1. Peter Skands Theoretical Physics, CERN / Fermilab Event Generators 1 A Practical Introduction to the Structure of High Energy Collisions Aachen, November 2007

2. Peter Skands Event Generators 1 - 2 Disclaimer Ask about … whatever ! If I become too incomprehensible, don’t hesitate (!) to ask, I assure you it’s very difficult to make me embarrassed: try! Focus on LHC. Even so, we will not cover: Heavy Ions Topics Specific to B Mesons Higgs Discovery SUSY and other BSM phenomenology Luminosity, Total cross sections, Diffractive, and Elastic Scattering All = Important Topics, on which this particular lecturer is worthless 

3. Peter Skands Event Generators 1 - 3 Disposition Fundamental Topics (1 st class) Beyond Fixed-Order Perturbation Theory Parton Showers Hadronisation Monte Carlo generators HERWIG and PYTHIA He who wishes to do everything … Advanced Topics (2 nd and 3 rd classes) Focus on Hadron Collisions What we know and don’t know about hadron collisions The Underlying Event Matching WedThuFri 10-12 : Fundamental Topics 10-12: Advanced Topics 1 10-12: Advanced Topics 2 + Q&A 13-15:30: Hands-on Session: Pythia and Alpgen

4. Peter Skands Theoretical Physics, CERN / Fermilab Fundamental Topics Beyond Fixed-Order Perturbation Theory: Parton Showers Hadronisation The HERWIG and PYTHIA Generators

5. Peter Skands Event Generators 1 - 5 Classical Example: counting tracks Simple Models ~ Poisson Can ‘tune’ to describe average, but not the fluctuations  insufficient hypothesis More Physics: Models with multiple parton-parton interactions Once upon a time … UA5, pp (546 GeV ), charged track multiplicity in minimum-bias events Low-p T only Low-p T + Hard int Low-p T + Hard int + ISR + FSR The point of this story 1)It is not possible to ‘tune’ better than the underlying physics model allows 2)The failure of a physical model usually indicates deeper physics (more than you get from a fit that stops working).

6. Peter Skands Event Generators 1 - 6 Prerequisites / Discussion You know (a little) about Perturbative Quantum Field Theory Matrix Elements Not how to calculate them necessarily, but what they represent physically and which general features they contain: propagators, phase space integrals, how to go from matrix elements to cross sections, etc The role of the observable The difference between exclusive and inclusive observables The perturbative expansion Through the hoops: Legs and loops Computer Physics Monte Carlo integration as a numerical tool Markov Chains, e.g., as describing nuclear decay Like me, you know (almost) nothing about Non-perturbative quantum field theory Reggeons, Pomerons, Strings (incl AdS/CFT), OPE, EFT’s, χPT, HQET, … And you hate talks with C++ class diagrams (or F77 common blocks …)

7. Peter Skands Event Generators 1 - 7 Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory Example: Q uantum C hromo D ynamics Reality is more complicated High-transverse momentum interaction

8. Peter Skands Event Generators 1 - 8 Fixed Order (all orders) “Experimental” distribution of observable O in production of X : k : legsℓ : loops {p} : momenta Monte Carlo at Fixed Order High-dimensional problem (phase space) d≥5  Monte Carlo integration Principal virtues 1.Stochastic error O(N -1/2 ) independent of dimension 2.Full (perturbative) quantum treatment at each order 3.(KLN theorem: finite answer at each (complete) order) Note 1: For k larger than a few, need to be quite clever in phase space sampling Note 2: For ℓ > 0, need to be careful in arranging for real- virtual cancellations “Monte Carlo”: N. Metropolis, first Monte Carlo calcultion on ENIAC (1948), basic idea goes back to Enrico Fermi

9. Peter Skands Event Generators 1 - 9 Parton Showers High-dimensional problem (phase space) d≥5  Monte Carlo integration + Formulation of fragmentation as a “Markov Chain”: 1.Parton Showers: iterative application of perturbatively calculable splitting kernels for n  n+1 partons 2.Hadronization: iteration of X  X’ + hadron, according to phenomenological models (based on known properties of QCD, on lattice, and on fits to data). A. A. Markov: Izvestiia Fiz.-Matem. Obsch. Kazan Univ., (2nd Ser.), 15(94):135 (1906) S: Evolution operator. Generates event, starting from {p} X

10. Peter Skands Event Generators 1 - 10 Traditional Generators Generator philosophy: Improve Born-level perturbation theory, by including the ‘most significant’ corrections  complete events 1.Parton Showers 2.Hadronisation 3.The Underlying Event 1.Soft/Collinear Logarithms 2.Power Corrections 3.All of the above (+ more?) roughly (+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) Asking for fully exclusive events is asking for quite a lot …

11. Peter Skands Event Generators 1 - 11 Be wary of oracles PYTHIA Manual, Sjöstrand et al, JHEP 05(2006)026 Be even more wary if you are not told to be wary! We are really only operating at the first few orders (fixed + logs + twists + powers) of a full quantum expansion

12. Peter Skands Event Generators 1 - 12 Non-perturbative hadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton ratio, kaon/pion ratio,... Soft Jets and Jet Structure Soft/collinear radiation (brems), underlying event (multiple perturbative 2  2 interactions + … ?), semi-hard brems jets, … Resonance Masses… Hard Jet Tail High-p T jets at large angles & Widths + Un-Physical Scales: Q F, Q R : Factorization(s) & Renormalization(s) s Inclusive Exclusive Hadron Decays Collider Energy Scales

13. Peter Skands Event Generators 1 - 13 T he B ottom L ine The S matrix is expressible as a series in g i, g i n /Q m, g i n /x m, g i n /m m, g i n /f π m, … To do precision physics: Solve more of QCD Combine approximations which work in different regions: matching Control it Good to have comprehensive understanding of uncertainties Even better to have a way to systematically improve Non-perturbative effects don’t care whether we know how to calculate them FODGLAP BFKL HQET χPT

14. Peter Skands Event Generators 1 - 14 The Monte Carlo Method Want to generate events in as much detail as Mother Nature  Get average and fluctuations right  Make random choices, ~ as in nature σ final state = σ hard process P tot, hard process  final state where P tot = P res P ISR P FSR P MI P Remnants P Hadronization P decays With P i = Π j P ij = Π j Π k P ijk = … in its turn  Divide and conquer Hard Part Up to E cm Parton Showers + Multiple Interactions Multi-GeV Hadron Decays Hadronization + Remnants ~ 1 GeV ~ 10 -15 m σ hard process, P res P ISR, P FSR, P MI P remnants, P hadronization P decays = the S operator from before

15. Peter Skands Event Generators 1 - 15 Problem 1: bremsstrahlung corrections are singular for soft/collinear configurations  spoils fixed-order truncation e + e -  3 jets Beyond Fixed Order

16. Peter Skands Event Generators 1 - 16 Diagrammatical Explanation 1 dσ X = … dσ X+1 ~ dσ X g 2 s ab /(s a1 s 1b ) ds a1 ds 1b dσ X+2 ~ dσ X+1 g 2 s ab /(s a2 s 2b ) ds a2 ds 2b dσ X+3 ~ dσ X+2 g 2 s ab /(s a3 s 3b ) ds a3 ds 3b But it’s not yet an “evolution” What’s the total cross section we would calculate from this? σ X;tot = int( dσ X ) + int( dσ X+1 ) + int( dσ X+2 ) +... Probability not conserved, events “multiply” with nasty singularities! Just an approximation of a sum of trees. But wait, what happened to the virtual corrections? KLN? dσXdσX α s ab s ai s ib dσ X+1 dσ X+2 This is an approximation of inifinite- order tree-level cross sections

17. Peter Skands Event Generators 1 - 17 Diagrammatical Explanation 2 dσ X = … dσ X+1 ~ dσ X g 2 s ab /(s a1 s 1b ) ds a1 ds 1b dσ X+2 ~ dσ X+1 g 2 s ab /(s a2 s 2b ) ds a2 ds 2b dσ X+3 ~ dσ X+2 g 2 s ab /(s a3 s 3b ) ds a3 ds 3b + Unitarisation: σ tot = int( dσ X )  σ X;PS = σ X - σ X+1 - σ X+2 - … Interpretation: the structure evolves! (example: X = 2-jets) Take a jet algorithm, with resolution measure “Q”, apply it to your events At a very crude resolution, you find that everything is 2-jets At finer resolutions  some 2-jets migrate  3-jets = σ X+1 (Q) = σ X;incl – σ X;excl (Q) Later, some 3-jets migrate further, etc  σ X+n (Q) = σ X;incl – ∑σ X+m<n;excl (Q) This evolution takes place between two scales, Q in and Q fin = Q F;ME and Q had σ X;PS = int( dσ X ) - int( dσ X+1 ) - int( dσ X+2 ) +... = int( dσ X ) EXP[ - int(α s ab /(s a1 s 1b ) ds a1 ds 1b ) ] dσXdσX α s ab s ai s ib dσ X+1 dσ X+2 Given a jet definition, an event has either 0, 1, 2, or … jets

18. Peter Skands Event Generators 1 - 18 Observation: the collinear limit is universal If Nature was perfectly described by this limit  calculate all corrections for all reactions in one fell swoop!  Exponentiated integration kernels (Altarelli-Parisi) (resummation) Iterative formulation = parton shower For any reaction, for any observable, generate all the most singular corrections of QCD (& QED) Ordered in a measure of resolution (Q ~ 1/time)  a series of successive factorisations; the last one  non-perturbative Limitations Missing terms (quantum interference) Kinematic ambiguities and “double counting” between fixed-order and resummation (see matching later …) Parton Showers

19. Peter Skands Event Generators 1 - 19 ME PS 1 PS 2 Problem: Necessary to describe both the hard and soft regions  “Matching” Bremsstrahlung - Example: SUSY @ LHC Comparisons: 1.Matrix Elements with 0,1,2 jets. 2.Parton Showers ~ resommation FIXED ORDER pQCD inclusive X + 1 “jet” inclusive X + 2 “jets” LHC - sps1a - m~600 GeVPlehn, Rainwater, PS (2005)

20. Peter Skands Event Generators 1 - 20 Note on Factorisation Parton showers are not “soft”, here is proof: Correction: Parton Showers are correct in the soft/collinear limit, but the neglected terms can be negative (the usual case?)  splitting kernels = over-estimate ME PS 1 PS 2 Sjöstrand et al, PLB185(1987)435, NPB289(1987)810, PLB449(1999)313, NPB603(2001)297 LHC - sps1a - m~600 GeVPlehn, Rainwater, PS (2005)

21. Peter Skands Event Generators 1 - 21 (Note on Factorisation) The problem of showers that “die” then? Caused by “cuts” in the phase space, not by the kernels Proposition: this is not intimately related to the “softness” of showers! One possibility: choose the factorisation scale such that “everything looks like 2-jets” in the beginning, that is choose the largest possible scale  s instead of s-hat  “power showers” (or something inbetween?) Have to admit that this is still somewhat controversial Plehn, Rainwater, PS: PLB645(2007)217 & hep-ph/0511306 hep-ph/0511306 Top pair + jet Tevatron Top pair + jet LHC

22. Peter Skands Event Generators 1 - 22 Coherence From T. Sjöstrand

23. Peter Skands Event Generators 1 - 23 Ordering Variables From T. Sjöstrand

24. Peter Skands Event Generators 1 - 24 Data Comparisons Showers describe LEP data fairly well … Now: a renaissance in this field! August-October ‘07: 4 new cascades, 1 based on “antennae”, 2 on “Catani-Seymour dipoles”, 1 on a hybrid scheme Important to keep power to constrain, event after the experiments are finished

25. Peter Skands Event Generators 1 - 25 Initial vs Final FSR and ISR : almost the same evolution From T. Sjöstrand

26. Peter Skands Event Generators 1 - 26 For FSR, LEP allowed studies “in isolation” Especially for quark jets  very good constraints b-jets could be studied separately Gluons  3-jet events, weaker constraints + Not always easy to separate non-perturbative   perturbative For ISR, our preferred lab is Drell-Yan (hadroproduction of dileptons) “Crossing of LEP”: direct constraints on ISR off light quarks PDF suppression  weaker constraints on ISR off b quarks  Z/W+b Corrections from the underlying event Few constraints on ISR off gluons and b quarks: Important to better know the environnement of Higgs  Higgs is an interesting theoretical lab, but hard to isolate The power to control Q 2 in Drell-Yan should be used to the max ISR / FSR: studies FSR ME HAD ME ISR F/I BR + DIS

27. Peter Skands Event Generators 1 - 27 Drell-Yan: physics with a muon chamber Muons = a direct light into the heart of the process  A very clean, highly controllable “probe” of Initial-State Radiation (ISR) Feed back into photon + jet  improve jet calibration Muons + tracking  can also study Underlying Event here (minijets, fragmentation, …) Evolution of UE and ISR as function of Q 2  good model constraints In preparation: PS, Les Houches ‘Physics at TeV colliders’ 2007

28. Peter Skands Event Generators 1 - 28 Summary – Parton Showers Parton Showers are very useful Applicable to any final state Parton Showers are limited So far, they only contain the “first orders” of logarithms Agreement with data is desirable but can also be deceptive; not always guaranteed to be universal Today, it is a field full of activity Many new ideas in the last ~ 5 years Many limitations are already lifted (cf. matching), but others remain … for you? Beyond leading logs? Subleading colour? Matching to higher orders? To other expansions (HQET, BFKL, … )?

29. Peter Skands Theoretical Physics, CERN / Fermilab Hadronisation P tot = P Res P ISR P FSR P UE P NP P Decays σ final state = σ hard process P tot,hard process  final state factorisation

30. Peter Skands Event Generators 1 - 30 to Landau Pole Probleme 2: QCD becomes non-perturbative below ~ 1 GeV (or more generally, in the resonance region) Resummed e + e -  3 jets Q uantum C hromo D ynamics

31. Peter Skands Event Generators 1 - 31 Hadronization / Fragmentation Perturbative  nonperturbative: not calculable from first principles! How to model? Ideology + “cookbook” Common Approaches: String fragmentation (most ideological) Cluster fragmentation (simplest?) Independent fragmentation (most cookbook)

32. Peter Skands Event Generators 1 - 32 The Lund String Model In QED the field lines go all the way to infinity In QCD, gluon self-interaction  the vacuum state contains quark (and gluon) Cooper pairs  at large distances the QCD field lines compressed into vortex lines  Linear confinement with string tension  Separation of transverse and longitudinal degrees of freedom  simple description as 1+1 dimensional worldsheet – string – with Lorentz invariant formalism

33. Peter Skands Event Generators 1 - 33 QCD on the Lattice Linear confinement in “quenched” QCD

34. Peter Skands Event Generators 1 - 34 Gluons = Transverse Excitations From T. Sjöstrand

35. Peter Skands Event Generators 1 - 35 Partons  Hadrons Hadron production arises from string breaks String breaks modeled by tunneling  Most fundamental : THE AREA LAW But also depends on spins, hadronic wave functions, phase space, baryon production, …  more complicated

36. Peter Skands Event Generators 1 - 36 The Iterative Ansatz From T. Sjöstrand

37. Peter Skands Event Generators 1 - 37 Hadronization – Final Remarks Evidence for “the string effect” was first seen at JADE (1980) ~ coherence in non-perturbative context. Further numerous and detailed tests at LEP favour string picture Model well-constrained (perhaps excepting baryon production) However, much remains uncertain for hadron collisions … At LEP, there was no colour in the initial state And there was a quite small total density of strings How well do we (need to) understand fragmentation at LHC?

38. Peter Skands Event Generators 1 - 38 D. B. Leinweber, hep-lat/0004025 Anti-Triplet Triplet pbar beam remnant p beam remnant bbar from tbar decay b from t decay qbar from W q from W hadronization ? q from W In reality, all of this takes place in the same space-time interval. (except maybe: long- lived resonances) The (QCD) Landscape

39. Peter Skands Event Generators 1 - 39 Questions At LEP, we didn’t have UE (multiple interactions) generating a large density of strings Should new phenomena appear  string interactions? Is there a critical density? Is it related to the physics of heavy ions? At LEP, we didn’t have the background of the proton Is the Cronin effect important? (rescattering) Is fragmentation affected by the “color wakefields” generated by the beam protons? Are there new coherence phenomena?

40. Peter Skands Event Generators 1 - 40 Recent Example: Colour Annealing D. Wicke + PS, EPJC52(2007)133 Δ(mtop) ~ 0.5 GeV from infrared effects Early days. May be under- or overestimated. Primitive models, mostly useful for reconnaissance and order-of-magnitude Pole mass does have infrared sensitivity. Can we figure out some different observable which is more stable? Infrared physics ~ universal?  use complimentary samples to constrain it. Already used a few min-bias distributions, but more could be included  Drell-Yan, dijets, … ? Sep 2007 Postulate string interactions, make a simple model, just to see:

41. Peter Skands Theoretical Physics, CERN / Fermilab Next Lecture: Advanced Topics