Introduction to Event Generators Peter Z. Skands Fermilab Theoretical Physics Department (Significant parts adapted from T. Sjöstrand (Lund U & CERN) )

Introduction to Event Generators

Peter Z. SkandsPeter Z. Skands

Fermilab Theoretical Physics Department Fermilab Theoretical Physics Department

(Significant parts adapted from T. Sjöstrand (Lund U & (Significant parts adapted from T. Sjöstrand (Lund U & CERN) )CERN) )

Topical Meeting on LHC Physics, HRI, Allahabad, Dec 2006

Peter Skands Introduction 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


QQuantumuantumCChromohromoDDynamicsynamics


D. B. Leinweber, hep-lat/0004025

Anti-Triplet

Triplet

pbar beam remnant

p beam remnantbbar

from

tbar

deca

y

b from

t d

ecay

qbar fro

m W

q from W

hadroniza

tion

?

q from W

In reality, this all happens on top of each other.

(only possible exception: long-lived colour singlet)

The (QCD) Landscape


Non-perturbativehadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton, kaon/pion, ...

Soft Jets + Jet StructureMultiple collinear/soft emissions (initial and final state brems radiation), Underlying Event (multiple perturbative 22 interactions + … ?), semi-hard separate brems jets

Resonance Masses …

Hard Jet TailHigh-pT wide-angle jets

& W

idths

+ “UNPHYSICAL” SCALES:+ “UNPHYSICAL” SCALES:

• QF , QR : Factorisation(s) & Renormalisation(s)

sInclusive

Exclusive

Hadron Decays

Collider Energy Scales


The Event Generator Position


Monte Carlo GeneratorsLarge-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


The Monte Carlo Method


The Generator Landscape

Matrix ElementsThe short-distance physics – Hard Subprocesses


Cross Sections and Kinematics► Starting point 2n hard scattering ME

► Fold with parton distribution functions pp cross section


Parton Distribution Functions

Initial conditions non-perturbative

Evolution Perturbative (DGLAP)

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


“Hardcoded” Subprocesses

+ The Les Houches interfaces to external packages (tomorrow)

Parton ShowersResummation of Multiple Perturbative QCD and QED Emissions



e+e¡ ! q¹qg:

Problem 1: bremsstrahlung corrections singular for soft and collinear configurations


► 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


Problem: Need to get both

soft and hard emissions

“right” “Matching”

(tomorrow)

Bremsstrahlung Example: SUSY @ 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 GeV Plehn, Rainwater, PS (2005)

p? ;jet


1. 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 !

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) = N1 exp(-|A|2 t)

Δ(Q12,Q2

2)

The Sudakov Form Factor

¢ (t1;t2) = exp³¡

Rt2

t1dtjAj2

´The Sudakov Form Factor:

instantaneous decay probability: dΔ/dt

Sudakov = generating function for parton shower

Random numbers sequence of parton ‘decays’ = branchings


Coherence


Ordering Variables


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


Initial vs. Final State Showers

► Both controlled by same evolution equation



e+e¡ ! q¹qg:

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

HadronizationModels 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)


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


QCD on the Lattice► Linear confinement in “quenched” QCD


Gluons = Transverse Excitations


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


The Iterative Ansatz


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)


Overview1. 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


Utilities


Hard Processes – Basics


Hard Processes – Specialized


Parton Distributions and Scales


Resonances


Final-State Showers


Initial-State Showers (+Interference)


(Beam Remnants and Multiple Interactions)


Hadronization► Tuned to LEP, so if jet universality, minor issue


Particle Data and Decays


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

Documents

Introduction to Event Generators Peter Z. Skands Fermilab Theoretical Physics Department (Significant parts adapted from T. Sjöstrand (Lund U & CERN) )