# Presentation: 513330

## 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

## 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

- Peter Skands

## QuantumChromoDynamics

- QuantumChromoDynamics

- Introduction to Event Generators

- Peter Skands

## The (QCD) Landscape

- D. B. Leinweber, hep-lat/0004025

- In reality, this all happens on top of each other.
- (only possible exception: long-lived colour singlet)

- Introduction to Event Generators

- Peter Skands

## Collider Energy Scales

- 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-pT wide-angle jets

-  & Widths

- + “UNPHYSICAL” SCALES:
-  QF , QR : Factorisation(s) & Renormalisation(s)

- s

**Inclusive**

**Exclusive**

- Hadron Decays

- Introduction to Event Generators

- Peter Skands

## The Event Generator Position

- Introduction to Event Generators

- Peter Skands

## 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
- 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

- Introduction to Event Generators

- Peter Skands

## The Monte Carlo Method

- Introduction to Event Generators

- Peter Skands

## The Generator Landscape

- Introduction to Event Generators

- Peter Skands

## Matrix Elements

- The short-distance physics – Hard Subprocesses

## Cross Sections and Kinematics

- Starting point 2n hard scattering ME

- Fold with parton distribution functions  pp cross section

- Introduction to Event Generators

- Peter Skands

## Parton Distribution Functions

**Initial conditions non-perturbative**

**Evolution Perturbative (DGLAP)**

- http://durpdg.dur.ac.uk/hepdata/pdf.html

- Introduction to Event Generators

- Peter Skands

## “Hardcoded” Subprocesses

**+ **The Les Houches interfaces to external packages **(tomorrow)**

- Introduction to Event Generators

- Peter Skands

## Parton Showers

- Resummation of Multiple Perturbative QCD and QED Emissions

## QuantumChromoDynamics

- QuantumChromoDynamics

- Problem 1: bremsstrahlung corrections singular for soft and collinear configurations

- Introduction to Event Generators

- Peter Skands

## 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

- 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

- Introduction to Event Generators

- Peter Skands

## Bremsstrahlung Example: SUSY @ LHC

- Problem: Need to get both
- soft and hard emissions
- “right”  “Matching”
- (tomorrow)

- Comparison:
- Matrix Elements with  explicit jets.
- Parton Showers / Resummation to infinite order in singular limits

- Introduction to Event Generators

- Peter Skands

## 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 ) < 0 for 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) 

- Suppose N1 nuclei at time t = t1
- Decay probability per unit time = |A|2
- dN/dt = |A|2  N(t) = N1 (1 - |A|2t ) **< 0** for 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)

**Δ****(Q****1****2****,Q****2****2****)**

- The Sudakov Form Factor

-  Sudakov = generating function for parton shower

**Random numbers**** ******** ****sequence of parton ‘decays’ ****=**** branchings**

- Introduction to Event Generators

- Peter Skands

## Coherence

- Introduction to Event Generators

- Peter Skands

## Ordering Variables

- Introduction to Event Generators

- Peter Skands

## 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

- Peter Skands

## Initial vs. Final State Showers

- Both controlled by same evolution equation

- Introduction to Event Generators

- Peter Skands

## QuantumChromoDynamics

- QuantumChromoDynamics

- 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**

- Introduction to Event Generators

- Peter Skands

## Hadronization

- Models of Non-Perturbative Effects

## 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

- Peter Skands

## 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

- Peter Skands

## QCD on the Lattice

- Linear confinement in “quenched” QCD

- Introduction to Event Generators

- Peter Skands

## Gluons = Transverse Excitations

- Introduction to Event Generators

- Peter Skands

## 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

- Peter Skands

## The Iterative Ansatz

- Introduction to Event Generators

- Peter Skands

## 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

- Peter Skands

## Useful PYTHIA Parameters

- (hardcopies will be available during exercises)

## 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

- Peter Skands

## Utilities

- Introduction to Event Generators

- Peter Skands

## Hard Processes – Basics

- Introduction to Event Generators

- Peter Skands

## Hard Processes – Specialized

- Introduction to Event Generators

- Peter Skands

## Parton Distributions and Scales

- Introduction to Event Generators

- Peter Skands

## Resonances

- Introduction to Event Generators

- Peter Skands

## Final-State Showers

- Introduction to Event Generators

- Peter Skands

## Initial-State Showers (+Interference)

- Introduction to Event Generators

- Peter Skands

## (Beam Remnants and Multiple Interactions)

- Introduction to Event Generators

- Peter Skands

## Hadronization

- Tuned to LEP, so _*if*_ jet universality, minor issue

- Introduction to Event Generators

- Peter Skands

## Particle Data and Decays

- Introduction to Event Generators

- Peter Skands

## 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](http://www.ippp.dur.ac.uk/montecarlo/BSM)_
- PS: A Quick Guide to SUSY Tools:
- hep-ph/0601103

- Introduction to Event Generators

- Peter Skands