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Introduction to Event Generators

PYTHIA mini-tutorial, Carleton U., May 2007. Introduction to Event Generators. Peter Z. Skands Fermilab Theoretical Physics Department (Significant parts adapted from T. Sjöstrand (Lund U & CERN) ). Apologies. This tutorial is focused on LHC Even so, it will not cover: Heavy-ion physics

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Introduction to Event Generators

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  1. PYTHIA mini-tutorial, Carleton U., May 2007 Introduction to Event Generators Peter Z. Skands Fermilab Theoretical Physics Department (Significant parts adapted from T. Sjöstrand (Lund U & CERN) )

  2. Apologies • This tutorial 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 • Main Tool • Matrix Elements in perturbative Quantum Field Theory • Example: Reality is more complicated Introduction to Event Generators

  4. Classic Example: Number of tracks More Physics: Multiple interactions + impact-parameter dependence UA5 @ 540 GeV, single pp, charged multiplicity in minimum-bias events Simple physics models ~ Poisson Can ‘tune’ to get average right, but much too small fluctuations  inadequate physics model • Morale (will return to the models later): • It is not possible to ‘tune’ anything better than the underlying physics model allows • Failure of a physically motivated model usually points to more, interesting physics Introduction to Event Generators

  5. Traditional Event Generators • Basic aim: improve lowest order perturbation theory by including leading corrections  exclusive event samples • sequential resonance decays • bremsstrahlung • underlying event • hadronization • hadron (and τ) decays E.g. PYTHIA 2006: first publication of PYTHIA manual JHEP 0605:026,2006 (FERMILAB-PUB-06-052-CD-T) Introduction to Event Generators

  6. 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

  7. The Event Generator Position Introduction to Event Generators

  8. 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

  9. The Monte Carlo Method Introduction to Event Generators

  10. The Generator Landscape Introduction to Event Generators

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

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

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

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

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

  16. QuantumChromoDynamics e+e- 3 jets Problem 1: bremsstrahlung corrections singular for soft and collinear configurations Introduction to Event Generators

  17. 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

  18. 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

  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 e+e-  3 jets 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. 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

  33. Colour Annealing • Toy modelof (non-perturbative) color reconnections, applicable to any final state • at hadronisation time, each string piece has a probability to interact with the vacuum / other strings: Preconnect = 1 – (1-χ)n • χ = strength parameter: fundamental reconnection probability (free parameter) • n = # of multiple interactions in current event ( ~ counts # of possible interactions) • For the interacting string pieces: • New string topology determined by annealing-like minimization of ‘Lambda measure’ • Similar to area law for fundamental strings: Lambda ~ potential energy ~ string length ~ log(m) ~ N •  good enough for order-of-magnitude Sandhoff + PS, in Les Houches ’05 SMH Proceedings, hep-ph/0604120 Introduction to Event Generators

  34. Delta(mtop) ~ 1 GeV from parton shower To some extent should be already accounted for by HERWIG – PYTHIA systematic, but should still be investigated further Match to hard matrix elements for top + jets + further constrain shower parameters Delta(mtop) ~ 0.5 GeV from infrared effects Early days. May be under- or overestimated. Models are crude, 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? It may be difficult to derive one from first principles, given the complicated environment, but proposals could still be tested on models Infrared physics ~ universal?  use complimentary samples to constrain it. Already used a few min-bias distributions, but more could be included Recent Example: Colour Annealing D. Wicke + PS, hep-ph/0703081 Introduction to Event Generators

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

  36. Overview • The Event Record • 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

  37. Standard PC  ~ 1M evts / hr. SM Higgs Factory Pythia Event Record: Event listing (summary) I particle/jet KS KF orig p_x p_y p_z E m 1 !mu+! 21 -13 0 0.000 0.000 60.000 60.000 0.106 2 !mu-! 21 13 0 0.000 0.000 -60.000 60.000 0.106 ============================================================================== 3 !mu+! 21 -13 1 0.000 0.000 60.000 60.000 0.000 4 !mu-! 21 13 2 0.000 0.000 -60.000 60.000 0.000 5 !mu+! 21 -13 3 0.000 0.000 60.000 60.000 0.000 6 !mu-! 21 13 4 0.000 0.000 -60.000 60.000 0.000 7 !h0! 21 25 0 0.000 0.000 0.000 120.000 120.000 8 !b! 21 5 7 -27.886 6.281 52.534 60.000 4.800 9 !bbar! 21 -5 7 27.886 -6.281 -52.534 60.000 4.800 ============================================================================== 10 (h0) 11 25 7 0.000 0.000 0.000 120.000 120.000 11 gamma 1 22 1 0.000 0.000 0.000 0.000 0.000 12 gamma 1 22 2 0.000 0.000 0.000 0.000 0.000 13 (ubar) A 12 -2 8 -0.243 -0.347 0.397 0.668 0.330 14 (g) I 12 21 8 0.173 -0.630 0.658 0.927 0.000 15 (g) I 12 21 8 -0.887 -0.091 1.462 1.712 0.000 16 (b) V 11 5 8 -9.565 10.722 44.056 46.587 4.800 17 (u) A 12 2 8 -12.758 -3.627 -0.934 13.300 0.330 18 (g) I 12 21 8 -1.441 -0.459 0.931 1.775 0.000 19 (g) I 12 21 9 0.620 0.004 -0.189 0.648 0.000 20 (g) I 12 21 9 -0.081 1.305 -1.532 2.014 0.000 21 (g) I 12 21 9 -0.101 0.355 -0.413 0.554 0.000 22 (g) I 12 21 9 0.773 -0.305 -0.065 0.834 0.000 23 (g) I 12 21 9 0.332 0.059 -0.228 0.407 0.000 24 (bbar) V 11 -5 9 23.177 -6.986 -44.142 50.572 4.800 ============================================================================== 25 (string) 11 92 13 -10.522 9.654 46.573 49.895 10.799 26 (omega) 11 223 25 -0.253 -0.461 1.549 1.812 0.778 27 (pi0) 11 111 25 -0.480 -0.281 0.321 0.656 0.135 28 (pi0) 11 111 25 -1.442 2.077 7.957 8.350 0.135 29 (rho-) 11 -213 25 -1.077 1.453 5.978 6.291 0.754 30 (B*bar0) 11 -513 25 -7.270 6.866 30.767 32.786 5.325 31 (string) 11 92 17 10.522 -9.654 -46.573 70.105 50.416 32 (rho0) 11 113 31 -5.421 -1.084 -0.402 5.565 0.492 33 (K*+) 11 323 31 -4.307 -1.543 0.409 4.674 0.870 34 K- 1 -321 31 -1.770 -0.800 -0.443 2.052 0.494 35 p+ 1 2212 31 -2.323 -0.381 -0.291 2.551 0.938 36 (eta') 11 331 31 -0.351 0.200 0.439 1.128 0.958 37 (Deltabar-) 11 -2214 31 1.141 1.009 -1.561 2.513 1.248 38 pi+ 1 211 31 0.105 -0.415 -1.261 1.339 0.140 39 (rho-) 11 -213 31 5.155 -1.570 -8.550 10.137 0.790 40 pi+ 1 211 31 0.981 0.012 -2.262 2.469 0.140 41 (B0) 11 511 31 17.310 -5.083 -32.651 37.676 5.279 Examples using PYTHIA 6.410 T. Sjöstrand, S. Mrenna, PS, JHEP 05 (2006) 026 http://projects.hepforge.org/pythia6/ Introduction to Event Generators

  38. Utilities Introduction to Event Generators

  39. Hard Processes – Basics Introduction to Event Generators

  40. Hard Processes – Specialized Introduction to Event Generators

  41. Parton Distributions and Scales Introduction to Event Generators

  42. Resonances Introduction to Event Generators

  43. Final-State Showers Introduction to Event Generators

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

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

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

  47. Particle Data and Decays Introduction to Event Generators

  48. 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

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