Introduction to Event Generators

1. Topical Meeting on LHC Physics, HRI, Allahabad, Dec 2006 Introduction to Event Generators Peter Z. Skands Fermilab Theoretical Physics Department (Significant parts adapted from T. Sjöstrand (Lund U & CERN) )

2. Apologies • This talk is focused on LHC • Even so, it will not cover: • Heavy-ion physics • Specific physics studies for topics such as • B production • Higgs discovery • SUSY phenomenology • Other new physics discovery potential • The modeling of elastic and diffractive topologies • It will cover the “normal” physics that will be there in (essentially) all LHC pp events, from QCD to exotics, with special emphasis on • Parton Showering • Underlying Event ( tomorrow) • Hadronization ( tomorrow) • And how these things are addressed by generators Introduction to Event Generators

3. QuantumChromoDynamics Introduction to Event Generators

4. The (QCD) Landscape hadronization bbar from tbar decay pbar beam remnant p beam remnant qbar from W q from W q from W b from t decay ? Triplet Anti-Triplet In reality, this all happens on top of each other. (only possible exception: long-lived colour singlet) D. B. Leinweber, hep-lat/0004025 Introduction to Event Generators

5. Collider Energy Scales Hadron Decays Non-perturbative hadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton, kaon/pion, ... Soft Jets + Jet Structure Multiple collinear/soft emissions (initial and final state brems radiation), Underlying Event (multiple perturbative 22 interactions + … ?), semi-hard separate brems jets Exclusive & Widths Resonance Masses … Hard Jet Tail High-pT wide-angle jets Inclusive s • + “UNPHYSICAL” SCALES: • QF , QR : Factorisation(s) & Renormalisation(s) Introduction to Event Generators

6. The Event Generator Position Introduction to Event Generators

7. Main virtues Error is stochastic O(N-1/2) and independent of dimension Fully exclusive final states (for better or worse – cf. the name ‘Pythia’ … ) Only need to redo part of calculation for each different observable. Have proven essential for detailed experimental studies: can compute detector response event by event Monte Carlo Generators • Large-dimensional phase spaces •  Monte Carlo integration • + Markov Chain formulation of fragmentation: • 1. Parton showers:iterative application of universal and pertubatively calculable kernels for n  n+1 partons ( = resummation of soft/collinear Sudakov logarithms) • 2. Hadronization:iteration of X  X + hadron, at present according to phenomenological models based on known properties of nonperturbative QCD, lattice studies, and fits to data. Introduction to Event Generators

8. The Monte Carlo Method Introduction to Event Generators

9. The Generator Landscape Introduction to Event Generators

10. Matrix Elements The short-distance physics – Hard Subprocesses

11. Cross Sections and Kinematics • Starting point 2n hard scattering ME • Fold with parton distribution functions  pp cross section Introduction to Event Generators

12. Parton Distribution Functions Initial conditions non-perturbative Evolution Perturbative (DGLAP) http://durpdg.dur.ac.uk/hepdata/pdf.html Introduction to Event Generators

13. “Hardcoded” Subprocesses +The Les Houches interfaces to external packages (tomorrow) Introduction to Event Generators

14. Parton Showers Resummation of Multiple Perturbative QCD and QED Emissions

15. QuantumChromoDynamics + ¡ ¹ e e q q g : ! Problem 1: bremsstrahlung corrections singular for soft and collinear configurations Introduction to Event Generators

16. Parton Showers • Starting observation: collinear limit of perturbative QCD is universal (process-independent) • QCD corrections can be worked out to all orders once and for all •  exponentiated (Altarelli-Parisi) integration kernels • Iterative (Markov chain) formulation = parton shower • can be used to generate the collinear singular parts of QCD corrections to any process to infinite order in the coupling • ordered in a measure of resolution  a series of successive factorizations the lower end of which can be matched to a non-perturbative description at some fixed low scale • Limitations • misses interference terms relevant in the deep non-singular region • kinematic ambiguities and double counting between fixed order part and resummed part Introduction to Event Generators

17. Bremsstrahlung Example: SUSY @ LHC LHC - sps1a - m~600 GeV Plehn, Rainwater, PS (2005) p ? j t e ; FIXED ORDER pQCD inclusiveX + 1 “jet” inclusiveX + 2 “jets” Comparison: • Matrix Elements with explicit jets. • Parton Showers / Resummation to infinite order in singular limits Problem: Need to get both soft and hard emissions “right”  “Matching” (tomorrow) Introduction to Event Generators

18. The Sudakov Form Factor ³ ´ t 2 R 2 ( ) j j d ¢ A t t t ¡ e x p = 1 2 ; t 1 The Sudakov Form Factor: •  instantaneous decay probability: dΔ/dt Δ(Q12,Q22) • Nuclear Decay (naïve approach ~ fixed order MEs): • Suppose N1 nuclei at time t = t1 • Decay probability per unit time =|A|2 • dN/dt = |A|2N(t) = N1 (1 - |A|2t ) < 0for late times ! • Nuclear Decay (“resummed” approach ~ PS) • Reason: only first term in expansion. • For late times must include each nucleus can only decay once: • dN(t)/dt = |A|2  N(t) = N1 exp(-|A|2 t)  Sudakov = generating function for parton shower Random numbers sequence of parton ‘decays’ = branchings Introduction to Event Generators

19. Coherence Introduction to Event Generators

20. Ordering Variables Introduction to Event Generators

21. Data Comparisons • All 3 do a reasonable job of describing LEP data, but typically ARIADNE (pT2) > PYTHIA (m2) > HERWIG (θ) • + improvements and new algorithms being developed, cf. ‘new’ pT-ordered PYTHIA showers, VINCIA antenna showers, etc Introduction to Event Generators

22. Initial vs. Final State Showers • Both controlled by same evolution equation Introduction to Event Generators

23. QuantumChromoDynamics + ¡ ¹ e e q q g : ! DONE to Landau Pole Problem 1: bremsstrahlung corrections singular for soft and collinear configurations Problem 2: QCD becomes non-perturbative at scales below ~ 1 GeV Introduction to Event Generators

24. Hadronization Models of Non-Perturbative Effects

25. Hadronization / Fragmentation • Perturbative  nonperturbative: not calculable from first principles! • Model building = Ideology + “cookbook” • Common Approaches: • String fragmentation • (most ideological) • Cluster fragmentation • (simplest?) • Independent fragmentation • (most cookbook) • Local parton-hadron duality • (simply wrong) Introduction to Event Generators

26. 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 Introduction to Event Generators

27. QCD on the Lattice • Linear confinement in “quenched” QCD Introduction to Event Generators

28. Gluons = Transverse Excitations Introduction to Event Generators

29. Partons  Hadrons • Hadron production arises from string breaks • String breaks modeled by tunneling  Most fundamental : AREA LAW • But also depends on spins, hadronic wave functions, phase space, baryon production, …  more complicated Introduction to Event Generators

30. The Iterative Ansatz Introduction to Event Generators

31. 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) by LEP • 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? • But since this is an introduction, we skip all that for now … Introduction to Event Generators

32. Useful PYTHIA Parameters (hardcopies will be available during exercises)

33. Overview • Utilities • Hard Processes – Basics • Hard Processes – Specialized • Parton Densities and Scales • Resonances • Final-State Showers • Initial-State Showers (+ interference) • Beam Remnants & Multiple Interactions • Hadronization • Particle Data and Decays Note: here we only scratch the surface, ~ 600 page manual gives the full story Introduction to Event Generators

34. Utilities Introduction to Event Generators

35. Hard Processes – Basics Introduction to Event Generators

36. Hard Processes – Specialized Introduction to Event Generators

37. Parton Distributions and Scales Introduction to Event Generators

38. Resonances Introduction to Event Generators

39. Final-State Showers Introduction to Event Generators

40. Initial-State Showers (+Interference) Introduction to Event Generators

41. (Beam Remnants and Multiple Interactions) Introduction to Event Generators

42. Hadronization • Tuned to LEP, so if jet universality, minor issue Introduction to Event Generators

43. Particle Data and Decays Introduction to Event Generators

44. Some Useful References • T. Sjöstrand: Monte Carlo Generators • hep-ph/0611247 • The Les Houches Guidebook to MC Generators for Hadron Collider Physics • hep-ph/0403045 • The Les Houches Web Repository for BSM Tools: • http://www.ippp.dur.ac.uk/montecarlo/BSM • PS: A Quick Guide to SUSY Tools: • hep-ph/0601103 Introduction to Event Generators