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Transcript of Introduction to Event Generators Peter Z. Skands Fermilab Theoretical Physics Department...
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
Peter Skands Introduction to Event Generators 3
QQuantumuantumCChromohromoDDynamicsynamics
Peter Skands Introduction to Event Generators 4
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
Peter Skands Introduction to Event Generators 5
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
Peter Skands Introduction to Event Generators 6
The Event Generator Position
Peter Skands Introduction to Event Generators 7
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
Peter Skands Introduction to Event Generators 8
The Monte Carlo Method
Peter Skands Introduction to Event Generators 9
The Generator Landscape
Matrix ElementsThe short-distance physics – Hard Subprocesses
Peter Skands Introduction to Event Generators 11
Cross Sections and Kinematics► Starting point 2n hard scattering ME
► Fold with parton distribution functions pp cross section
Peter Skands Introduction to Event Generators 12
Parton Distribution Functions
Initial conditions non-perturbative
Evolution Perturbative (DGLAP)
http://durpdg.dur.ac.uk/hepdata/pdf.html
Peter Skands Introduction to Event Generators 13
“Hardcoded” Subprocesses
+ The Les Houches interfaces to external packages (tomorrow)
Parton ShowersResummation of Multiple Perturbative QCD and QED Emissions
Peter Skands Introduction to Event Generators 15
QQuantumuantumCChromohromoDDynamicsynamics
e+e¡ ! q¹qg:
Problem 1: bremsstrahlung corrections singular for soft and collinear configurations
Peter Skands Introduction 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 Skands Introduction to Event Generators 17
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
Peter Skands Introduction to Event Generators 18
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
Peter Skands Introduction to Event Generators 19
Coherence
Peter Skands Introduction to Event Generators 20
Ordering Variables
Peter Skands 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
Peter Skands Introduction to Event Generators 22
Initial vs. Final State Showers
► Both controlled by same evolution equation
Peter Skands Introduction to Event Generators 23
QQuantumuantumCChromohromoDDynamicsynamics
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
Peter Skands Introduction 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 Skands 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
Peter Skands Introduction to Event Generators 27
QCD on the Lattice► Linear confinement in “quenched” QCD
Peter Skands Introduction to Event Generators 28
Gluons = Transverse Excitations
Peter Skands 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
Peter Skands Introduction to Event Generators 30
The Iterative Ansatz
Peter Skands 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 …
Useful PYTHIA Parameters
(hardcopies will be available during exercises)
Peter Skands Introduction to Event Generators 33
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
Peter Skands Introduction to Event Generators 34
Utilities
Peter Skands Introduction to Event Generators 35
Hard Processes – Basics
Peter Skands Introduction to Event Generators 36
Hard Processes – Specialized
Peter Skands Introduction to Event Generators 37
Parton Distributions and Scales
Peter Skands Introduction to Event Generators 38
Resonances
Peter Skands Introduction to Event Generators 39
Final-State Showers
Peter Skands Introduction to Event Generators 40
Initial-State Showers (+Interference)
Peter Skands Introduction to Event Generators 41
(Beam Remnants and Multiple Interactions)
Peter Skands Introduction to Event Generators 42
Hadronization► Tuned to LEP, so if jet universality, minor issue
Peter Skands Introduction to Event Generators 43
Particle Data and Decays
Peter Skands 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