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TRANSCRIPT
CERN Summer Student LecturePart 2, 20 July 2012
Introduction toMonte Carlo Techniquesin High Energy Physics
Torbjorn Sjostrand
How are complicated multiparticle events created?
How can such events be simulated with a computer?
Lectures Overview
yesterday: Introduction the Standard ModelQuantum Mechanicsthe role of Event Generators
Monte Carlo random numbersintegrationsimulation
today: Physics hard interactionsparton showersmultiparton interactionshadronization
Generators Herwig, Pythia, SherpaMadGraph, AlpGen, . . .common standards
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 2/40
The Structure of an Event – 1
Warning: schematic only, everything simplified, nothing to scale, . . .
pp/p
Incoming beams: parton densities
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 3/40
The Structure of an Event – 2
pp/p
ug
W+
d
Hard subprocess: described by matrix elements
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 4/40
The Structure of an Event – 3
pp/p
ug
W+
d
c s
Resonance decays: correlated with hard subprocess
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 5/40
The Structure of an Event – 4
pp/p
ug
W+
d
c s
Initial-state radiation: spacelike parton showers
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 6/40
The Structure of an Event – 5
pp/p
ug
W+
d
c s
Final-state radiation: timelike parton showers
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 7/40
The Structure of an Event – 6
pp/p
ug
W+
d
c s
Multiple parton–parton interactions . . .
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 8/40
The Structure of an Event – 7
pp/p
ug
W+
d
c s
. . . with its initial- and final-state radiation
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 9/40
The Structure of an Event – 8
Beam remnants and other outgoing partons
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 10/40
The Structure of an Event – 9
Everything is connected by colour confinement stringsRecall! Not to scale: strings are of hadronic widths
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 11/40
The Structure of an Event – 10
The strings fragment to produce primary hadrons
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 12/40
The Structure of an Event – 11
Many hadrons are unstable and decay further
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 13/40
The Structure of an Event – 12
These are the particles that hit the detector
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 14/40
Hard Processes
Defines the character of the event:QCD, top, Z0, W±, H0, SUSY, ED, TC, . . .
Obtained by perturbation theory:σZ0 = αemM0 + αemαsM1 + αemα2
sM2 + . . .= LO + NLO + NNLO + . . .
Involves subtle cancellations between real and virtual contributions:
Next-to-leading order (NLO) graphs
Torbjorn Sjostrand PPP 2: Phase sapce and matrix elements slide 42/48
These days • LO easy• NLO tough but doable• NNLO only in very few cases
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 15/40
QED Bremsstrahlung
Accelerated electric charges radiate photons ,
see e.g. J.D. Jackson, Classical Electrodynamics.A charge ze that changes its velocity vector from β to β′ radiates a spectrum ofphotons that depends on its trajectory. In the long-wavelength limit it reduces to
limω→0
d2I
dωdΩ=
z2e2
4π2
˛ε∗
„β′
1− nβ′−
β
1− nβ
«˛2where n is a vector on the unit sphere Ω, ω is the energy of the radiated photon, and
ε its polarization.
1 For fast particles radiation collinear with the initial (β) andfinal (β′) directions is strongly enhanced.
2 dN/dω = (1/ω)dI/dω ∝ 1/ω so infinitely many infinitely softphotons are emitted, but the net energy taken away is finite.
3 For ω → 0 the radiation pattern is independent of the spinof the radiator ⇒ universality.
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 16/40
QCD Bremsstrahlung – 1
QCD ≈ QED with e → eγ ⇒ q → qgαem ⇒ (4/3)αs
More precisely:
dPq→qg ≈αs
2π
dQ2
Q2
4
3
1 + z2
1− zdz
where
mass (or collinear) singularity:
dQ2
Q2≈ dθ2
θ2≈ dm2
m2≈
dp2⊥
p2⊥
soft singularity:
z ≈Eq,after
Eq,before= 1− ω
Eq,beforeso
dz
1− z=
dω
ω
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 17/40
QCD Bremsstrahlung – 2
But QCD is non-Abelian so additionally
g → gg similarly divergent
αs(Q2) diverges for Q2 → 0
DGLAP (Dokshitzer–Gribov–Lipatov–Altarelli–Parisi)
dPa→bc =αs(Q
2)
2π
dQ2
Q2Pa→bc(z) dz
Pq→qg =4
3
1 + z2
1− z
Pg→gg = 3(1− z(1− z))2
z(1− z)
Pg→qq =nf
2(z2 + (1− z)2) (nf = no. of quark flavours)
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 18/40
The iterative structure
Generalizes to many consecutive emissions if strongly ordered,Q2
1 Q22 Q2
3 . . . (≈ time-ordered).To cover “all” of phase space use DGLAP in whole regionQ2
1 > Q22 > Q2
3 . . ., although only approximately valid.
Must be clever when you write a shower algorithm.
Iteration givesfinal-stateparton showers:
Need soft/collinear cuts to stay away from nonperturbative physics.Details model-dependent, but around 1 GeV scale.
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 19/40
The Parton-Shower Approach
Showers: approximation method for higher-order matrix elements.
Universality: any matrix element reduces to DGLAP in collinear limit.
2 → n ≈ (2 → 2) ⊕ ISR ⊕ FSR
ISR = Initial-State Radiation: Q2i ∼ −m2 > 0 increasing
FSR = Final-State Radiation: Q2i ∼ m2 > 0 decreasing
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 20/40
Reminder: Radioactive Decay and the Veto Algorithm
Recall discussion on radioactive decays from Lecture 1:
Naively P(t) = c =⇒ N(t) = 1− ct.Wrong! Conservation of probabilitydriven by depletion:a given nucleus can only decay once
CorrectlyP(t) = cN(t) =⇒ N(t) = exp(−ct)i.e. exponential dampeningP(t) = c exp(−ct)
For P(t) = f (t)N(t), f (t) ≥ 0, this generalizes to
P(t) = f (t) exp
(−
∫ t
0f (t ′) dt ′
)which can be Monte Carlo-simulated using the veto algorithm.
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 21/40
The Sudakov form factor
Correspondingly, with Q ∼ 1/t (Heisenberg)
dPa→bc =αs
2π
dQ2
Q2Pa→bc(z) dz
× exp
−∑b,c
∫ Q2max
Q2
dQ ′2
Q ′2
∫αs
2πPa→bc(z
′) dz ′
where the exponent is (one definition of) the Sudakov form factor.
A given parton can only branch once, i.e. if it did not already do so
Note that∑
b,c
∫ ∫dPa→bc ≡ 1 ⇒ convenient for Monte Carlo
(≡ 1 if extended over whole phase space, else possibly nothinghappens before you reach Q0 ≈ 1 GeV).
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 22/40
Matching Showers and Matrix Elements
Showers: approximation to matrix elements (MEs).Shower emissions ≈ real part of higher orders.Shower Sudakovs ≈ virtual (loop) part of higher orders.
Real MEs manageable, virtual MEs tough, so want to combine.Key issue is to avoid doublecounting.
Active and rich field of study, with many methods, e.g.:
Merging: correct first shower emission to MEs,using veto algorithm.
CKKW(-L): generate several multiplicities with real MEs,use shower Sudakovs to include virtual corrections.
MLM: real MEs as above, but veto events that showersmigrate to another jet multiplicity.
MC@NLO: split σNLO into real LO+1 event and real+virtualLO ones.
POWHEG: like merging, with overall rate normalized to σNLO.
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 23/40
Parton Distribution Functions (PDFs)
Hadrons are composite: p = uud + gluons + sea qq.Higher virtuality scale Q ⇒ more partons resolved.fi (x ,Q2) = number density of partons i at momentum fraction xand probing scale Q2.
Initial conditions at small Q20 unknown: nonperturbative.
Resolution dependence perturbative, by DGLAP:
DGLAP (Dokshitzer–Gribov–Lipatov–Altarelli–Parisi)
dfb(x ,Q2)
d(lnQ2)=
∑a
∫ 1
x
dz
zfa(y ,Q2)
αs
2πPa→bc
(z =
x
y
)
σ =
∫ 1
0dx1
∫ 1
0dx2 fi (x1,Q
2) fj(x2,Q2) σ(x1x2E
2cm,Q2)
Continuous ongoing activity to provide best overall fit to data,consistent with theoretical evolution: CTEQ, MSTW, NNPDF, . . .
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 24/40
PDF examples
Convenient plotting interface:http://hepdata.cedar.ac.uk/pdf/pdf3.html
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 25/40
What is Pileup?
Protons in LHC collected in bunches.1 bunch ≈ 1.5× 1011 protons.Two bunches passing through each other ⇒ several pp collisions.Current LHC machine conditions ⇒ µ = 〈n〉 ≈ 20.Pileup introduces no new physics, so is uninteresting here.
But analogy: a proton is a bunch of partons (quarks and gluons)
so several parton–parton collisions when two protons cross .
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 26/40
MultiParton Interactions (MPIs)
Many parton-parton interactionsper pp event: MPI.
Most have small p⊥,∼ 2 GeV⇒ not visible as separate jets,but contribute to event activity.
Solid evidence that MPIs playcentral role for event structure.
Problem:
σint =
∫∫∫dx1 dx2 dp2
⊥ f1(x1, p2⊥) f2(x2, p
2⊥)
dσ
dp2⊥
= ∞
since∫
dx f (x , p2⊥) = ∞ and dσ/dp2
⊥ ≈ 1/p4⊥ →∞ for p⊥ → 0.
Requires empirical dampening at small p⊥,owing to colour screening (proton finite size).
Many aspects beyond pure theory ⇒ model building.
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 27/40
Hadronization
Nonperturbative =⇒ not calculable from first principles!
Model building = ideology + “cookbook”
Two common approaches:
String fragmentation:most ideological
Cluster fragmentation:simplest
Both contain manyparameters to bedetermined from data,preferably LEP e+e− →γ∗/Z0 → qq/qqg/ . . .
DELPHI Interactive AnalysisRun: 39265Evt: 4479
Beam: 45.6 GeV
Proc: 4-May-1994
DAS : 5-Jul-1993 14:16:48
Scan: 3-Jun-1994
TD TE TS TK TV ST PA
Act
Deact
95(145) 0
( 0)
173(204) 0
( 20)
0( 0) 0
( 0)
38( 38) 0
( 42)
0( 0) 0
( 0)
0( 0) 0
( 0)
0( 0) 0
( 0)
X
Y
Z
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 28/40
The Lund String Model
In QCD, for large charge separation, field lines seem to becompressed to tubelike region(s) ⇒ string(s)
by self-interactions among soft gluons in the “vacuum”.
Gives linear confinement with string tension:F (r) ≈ const = κ ≈ 1 GeV/fm ⇐⇒ V (r) ≈ κr
String breaks into hadrons along its length,with roughly uniform probability in rapidity,by formation of new qq pairs that screen endpoint colours.
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 29/40
The Lund Gluon Picture
Gluon = kink on string
Force ratio gluon/ quark = 2,cf. QCD NC/CF = 9/4, → 2 for NC →∞No new parameters introduced for gluon jets!
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 30/40
The HERWIG Cluster Model
1 Introduce forced g → qq branchings2 Form colour singlet clusters3 Clusters decay isotropically to 2 hadrons according to
phase space weightTorbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 31/40
Event Generators
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 32/40
The Generator LandscapeGenerator Landscape
Hard Processes
Resonance Decays
Parton Showers
Underlying Event
Hadronization
Ordinary Decays
General-Purpose
HERWIG
PYTHIA
SHERPA
......
Specialized
MadGraph, AlpGen, . . .
HDECAY, . . .
Ariadne/LDC, VINCIA, . . .
PHOJET/DPMJET
none (?)
TAUOLA, EvtGen
specialized often best at given task, but need General-Purpose coreSpecialized often best at given task, but need General-Purpose core
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 33/40
The Workhorses: What are the Differences?
HERWIG, PYTHIA and SHERPA offer convenient frameworksfor LHC physics studies, but with slightly different emphasis:
PYTHIA (successor to JETSET, begun in 1978):• originated in hadronization studies: the Lund string• leading in development of MPI for MB/UE• pragmatic attitude to showers & matching
HERWIG (successor to EARWIG, begun in 1984):• originated in coherent-shower studies (angular ordering)• cluster hadronization & underlying event pragmatic add-on• large process library with spin correlations in decays
SHERPA (APACIC++/AMEGIC++, begun in 2000):• own matrix-element calculator/generator• extensive machinery for CKKW ME/PS matching• hadronization & min-bias physics under development
PYTHIA & HERWIG originally in Fortran, now all C++
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 34/40
A Commercial: MCnet
? “Trade Union” of (QCD) Event Generator developers ?Collects HERWIG, SHERPA and PYTHIA.Also ThePEG, ARIADNE, VINCIA, . . . ,
generator validation (RIVET) and tuning (PROFESSOR)(CERN, Durham, Lund, Karlsruhe, UC London, + associated).
? Funded by EU Marie Curie training network 2007–2010 ?New applications for continued activities: no luck so far.
? Annual Monte Carlo school: ?Next: MCnet-LPCC, 23–27 July 2012, CERN
+ Lectures on QCD & Generators at many other schools +Much relevant material at http://www.montecarlonet.org/
MCPLOTS: repository of comparisons between generators anddata, based on RIVET, see http://mcplots.cern.ch/
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 35/40
The Bigger Picture
Need standardized interfaces: see next!
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 36/40
PDG Particle Codes
A. Fundamental objects
1 d 11 e− 21 g
2 u 12 νe 22 γ 32 Z′0
3 s 13 µ− 23 Z0 33 Z′′0
4 c 14 νµ 24 W+ 34 W′+
5 b 15 τ− 25 h0 35 H0 37 H+
6 t 16 ντ 36 A0 39 Graviton
add − sign for antiparticle, where appropriate
B. Mesons100 |q1|+ 10 |q2|+ (2s + 1) with |q1| ≥ |q2|C. Baryons1000 q1 + 100 q2 + 10 q3 + (2s + 1)with q1 ≥ q2 ≥ q3, or Λ-like q1 ≥ q3 ≥ q2
. . . and many more
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 37/40
Interfaces
LHA: Les Houches Accord,transfers info on processes, cross sections, parton-level events,. . . , via two Fortran commonblocks
LHEF: Les Houches Event Files,same information, but stored as a single plaintext file
HepMC: output of complete generated events(intermediate stages and final state with hundreds of particles)for subsequent detector simulation or analysis
SLHA: SUSY Les Houches Accord,file with info on SUSY (or other BSM) model:parameters, masses, mixing matrices, branching ratios, . . . .
LHAPDF: uniform interface to PDF parametrizations
Binoth LHA: one-loop virtual corrections
FeynRules: nascent standard for input of Lagrangian andoutput of Feynman rules
. . .Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 38/40
The Road Ahead
Event generators crucial since the start of LHC studies.
Qualitatively predictive already 25 years ago.
Quantitatively steady progress, continuing today:? continuous dialogue with experimental community,? more powerful computational techniques and computers,? new ideas.
As LHC needs to study more rare phenomena and more subtleeffects, generators must keep up by increased precision.
But it often happens that the physics simulations provided bythe Monte Carlo generators carry the authority of data itself.They look like data and feel like data, and if one is not carefulthey are accepted as if they were data.
J.D. Bjorkenfrom a talk given at the 75th anniversary celebration of the Max-Planck Institute of Physics, Munich, Germany,
December 10th, 1992. As quoted in: Beam Line, Winter 1992, Vol. 22, No. 4
Torbjorn Sjostrand Introduction to Monte Carlo Techniques in High Energy Physics – lecture 2 slide 39/40