developed...

37.     central exclusive production compare … • p + p  H + X • the rate (parton,pdfs, αS) • the kinematic distribtns. (d/dydpT) • the environment (jets, underlying event, backgrounds, …) with … • p + p  p + H + p • a real challenge for theory (pQCD + npQCD) and experiment (tagging forward protons, triggering, …) b b

38. gap survival central exclusive production – theory p + p → p  X  p • colliding protons interact via a colour singlet exchange and remain intact: can be triggered by adding proton detectors far down the beam-pipe or by using large rapidity gaps • a system of mass MXis produced at the collision point, and only its decay products are present in the central detector region. • the generic process pp → p + X + p is modeled perturbatively by the exchange of two t-channel gluons(‘Durham Model’ – Khoze Martin Ryskin) • the possibility of additional soft rescatterings filling the rapidity gaps is encoded in ‘eikonal’ and ‘enhanced’ survival factors X

39. CEP at LHC? p + p → p  X  p • in the limit that the outgoing protons scatter at zero angle, the centrally produced state X must have JZP = 0+ quantum numbers→ spin-parity filter/analyser • in certain regions of MSSM parameter space, couplings of Higgs to bb is enhanced, and CEP could be the discovery channel • or anyexotic 0++state, which couples strongly to glue, is a real possibility: radions, gluinoballs, … • in the meantime, many ‘standard candle’ processes at RHIC, Tevatron, LHC: X= jj, , c, b, … • example: X Durham/St Petersburg /Cambridge (Khoze, Martin, Ryskin, S, Harland-Lang,....) Manchester (Cox, Forshaw, Monk, Pilkington, Coughlin, ...) Helsinki (Orava, ...) Saclay (Royon, ...) Cracow (Szczurek, ...) … CDF(arXiv:0902.1271): KHRYSTHAL (Khoze, Ryskin, S, Harland-Lang, arXiv:1005.0695 ):

40. DPS + SPS SPS single and double hard parton scattering e.g. X,Y = jj,bb,W,Z,J/,.. • folklore • studies of +3j production by CDF and D0 suggest eff≈ 15 mb • use shape variables as a discriminator for DPS • however, simple factorisation hypothesis • now being called into question •  much recent theoretical activity, see X,Y distinct: m=2 X,Y same: m=1 MPI@LHC 2010: 2nd International Workshop on Multiple Partonic Interactions at the LHC, Glasgow, November 2010, www.mpi2010.physics.gla.ac.uk

41. summary • relentless advance in improving phenomenology tools for precision hadron collider physics in recent years • the NLOrevolution (but still ‘scale choice/variation’ issues), with NNLO the next frontier (but no “+jet” processes yet) • PDFs: convergence among groups and first precision tests at LHC • Monte Carlo: improved modelling, new tunes to LHC and increasing number of NLO processes included (e.g. MC@NLO, POWHEG, ... ) • … and don’t forget other more novel applications of pQCD (hard diffraction, multiple parton interactions, etc.) where more theoretical work and experimental data are needed

42. extra slides

43. pdfs and S(MZ2) • MSTW08, ABKM09 and GJR08: S(MZ2) values and uncertainty determined by global fit • NNLO value about 0.003  0.004 lower than NLO value, e.g. for MSTW08 • CTEQ, NNPDF, HERAPDF choose standard values and uncertainties • world average (PDG 2009) • note that the pdfs andS are correlated! • e.g. gluon – S anticorrelation at small x and quark – S anticorrelation at large x

44. a b parton luminosity functions • a quick and easy way to assess the mass, collider energy and pdf dependence of production cross sections s X • i.e. all the mass and energy dependence is contained in the X-independent parton luminosity function in [ ] • useful combinations are • and also useful for assessing the uncertainty on cross sections due to uncertainties in the pdfs (see later)

45. CEP hMSSMbbat LHC 3 statistical significance contours, Mhmax scenario Heinemeyer, Khoze, Ryskin, S, Tasevsky, Weiglein: arXiv:0708.3052 Trest 2007