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

Peter SkandsIntroduction to Event Generators 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

Peter SkandsIntroduction to Event Generators 3 Q uantum C hromo D ynamics

Peter SkandsIntroduction to Event Generators 4 D. B. Leinweber, hep-lat/ 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, this all happens on top of each other. (only possible exception: long-lived colour singlet) The (QCD) Landscape

Peter SkandsIntroduction to Event Generators 5 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 Resonance Masses … Hard Jet Tail High-p T wide-angle jets & Widths + “UNPHYSICAL” SCALES: Q F, Q R : Factorisation(s) & Renormalisation(s) s Inclusive Exclusive Hadron Decays Collider Energy Scales

Peter SkandsIntroduction to Event Generators 6 The Event Generator Position

Peter SkandsIntroduction to Event Generators 7 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. Main virtues 1.Error is stochastic O(N -1/2 ) and independent of dimension 2.Fully exclusive final states (for better or worse – cf. the name ‘Pythia’ … ) 3.Only need to redo part of calculation for each different observable. 4.Have proven essential for detailed experimental studies: can compute detector response event by event

Peter SkandsIntroduction to Event Generators 8 The Monte Carlo Method

Peter SkandsIntroduction to Event Generators 9 The Generator Landscape

Matrix Elements The short-distance physics – Hard Subprocesses

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

Peter SkandsIntroduction to Event Generators 12 Parton Distribution Functions Initial conditions non- perturbative Evolution Perturbative (DGLAP)

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

Parton Showers Resummation of Multiple Perturbative QCD and QED Emissions

Peter SkandsIntroduction to Event Generators 15 Q uantum C hromo D ynamics e + e ¡ ! q ¹ qg: Problem 1: bremsstrahlung corrections singular for soft and collinear configurations

Peter SkandsIntroduction to Event Generators 16 ► 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 Parton Showers

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

Peter SkandsIntroduction to Event Generators 18 1.Nuclear Decay (naïve approach ~ fixed order MEs): Suppose N 1 nuclei at time t = t 1 Decay probability per unit time = |A| 2 dN/dt = |A| 2  N(t) = N 1 (1 - |A| 2 t ) < 0 for late times ! 2.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) = N 1 exp(-|A| 2 t) Δ(Q 1 2,Q 2 2 ) The Sudakov Form Factor ¢ ( t 1 ; t 2 ) = exp ³ ¡ R t 2 t 1 d t j A j 2 ´ The Sudakov Form Factor:  instantaneous decay probability: dΔ/dt  Sudakov = generating function for parton shower Random numbers  sequence of parton ‘decays’ = branchings

Peter SkandsIntroduction to Event Generators 19 Coherence

Peter SkandsIntroduction to Event Generators 20 Ordering Variables

Peter SkandsIntroduction to Event Generators 21 Data Comparisons ► All 3 do a reasonable job of describing LEP data, but typically ARIADNE (p T 2 ) > PYTHIA (m 2 ) > HERWIG (θ) ► + improvements and new algorithms being developed, cf. ‘new’ p T -ordered PYTHIA showers, VINCIA antenna showers, etc

Peter SkandsIntroduction to Event Generators 22 Initial vs. Final State Showers ► Both controlled by same evolution equation

Peter SkandsIntroduction to Event Generators 23 Q uantum C hromo D ynamics e + e ¡ ! q ¹ qg: Problem 1: bremsstrahlung corrections singular for soft and collinear configurations to Landau Pole Problem 2: QCD becomes non-perturbative at scales below ~ 1 GeV DONE

Hadronization Models of Non-Perturbative Effects

Peter SkandsIntroduction to Event Generators 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)

Peter SkandsIntroduction 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

Peter SkandsIntroduction to Event Generators 27 QCD on the Lattice ► Linear confinement in “quenched” QCD

Peter SkandsIntroduction to Event Generators 28 Gluons = Transverse Excitations

Peter SkandsIntroduction 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

Peter SkandsIntroduction to Event Generators 30 The Iterative Ansatz

Peter SkandsIntroduction 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 …

Useful PYTHIA Parameters (hardcopies will be available during exercises)

Peter SkandsIntroduction to Event Generators 33 Overview 1.Utilities 2.Hard Processes – Basics 3.Hard Processes – Specialized 4.Parton Densities and Scales 5.Resonances 6.Final-State Showers 7.Initial-State Showers (+ interference) 8.Beam Remnants & Multiple Interactions 9.Hadronization 10.Particle Data and Decays Note: here we only scratch the surface, ~ 600 page manual gives the full story

Peter SkandsIntroduction to Event Generators 34 Utilities

Peter SkandsIntroduction to Event Generators 35 Hard Processes – Basics

Peter SkandsIntroduction to Event Generators 36 Hard Processes – Specialized

Peter SkandsIntroduction to Event Generators 37 Parton Distributions and Scales

Peter SkandsIntroduction to Event Generators 38 Resonances

Peter SkandsIntroduction to Event Generators 39 Final-State Showers

Peter SkandsIntroduction to Event Generators 40 Initial-State Showers (+Interference)

Peter SkandsIntroduction to Event Generators 41 (Beam Remnants and Multiple Interactions)

Peter SkandsIntroduction to Event Generators 42 Hadronization ► Tuned to LEP, so if jet universality, minor issue

Peter SkandsIntroduction to Event Generators 43 Particle Data and Decays

Peter SkandsIntroduction to Event Generators 44 Some Useful References ► T. Sjöstrand: Monte Carlo Generators hep-ph/ ► The Les Houches Guidebook to MC Generators for Hadron Collider Physics hep-ph/ ► The Les Houches Web Repository for BSM Tools: ► PS: A Quick Guide to SUSY Tools: hep-ph/