1. Introduction to Monte Carlo Event Generators
Rachid Mazini
Academia Sinica, Taiwan
6th School for LHC Physics NCP Islamabad, Pakistan
21-31 August 2017

2. Outline Hadron-level event generation Parton showering
Hadronization and underlying event
Examples of results
MC Simulation
Introduction to MC Event Generators
R. Mazini Academia Sinica

3. A high-mass dijet event
Mjj = 5.15 TeV
CMS PAS EXO
Introduction to MC Event Generators
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4. LHC dijet p Hard process Introduction to MC Event Generators
R. Mazini Academia Sinica

5. LHC dijet p Hard process Parton showers
Introduction to MC Event Generators
R. Mazini Academia Sinica

6. LHC dijet p Hard process Parton showers Underlying event
Introduction to MC Event Generators
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7. LHC dijet p Hard process Parton showers Underlying event Confinement
Introduction to MC Event Generators
R. Mazini Academia Sinica

8. )
LHC dijet
quark jet ) p
beam jet
beam jet p
Hard process Parton showers Underlying event Confinement Hadronization
quark jet
Introduction to MC Event Generators )
R. Mazini Academia Sinica

9. Theoretical Status p Hard process
Exact fixed-order perturbation theory p
Hard process
Introduction to MC Event Generators
R. Mazini Academia Sinica

10. Theoretical Status p Hard process Parton showers
Exact fixed-order perturbation theory Approximate all-order perturbation theory p
Hard process
Parton showers
Introduction to MC Event Generators 10
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11. Theoretical Statusquark jet)
Theoretical Statusquark jet
Exact fixed-order perturbation theory Approximate all-order perturbation theory
Semi-empirical )
local models only p
beam jet
beam jet p
Hard process
Parton showers
Underlying event
Confinement Hadronization
quark jet
Introduction to MC Event Generators )
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12. QCD Factorization
momentum fractions
parton distributions
at scale µ2
hard process cross section
Jet formation and underlying event take place over a much longer time scale, with unit probability
Hence they cannot affect the cross section
Scale dependences of parton distributions and hard process cross section are perturbatively calculable, and cancel order by order
Introduction to MC Event Generators
R. Mazini Academia Sinica

13. Parton Shower 0 1
E3 3
hard process
Ei+1
z = Ei E0 E1
E2 2
Shower = sequence of emissions with decreasing angles and energies
Approximation: keep only contributions  1/
For very small energy and/or angle, emission is “unresolvable”
Introduction to MC Event Generators
R. Mazini Academia Sinica

14. Parton Shower Ei+1 hard process E0 E1 E3 ✓0 ✓1 ✓3 ✓2E2 ✓4 E4 z = Ei
Introduction to MC Event Generators
R. Mazini Academia Sinica

15. Parton Shower Evolution
hard process ✓0 ✓1
Ei+1
z = ✓3
✓2E2
✓4 E4 Ei E0 E1 E3 ✓0
4 1 + z2
H A D
Pq!q (z) = 3 1 z
R O
(E1, ✓1)
N I Z A T I O N
(E2, ✓2)
(E3, ✓3)
(E4, ✓4)
E✓ < Qmin E0
Introduction to MC Event Generators 15
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16. Parton Shower Evolution
hard process ✓0 ✓1
Ei+1
z = ✓3
✓2E2
✓4 E4 Ei E0 E1 E3 ✓0
4 1 + z2
H A D
Pq!q (z) = 3 1
Pg!g (z) = z
R O
(E0 - E1, ✓1)
(E1, ✓1)
N I Z A T I O N ✓
1 + z + (1 - z) 3
z(1 - z)
4 4
(E2, ✓2)
(E3, ✓3) 1 2
(E4, ✓4) ⇥z 2 2⇤
Pg!q =
+ (1 - z)
E✓ < Qmin E E0
Introduction to MC Event Generators
R. Mazini Academia Sinica

17. Hadronization Models
In parton shower, relative transverse momenta evolve from a high scale Q towards lower values
At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed
Before that, at scales ~ few x LQCD, there is universal preconfinement of colour
Colour, flavour and momentum flows are only locally redistributed by hadronization
Introduction to MC Event Generators
R. Mazini Academia Sinica

18. Hadronization Models
In parton shower, relative transverse momenta evolve from a high scale Q towards lower values
At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed
Before that, at scales ~ few x LQCD, there is universal preconfinement of colour
Colour, flavour and momentum flows are only locally redistributed by hadronization
Introduction to MC Event Generators
R. Mazini Academia Sinica

19. String Hadronization Model
In parton shower, relative transverse momenta evolve from a high scale Q towards lower values
At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed
Before that, at scales ~ few x LQCD, there is universal preconfinement of colour
Colour flow dictates how to connect hadronic string (width ~ few x LQCD) with shower
Introduction to MC Event Generators
R. Mazini Academia Sinica

20. String Hadronization Model
In parton shower, relative transverse momenta evolve from a high scale Q towards lower values
At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed
Before that, at scales ~ few x LQCD, there is universal preconfinement of colour
Colour flow dictates how to connect hadronic string (width ~ few x LQCD) with shower
Introduction to MC Event Generators
R. Mazini Academia Sinica

21. String Hadronization Model
At short distances (large Q), QCD is like QED: colour field lines spread out (1/r potential)
At long distances, gluon self-attraction gives rise to colour string (linear potential, quark confinement)
Intense colour field induces quark-antiquark pair creation: hadronization + –
Introduction to MC Event Generators
R. Mazini Academia Sinica

22. Cluster Hadronization Model
In parton shower, relative transverse momenta evolve from a high scale Q towards lower values
At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed
Before that, at scales ~ few x LQCD, there is universal preconfinement of colour
Decay of preconfined clusters provides a direct basis for hadronization
Introduction to MC Event Generators
R. Mazini Academia Sinica

23. Cluster Hadronization Model
In parton shower, relative transverse momenta evolve from a high scale Q towards lower values
At a scale near LQCD~200 MeV, perturbation theory breaks down and hadrons are formed
Before that, at scales ~ few x LQCD, there is universal preconfinement of colour
Decay of preconfined clusters provides a direct basis for hadronization
Introduction to MC Event Generators
R. Mazini Academia Sinica

24. Cluster Hadronization Model
Mass distribution of preconfined clusters is universal
Phase-space decay model for most clusters
High-mass tail decays anisotropically (string-like)
Introduction to MC Event Generators
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25. Hadronization Status No fundamental progress since 1980s
Available non-perturbative methods (lattice, AdS/ QCD, ...) are not applicable
Less important in some respects in LHC era ✤
Jets, leptons and photons are observed objects, not hadrons
But still important for detector effects ✤ ✤
Jet response, heavy-flavour tagging, lepton and photon isolation, ...
Introduction to MC Event Generators
R. Mazini Academia Sinica

26. Underlying Event (MPI)
Multiple parton interactions in same collision ✤
Depends on density profile of proton
Assume QCD 2-to-2 secondary collisions ✤
Need cutoff at low pT
Need to model colour flow ✤
Colour reconnections are necessary
Introduction to MC Event Generators
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27. Sample of Event Generator Results
Introduction to MC Event Generators
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28. MC Event Generators HERWIG PYTHIA SHERPA
Angular-ordered parton shower, cluster hadronization v6 Fortran; Herwig++ Herwig 7
PYTHIA
kt-ordered parton shower, string hadronization v6 Fortran; v8 C++
SHERPA
Dipole-type parton shower, cluster hadronization
C++
“General-purpose event generators for LHC physics”,
A Buckley et al., arXiv: , Phys. Rept. 504(2011)145
Introduction to MC Event Generators
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29. Jets
Introduction to MC Event Generators
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30. Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3
Jet pT
7000 GeV pp
Jets
7000 GeV pp
Jets
d/dp [pb/GeV]
Rivet 1.8.3,  3M events
d/dp [pb/GeV]
107
Rivet 1.8.3,  3M events
106
Jet Transverse Momentum (anti
-k (0.4))
Jet Transverse Momentum (anti-k (0.4)) T
106 T
ATLAS
ATLAS T
105
Herwig++ (Def) Pythia 8 (Def) T
105
Herwig++ (Def) Pythia 8 (Def)
Sherpa (Def)
Sherpa (Def)
104
104
103
103
102
102 10 10 1
mcplots.cern.ch
mcplots.cern.ch 1
10-1
ATLAS_2011_S
ATLAS_2011_S
Herwig , Pythia 8.176, Sherpa 1.4.3
10-1
Herwig , Pythia 8.176, Sherpa 1.4.3
10-2
200
800
p (2nd jet) [GeV] T
p (leading jet) [GeV] T
Ratio to ATLAS
Ratio to ATLAS
1.5
1.5 1 1
0.5
0.5
Leading jet
800
Second jet
Introduction to MC Event Generators
R. Mazini Academia Sinica

31. Herwig++ 2.6.3, Pythia 8.176, Sherpa 1.4.3
Jet pT
7000 GeV pp
Jets
7000 GeV pp
Jets
d/dp [pb/GeV]
Rivet 1.8.3,  3M events
d/dp [pb/GeV]
104
Rivet 1.8.3,  3M events
106
105
104
103
102
Jet Transverse Momentum (anti-k (0.4))
Jet Transverse Momentum (anti-k (0.4)) T T
ATLAS
Herwig++ (Def)
Pythia 8 (Def) Sherpa (Def)
ATLAS
Herwig++ (Def)
Pythia 8 (Def) Sherpa (Def)
103 T T
102 10 10 1
10-1
10-2
10-3
10-4 1
mcplots.cern.ch
mcplots.cern.ch
ATLAS_2011_S
10-1
ATLAS_2011_S
Herwig , Pythia 8.176, Sherpa 1.4.3
Herwig , Pythia 8.176, Sherpa 1.4.3
100
p (3rd jet) [GeV] T
200
p (4th jet) [GeV] T
Ratio to ATLAS
Ratio to ATLAS
1.5
1.5 1 1
0.5
0.5
100
200
300
400
500
100
150
200
Extra jets from parton showers
Introduction to MC Event Generators
R. Mazini Academia Sinica

32. Jet event shapes Tc ⌘ max Âi |~p?,i · nˆ T| Âi |~p?,i ⇥ nˆ T,C |
7000 GeV pp
Jets
7000 GeV pp
Jets
dN/d ln(1-T ) C
Rivet 1.8.3,  4.1M events )
m,C
Rivet 1.8.3,  3M events
Central Transverse Thrust (125 < p < 200)
CMS
dN/d ln(T
Central Transverse Minor (90 < p < 125) 1
0.2
CMS
Herwig++ (Def)
Pythia 8 (Def) Sherpa (Def)
Herwig++ (Def) Pythia 8 (Def) Sherpa (Def)
1/N
1/N
0.15
0.1
10-1
0.05
mcplots.cern.ch
mcplots.cern.ch
CMS_2011_S
Herwig , Pythia 8.176, Sherpa 1.4.3
-10 -5
CMS_2011_S
Herwig , Pythia 8.176, Sherpa 1.4.3
-4 -2
10-2 -6
ln(1-T )
ln(T ) C
m,C
Ratio to CMS
Ratio to CMS
1.5
1.5 1 1
0.5
0.5
-10 -5 -6 -4 -2
Âi |~p?,i · nˆ T|
Âi |~p?,i ⇥ nˆ T,C |
Tc ⌘ max
Tm,C ⌘
i p?,i
nˆ T Â
i p?,i Â
Introduction to MC Event Generators
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33. Jet profile pT,i pT,i  1 dr r(r) = Â
1960 GeV ppbar
Jets
7000 GeV pp
Jets
(r/R)
Rivet 1.8.3,  5.8M events
(r)
Rivet 1.8.3,  577k events
Differential jet shape 
(r/R) (186 < p < 208) T
Differential jet shape (r/R)
CDF
Herwig++ (Def)
Pythia 8 (Def) Sherpa (Def)
ATLAS
Herwig++ (Def)
Pythia 8 (Def) Sherpa (Def) 10 10 1 1
mcplots.cern.ch
mcplots.cern.ch
10-1
10-1
CDF_2005_S
Herwig , Pythia 8.176, Sherpa 1.4.3
ATLAS_2011_S
Herwig , Pythia 8.176, Sherpa 1.4.3
0.5 1
0.2
0.4
0.6
r/R r
Ratio to CDF
Ratio to ATLAS
1.5
1.5 1 1
0.5
0.5
0.5 1
0.2
0.4
0.6 
rb ra R Â
ra <ri<rb
pT,i 1 dr
r(r) = Â
ri<R
pT,i
Introduction to MC Event Generators
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34. Jet multiplicity Multijets W+jets N jet Njet
7000 GeV pp
Jets
7000 GeV pp W
 [pb]
108
Rivet 1.8.3,  2.9M events
(W +  N jets) [pb]
Rivet 1.8.3,  6.8M events
Jet multiplicity (anti-k (0.4))
Jet multiplicity ((E >20,|_j|<2.8,E >20,|_e|<2.47 ,p ^>25,M_T>40,R >0.5)) * T
Tj Te T  j
107
ATLAS
ATLAS
jet
Herwig++ (Def) Pythia 8 (Def)
104
Herwig++ (Def) Pythia 8 (Def)
106
Sherpa (Def)
Sherpa (Def)
105
103
104
103
mcplots.cern.ch
102
mcplots.cern.ch
102
ATLAS_2011_S
Herwig , Pythia 8.176, Sherpa 1.4.3
ATLAS_2010_S
Herwig , Pythia 8.176, Sherpa 1.4.3
1 2 10 2 4 6 3
N jet
Njet
Ratio to ATLAS
Ratio to ATLAS
1.5
1.5 1 1
0.5
0.5 2 4 6 1 2 3
Multijets
W+jets
Introduction to MC Event Generators
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35. Hadrons from Z0 decay 10-1 Nch Nch ⇡± ⇡0 K± K0 D0,± B0,± ⌃± ⌘0
Hadron multiplicities in e+e- at 91 GeV
multiplicity
Nch ⇡± ⇡0
LEP, SLD
Pythia 8.145
Sherpa 1.2.3
Herwig
10 1 K± K0 ⌘ 1
p K⇤0 ⇤
D0,±
B0,± ⌘0 ⌃±
10-1
1.3
1.2
1.1
1.0
0.9
0.8
0.7
MC/data
Nch 1 2 5
mass [GeV]
Introduction to MC Event Generators
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36. Underlying Event Introduction to MC Event Generators
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37. Underlying Event Transverse charged particle density
900 GeV pp
Underlying Event
7000 GeV pp
Underlying Event
d2 N/dd
Rivet 1.8.3,  7.3M events
d N chg/dd
Rivet 1.8.3,  6.8M events
0.9 3
Average Charged Particle Density (TRNS)
Average Charged Particle Density (TRNS) (|
| < 2.5, p > 0.1 GeV/c) T
0.8
CMS
ATLAS
Herwig++ (Def)
2.5
Herwig++ (Def) 2
Pythia 8 (Def) Sherpa (Def)
Pythia 8 (Def) Sherpa (Def)
0.7
leading jet
0.6 2
0.5 f Df
1.5
0.4
towards
|Df| < 600
0.3 1
mcplots.cern.ch
mcplots.cern.ch
0.2
transverse
600 < |Df| < 1200
transverse
600 < |Df| < 1200
CMS_2011_S
Herwig , Pythia 8.176, Sherpa 1.4.3
ATLAS_2010_S
Herwig , Pythia 8.176, Sherpa 1.4.3
0.5
0.1
10 20
p (leading track-jet) [GeV] T 20
away
|Df| > 1200
p (leading track) [GeV] T
Ratio to CMS
Ratio to ATLAS
1.5
1.5 1 1
0.5
0.5 10 20 5 10 15 20
Transverse charged particle density
Introduction to MC Event Generators
R. Mazini Academia Sinica

38. Underlying Event Transverse mean pT
900 GeV pp
Underlying Event
7000 GeV pp
Underlying Event
 p 
Rivet 1.8.3,  7.3M events
 p 
Rivet 1.8.3,  6.8M events T T
Average p vs p (TRNS) (|| < 2.5, p > 0.5 GeV/c)
T T1 T
1.6
Average p vs p (TRNS) (|| < 2.5, p > 0.5 GeV/c)
T T1 T
1.4
ATLAS
ATLAS
Herwig++ (Def) Pythia 8 (Def) Sherpa (Def)
Herwig++ (Def)
1.4
Pythia 8 (Def)
Sherpa (Def)
leading jet
1.2
1.2 1 1 f Df
0.8
towards
|Df| < 600
0.8
mcplots.cern.ch
mcplots.cern.ch
0.6
transverse
600 < |Df| < 1200
transverse
600 < |Df| < 1200
0.6
ATLAS_2010_S
Herwig , Pythia 8.176, Sherpa 1.4.3
ATLAS_2010_S
Herwig , Pythia 8.176, Sherpa 1.4.3
0.4
0.4 2
4 6 8 10 20
away
|Df| > 1200
p (leading track) [GeV] T
p (leading track) [GeV] T
Ratio to ATLAS
Ratio to ATLAS
1.5
1.5 1 1
0.5
0.5 2 4 6 8 10 5 10 15 20
Transverse mean pT
Introduction to MC Event Generators
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39. Vector Bosons Introduction to MC Event Generators
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40. Z0 pT Absolute normalization Normalized to data
1960 GeV ppbar
Z (Drell-Yan)
7000 GeV pp
Z (Drell-Yan)
d/dp (Z) [pb/GeV]
Rivet 1.8.3,  7.9M events
1/d/dp [GeV-1]
Rivet 1.8.3,  7M events
103
p (Z) (muon channel)
p (Z) (electron channel, dressed) T T 1
102 D0
Herwig++ (Def)
Pythia 8 (Def) Sherpa (Def) T
ATLAS
Herwig++ (Def)
Pythia 8 (Def) Sherpa (Def) T
10-1 10 1
10-2
10-1
10-3
10-2
10-4
10-3
mcplots.cern.ch
mcplots.cern.ch
10-5
10-4
D0_2010_S
Herwig , Pythia 8.176, Sherpa 1.4.3
ATLAS_2011_S
Herwig , Pythia 8.176, Sherpa 1.4.3
300
300
p (Z) [GeV] T
p (ee) [GeV] T
Ratio to D0
Ratio to ATLAS
1.5
1.5 1 1
0.5
0.5
100
200
300
100
200
300
Introduction to MC Event Generators
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41. Limitations of LO+parton shower•
Hard process: qq¯  Z0/W±
pT(Z)
pT(jet 1)
pT(jet 2)
need next-to-LO (NLO) need multijet merging
Leading-order (LO) normalization Worse for high pT and/or extra jets •
Introduction to MC Event Generators
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42. Latest Z0+jets (13 TeV)
MG5_aMC+Py8 … = NLO+multijet merged event generators
ATLAS, EPJC77(2017)361
Introduction to MC Event Generators
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43. Monte Carlo Simulation in HEP analysis
Physics process and detector simulation
data
storage
Simulation of many (billions) of events
simulate physics process
e.g. p p -> Z or p p -> H
plus the detector response to the produced particles
understand detector response and analysis parameters (lost particles, resolution, efficiencies, backgrounds )
and compare to real data
Note : simulations present from beginning to end of experiment, needed to make design choices
Exactly the same steps as
for the data

44. Monte Carlo Simulation

45. Monte Carlo Simulation: The Dream!

46. Monte Carlo Simulation: The reality

47. Summary Parton shower keeps large small-angle contributions
Shower gives preconfinement of colour
This allows local model of hadronization
String and cluster models both still viable
Underlying event due to multiple interactions
LO+PS event generators underestimate multijets
Further improvements (NLO+merging) now used
Introduction to MC Event Generators
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