Introduction to Monte-Carlo Event Generatorshome.thep.lu.se/~jbellm/VSOP/MONTE_CARLO_1_BELLM... · 2018. 8. 30. · Introduction to Monte-Carlo Event Generators — 24th Vietnam School

Introduction to Monte-Carlo

Event Generators —

24th Vietnam School of Physics

— Quy Nhon, Vietnam

Johannes Bellm, Lund University , 28.-30.5.2018

Outline: - Why MCEG? - Birds hit by balls - Modelling Collider Physics - The steps it needs..

Short notice lectures!!

I jumped in ans accepted to give this lectures two weeks ago…

Therefore these lectures are written in a hurry!! The last lecture is not even ready..

Many of the pictures/slides are from other lectures from:

Stefan Gieseke, Stefan Höche, Frank Krauss, Jonas Lindert Leif Lönnblad, Mike Seymour, Andrzej Siodmok, Torbjörn Sjöstrand

So I have to thank those!!


Tutorials

I tried to put some simplified examples together to allow you to get your hands on and see how the things I will explain actually work in practice.

Usually the installation and getting everything to work takes 20-40% of the tutorials. Let’s hope it will be better…

In the first parts we will use python notebooks to do some examples.

In the end I will make a live presentation of Herwig and how to use it.


Further Reading:

Books: The Black Book of Quantum Chromodynamics (Campbell,Huston,Krauss, 2018) QCD and Colliders Physics (Ellis, Stirling, Webber, 1996) Basics of Perturbative QCD (Dokshitzer, Khoze, Mueller, Troyan, 1991)

Other: Buckley et al.: General-purpose event generators for LHC physics Höche: Introduction to parton-shower event generators Skands: Introduction to QCD


http://inspirehep.net/record/884202



What topic am I trying to cover?

symmetrymagazine.org

…common words in the titles of the 2012 top 40 papers.


https://www.symmetrymagazine.org/article/may-2013/the-top-40-physics-hits-of-2012

symmetrymagazine.org

What topic am I trying to cover?


https://www.symmetrymagazine.org/article/may-2013/the-top-40-physics-hits-of-2012

Event Simulation

picture: arXiv:1411.4085

Goal: Describe Collider events as realistic as possible.


https://arxiv.org/pdf/1411.4085.pdf

BirdsGoal: Learn something about birds.

Properties:

Picture from: wikipedia.org/wiki/Bird

• average Size • typical Color • max. Speed • average Age • average Weight

• preferred Food • Relation between Species • Availability to flight • …

Measurement: • Design/Reuse methods to quantify the known properties.

• E.g. use same apparatus was used to quantify the weight of stones. • Construct experiments to find new observations.

• Travel around the world to find new species, relate them.Posible Outcomes: • Use observations to learn how to build planes. • Relate species and build a model of evolution.


Birds

We can observe birds with our eyes, touch them, put them in cages..

Good for bird watchers…



Birds


What if we could not see birds and birds would be extremely small objects?

— hard to touch — hard to catch — hard to observe


Birds



What if we could not see birds and birds would be extremely small objects?

Particle Physics (in the bird picture)

Data:

• Counting experiment: • Number of birds hit as a function of ball speed:

Independent of ball direction afterwards —> Inclusive w.r.t. ball direction —> sum/integrate over all possibilities.

• Differential measurement: • Measure for example the change of direction of the bird as a function of the

angle or transverse momentum w.r.t the bird-ball-axis.

Inclusive: Sum/integrate over degrees of freedom. Exclusive: Be sensitive to certain degrees of freedom. We will repeat this later…


Particle Physics (in the bird picture)

Theory:

• cross section definition + Feynman rules (see Lecture by G. Heinrich) can predict • the rate of birds getting hit if you throw (enough) balls. • the probability of the ball-bird-fusion to create an elephant and

decaying to modified ball-bird-system • the probability of exited ball states.

• It might be needed to describe the bird as a composite object (wings,head,tails) and extract ( f(x) ) the probabilities to hit a wing with different probabilities as a tail.

• Also a wing-hit might give a different functional form w.r.t. scattering angle.


Particle Physics (in the bird picture)Theory vs. Data comparison:

• Measure the wing-extraction p(wing,speed) probability as function of bird-speed in shooting experiments.

• Create a model of a bird and a ball and calculate probability distribution of ball directions modifications for different hits.

• Model the wind/detector/feather loss or estimate effect from other data. • Sum over all possible hits folded with the extraction probabilities. • Compare theory distribution with a lot of bird-hit-data measuring the angular

distribution. • Improve model:

• Allow feathers to modify impact of ball • Include feathers sticking to ball • Include rotation of bird and ball.

• Estimate uncertainties by variation of ball and bird size, different feather models….


Particle PhysicsGoal: Learn something about basic forces and particles in nature

Properties: • Mass • Forces & Charges • average Age (lifetime) • Relations between

hadrons (Symmetries)

• Production & Decay • Species & Families • Excitations • Resonances • …

Model: • Understand the underlying symmetries/forces as QFT and build a model to

describe the properties. —> SM (after years of development!)

Measurement: • Usually in collider experiments like LHC/LEP/Tevatron/fixed target… • Produce new particles by collision of particles.


Event Simulation — Break down to topics

Monte Carlo

Hard Process

Shower

Underlying Event

Hadronization

Goal: Describe Collider events as realistic as possible.


Shower

Hard Process

Hadronization &

Underlying Event

Phenomenology Events

Observables Predictions Calibration

MC methods

Event Simulation — Break down to topics

Lecture 3

Lecture 5

Lecture 4

Lecture 6

Lecture 2

Lecture 1

Overview


Buzzwords— Hard Process

— LO/NLO

— Parton Shower

— DGLAP and Splitting Kernels

— Herwig, Pythia, Sherpa…

— Hadronization

— Angular Ordering and Dipole

— ME corrections, Matching and Merging

— MC@NLO, POWHEG,

— MEPS@NLO, FxFx, UNLOPS,….

— QED and QCD

— Spin-Correlations and Decays

— Uncertainties

— Hard and Soft

— …


Observables — Stating the problem

MC Method ME PS Matching Merging MPI Hadronization Decays

Stating the problem

I Want to compute expectation values of observables

hOi =

X

n

Zd�n P (�n)O(�n)

�n - Point in n-particle phase-spaceP (�n) - Probability to produce �n

O(�n) - Value of observable at �n

I Problem #1: Computing P (�n)

I Problem #2: Performing the integral

I At LO and NLO problem #2 is harder to solveThis is where MC event generators come in

Stefan Hoche MC Event Generators 6


Fixed Order (in 𝛂)

Generator Idea of event/cross section: 1. At highest scale Q: • Extract quarks or gluons with PDFs • Calculate cross section (hard process, Feynman rules…).

P. Skands Introduction to QCD

Secondly, and more technically, at NLO and beyond one also has to settle on a factorization

scheme in which to do the calculations. For all practical purposes, students focusing on LHCphysics are only likely to encounter one such scheme, the modified minimal subtraction (MS)one already mentioned in the discussion of the definition of the strong coupling in Section 1.4.At the level of these lectures, we shall therefore not elaborate further on this choice here.

We note that factorization can also be applied multiple times, to break up a complicatedcalculation into simpler pieces that can be treated as approximately independent. This will bevery useful when dealing with successive emissions in a parton shower, section 3.2, or whenfactoring off decays of long-lived particles from a hard production process, section 3.4.

We round off the discussion of factorization by mentioning a few caveats the reader shouldbe aware of. (See [52] for a more technical treatment.)

Firstly, the proof only applies to the first term in an operator product expansion in “twist”= mass dimension - spin. Since operators with higher mass dimensions are suppressed by thehard scale to some power, this leading twist approximation becomes exact in the limit Q ! 1,while at finite Q it neglects corrections of order

Higher Twist :[ln(Q2

/⇤2)]m<2n

Q2n(n = 2 for DIS) . (43)

In section 5, we shall discuss some corrections that go beyond this approximation, in thecontext of multiple parton-parton interactions.

Secondly, the proof only really applies to inclusive cross sections in DIS [51] and in Drell-Yan [55]. For all other hadron-initiated processes, factorization is an ansatz. For a generalhadron-hadron process, we write the assumed factorizable cross section as:

d�h1h2 =X

i,j

Z1

0

dxi

Z1

0

dxj

X

f

Zd�f fi/h1

(xi, µ2

F ) fj/h2(xj , µ

2

F )d�ij!f

dxi dxj d�f. (44)

Note that, if d� is divergent (as, e.g., Rutherford scattering is) then the integral over d�fmust be regulated, e.g. by imposing some explicit minimal transverse-momentum cut and/orother phase-space restrictions.

2.2 Parton Densities

The parton density function, fi/h(x,µ2

F ), represents the effective density of partons of type/flavori, as a function of the momentum fraction14

xi, when a hadron of type h is probed at the fac-torization scale µF . The PDFs are non-perturbative functions which are not a priori calculable,but a perturbative differential equation governing their evolution with µF can be obtained byrequiring that physical scattering cross sections, such as the one for DIS in equation (42), beindependent of µF to the calculated orders [56]. The resulting renormalization group equation

(RGE) is called the DGLAP15 equation and can be used to “run” the PDFs from one pertur-bative resolution scale to another (its evolution kernels are the same as those used in partonshowers, to which we return in section 3.2).

This means that we only need to determine the form of the PDF as a function of x a single(arbitrary) scale, µ0. We can then get its form at any other scale µF by simple RGE evolution.

14Recall: the x fraction is defined in equation (41).15DGLAP: Dokshitzer-Gribov-Lipatov-Altarelli-Parisi [56–58].

— 20 —

Result: Fixed Order LO pp -> f


Lecture 3

Minimum Bias

Multiple Interactions

Underlying Eventsˇ

What happens at LHC? (13 TeV)

Total 100 mbNon-diffractive 56 mbElastic 22 mbDiffractive 22 mbJets p⊥ > 150 GeV 220 nbW+Z 200 nbTop 600 pbHiggs 30 pb

Event Generators IV 3 Leif Lönnblad Lund University


Lecture 3

„barn“

Minimum Bias

Multiple Interactions

Underlying Eventsˇ

What happens at LHC? (13 TeV)

Jets p⊥ > 2 GeV 900 mbJets p⊥ > 4 GeV 120 mbTotal 100 mbNon-diffractive 56 mbElastic 22 mbDiffractive 22 mbJets p⊥ > 150 GeV 220 nbW+Z 200 nbTop 600 pbHiggs 30 pbBSM ∼ 0? fb

Event Generators IV 3 Leif Lönnblad Lund University

??? That can’t

be true!!

Can this be true?Johannes Bellm, Lund University , 28.-30.5.2018

Lecture 6

Fixed Order (Corrections in 𝛂)

Higher order corrections: — Inclusion of virtual and real emission diagrams — Divergencies arise

• High Energy Loops (UV) -> Renormalisation of parameters • Small Resolution (infra red and collinear)

-> cancel between V and R (and C (PDF renormalisation))

0.2 0.4 0.6 0.8 1.0

-100

-50

50

100

q𝝳(q) ∞

LO (Born Approx.)

NLO (Loop / Virtual) NLO

(Real Emission)

Z

0

d�R

dqdq = 1

Z

0

✓d�R

dq+

d�V

dq

◆dq = finite


Event SimulationQED bremsstrahlung – 1

Accelerated electric charges radiate photons ,

see e.g. J.D. Jackson, Classical Electrodynamics.A charge ze that changes its velocity vector from � to �0 radiatesa spectrum of photons that depends on its trajectory. In thelong-wavelength limit it reduces to

lim!!0

d2I

d!d⌦=

z2e2

4⇡2

��✏⇤✓

�0

1� n�0 ��

1� n�

◆��2

where n is a vector on the unit sphere ⌦, ! is the energy of theradiated photon, and ✏ its polarization.

1 For fast particles radiation collinear with the � and �0

directions is strongly enhanced.

2 dN/d! = (1/!)dI/d! / 1/! so infinitely many infinitely softphotons are emitted, but the net energy taken away is finite.

Torbjorn Sjostrand PPP 3: Evolution equations and final-state showers slide 3/50


Event Simulation — Break down to topicsQED bremsstrahlung – 2

An electrical charge, say an electron,is surrounded by a field:

For a rapidly moving chargethis field can be expressed in terms ofan equivalent flux of photons:

dn� ⇡2↵em

⇡

d✓

✓

d!

!

Equivalent Photon Approximation,or method of virtual quanta (e.g. Jackson)(Bohr; Fermi; Weiszacker, Williams ⇠1934)

e�

e�

e�

e�

.

✓: collinear divergence, saved by me > 0 in full expression.

!: true divergence, n� /R

d!/! =1, but E� /R

! d!/! finite.

These are virtual photons: continuously emitted and reabsorbed.



TitleQED bremsstrahlung – 3

When an electron is kicked into a new direction,the field does not have time fully to react:

e�

Initial State Radiation (ISR):part of it continues ⇠ in original direction of e

Final State Radiation (FSR):the field needs to be regenerated around outgoing e,and transients are emitted ⇠ around outgoing e direction

Emission rate provided by equivalent photon flux in both cases.Approximate cuto↵s related to timescale of process:the more violent the hard collision, the more radiation!



Initial State and Final State RadiationThe Parton-Shower Approach

2! n = (2! 2) � ISR � FSR

FSR = Final-State Radiation = timelike showerQ2

i ⇠ m2 > 0 decreasingISR = Initial-State Radiation = spacelike showersQ2

i ⇠ �m2 > 0 increasing



Lecture 3

Parton ShowerZ

0

✓d�R

dq+

d�V

dq

◆dq = finite but: larged�R

dq

0.2 0.4 0.6 0.8 1.0

-100

-50

50

100

6.2 Shower dynamics

With the kinematics defined, we now consider the dynamics governing the parton branchings.Each parton branching is approximated by the quasi-collinear limit [62], in which the transversemomentum squared, p2

⊥, and the mass squared of the particles involved are small (compared top ·n) but p2

⊥/m2 is not necessarily small. In this limit the probability of the branching ij → i+ jcan be written as

dPeij→ij =αS

2π

dq2

q2dz Peij→ij (z, q) , (6.13)

where Peij→ij (z, q) are the quasi-collinear splitting functions derived in [62]. In terms of our light-cone momentum fraction and (time-like) evolution variable the quasi-collinear splitting functionsare

Pq→qg =CF

1 − z

[1 + z2 −

2m2q

zq2

], (6.14a)

Pg→gg = CA

[z

1 − z+

1 − z

z+ z (1 − z)

], (6.14b)

Pg→qq = TR

[1 − 2z (1 − z) +

2m2q

z (1 − z) q2

], (6.14c)

Pg→gg =CA

1 − z

[1 + z2 −

2m2g

zq2

], (6.14d)

Pq→qg =2CF

1 − z

[z −

mq

zq2

], (6.14e)

for QCD and singular SUSY QCD branchings12. These splitting functions give a correct physicaldescription of the dead-cone region p⊥ ! m, where the collinear singular limit of the matrixelement is screened by the mass m of the emitting parton.

The soft limit of the splitting functions is also important. The splitting functions with softsingularities Pq→qg, Pq→qg, Pg→gg, and Pg→gg, in which the emitted particle j is a gluon, all behaveas

limz→1

Peij→ij =2Ceij

1 − z

(1 −

m2i

q2

), (6.15)

in the soft z → 1 limit, where Ceij equals CF for Pq→qg and Pq→qg,12CA

13 for Pg→gg, and CA forPg→gg. In using these splitting functions to simulate the emission of a gluon from a time-likemother parton ij, associated to a general n parton configuration with matrix element Mn, oneis effectively approximating the matrix element for the process with the additional gluon, Mn+1,by

|Mn+1|2 =8παS

q2eij− m2

eij

Peij→ij |Mn|2 . (6.16)

12The Pg→gg splitting presented here is for final-state branching where the outgoing gluons are not identifiedand therefore it lacks a factor of two due to the identical particle symmetry factor. For initial-state branchingone of the gluons is identified as being space-like and one as time-like and therefore an additional factor of 2 isrequired.

13Note that for g → gg, there is also a soft singularity at z → 0 with the same strength, so that the totalemission strength for soft gluons from particles of all types in a given representation is the same: CF in thefundamental representation and CA in the adjoint.

37

Describe splitting in soft/collinear approximation with splitting functions. Not yet probabilities.

Pq!qg(z) =↵S

2⇡CF

1 + z2

1� z

Altarelli Parisi Splitting Kernel

AP: inspirehep:119585 6450 citations Johannes Bellm, Lund University , 28.-30.5.2018


Parton ShowerZ

0

✓d�R

dq+

d�V

dq

◆dq = finite but: large

d�R

dq

0.2 0.4 0.6 0.8 1.0

-100

-50

50

100

0.5 1.0 1.5 2.0

-1.0

-0.5

0.5

1.0

Using the definitions of our shower variables, Eq. (6.4), and making the soft emission approxi-mations qeij ≈ qi ≈ p, q2

i ≈ m2i = m2

eijin Eqs. (6.15, 6.16) we find [23]

limz→1

8παS

q2eij− m2

eij

Peij→ij = −4παSCeij

(n

n · qj−

p

p · qj

)2

. (6.17)

Recalling that we choose our Sudakov basis vector n to point in the direction of the colourpartner of the gluon emitter (ij/i), Eq. (6.17) is then just the usual soft eikonal dipole functiondescribing soft gluon radiation by a colour dipole [63], at least for the majority of cases wherethe colour partner is massless or nearly massless. In practice, the majority of processes we intendto simulate involve massless or light partons, or partons that are light enough that n reproducesthe colour partner momentum to high accuracy14.

For the case that the underlying process with matrix element Mn is comprised of a singlecolour dipole (as is the case for a number of important processes), the parton shower approxi-mation to the matrix element Mn+1, Eq. (6.16), then becomes exact in the soft limit as well as,and independently of, the collinear limit. This leads to a better description of soft wide angleradiation, at least for the first emission, which is of course the widest angle emission in the an-gular ordered parton shower. Should the underlying hard process consist of a quark anti-quarkpair, this exponentiation of the full eikonal current, Eq. (6.17), hidden in the splitting functions,combined with a careful treatment of the running coupling (Sect. 6.7), will resum all leadingand next-to-leading logarithmic corrections [32,64–66]. In the event that there is more than onecolour dipole in the underlying process, the situation is more complicated due to the ambiguityin choosing the colour partner of the gluon, and the presence of non-planar colour topologies.

In general, the emission probability for the radiation of gluons is infinite in the soft z → 1and collinear q → 0 limits. Physically these divergences would be canceled by virtual corrections,which we do not explicitly calculate but rather include through unitarity. We impose a physicalcutoff on the gluon and light quark virtualities and call radiation above this limit resolvable. Thecutoff ensures that the contribution from resolvable radiation is finite. Equally the uncalculatedvirtual corrections ensure that the contribution of the virtual and unresolvable emission belowthe cutoff is also finite. Imposing unitarity,

P (resolved) + P (unresolved) = 1, (6.18)

gives the probability of no branching in an infinitesimal increment of the evolution variable dq as

1 −∑

i,j

dPeij→ij, (6.19)

where the sum runs over all possible branchings of the particle ij. The probability that a partondoes not branch between two scales is given by the product of the probabilities that it did notbranch in any of the small increments dq between the two scales. Hence, in the limit dq → 0 theprobability of no branching exponentiates, giving the Sudakov form factor

∆ (q, qh) =∏

i,j

∆eij→ij (q, qh) (6.20)

14Even when the colour partner has a large mass, as in e+e− → tt, the fact that each shower evolves into theforward hemisphere, in the opposite direction to the colour partner, means that the difference between Eq. (6.17)and the exact dipole function is rather small in practice.

38

which is the probability of evolving between the scale qh and q without resolvable emission. Theno-emission probability for a given type of radiation is

∆eij→ij (q, qh) = exp

{−∫ qh

q

dq′2

q′2

∫dz

αS (z, q′)

2πPeij→ij (z, q′) Θ

(p2⊥ > 0

)}. (6.21)

The allowed phase space for each branching is obtained by requiring that the relative transversemomentum is real, or p2

⊥ > 0. For a general time-like branching ij → i + j this gives

z2 (1 − z)2 q2 − (1 − z) m2i − zm2

j + z (1 − z) m2eij

> 0, (6.22)

from Eq. (6.6).In practice rather than using the physical masses for the light quarks and gluon we impose a

cutoff to ensure that the emission probability is finite. We use a cutoff, Qg, for the gluon mass,and we take the masses of the other partons to be µ = max (m, Qg), i.e. Qg is the lowest massallowed for any particle.

There are two important special cases.

1. q → qg, the radiation of a gluon from a quark, or indeed any massive particle. In this caseEq. (6.22) simplifies to

z2(1 − z)2q2 > (1 − z)2 µ2 + zQ2g, (6.23)

which gives a complicated boundary in the (q, z) plane. However as

(1 − z)2 µ2 + zQ2g > (1 − z)2 µ2, z2Q2

g (6.24)

the phase space lies inside the region

µ

q< z < 1 −

Qg

q(6.25)

and approaches these limits for large values of q. In this case the relative transversemomentum of the branching can be determined from the evolution scale as

p⊥ =√

(1 − z)2 (z2q2 − µ2) − zQ2g . (6.26)

2. g → gg and g → qq, or the branching of a gluon into any pair of particles with the samemass. In this case the limits on z are

z− <z < z+, z± =1

2

(1 ±

√1 −

4µ

q

)and q > 4µ. (6.27)

Therefore analogously to Eq. (6.25) the phase space lies within the range

µ

q< z < 1 −

µ

q. (6.28)

In this case the relative transverse momentum of the branching can be determined fromthe evolution scale as

p⊥ =√

z2 (1 − z)2 q2 − µ2. (6.29)

39

Z Q

µdP(q)�(Q, q) +�(Q,µ) = 1

- Working with probabilities. - Missing finite corrections. - Valid in IRC limit.

Sudakov suppression

Sudakov peak


How to model?Divide and conquer

Partonic cross section from Feynman diagrams

ds = dsharddP(partons ! hadrons)

Note, that ZdP(partons ! hadrons) = 1 ,

I s remains unchangedI introduce realistic fluctuations into distributions.

Simulation steps governed by different scales�! separation into (Q0 ⇡ 1GeV > LQCD)

dP(partons ! hadrons) = dP(resonance decays) [G > Q0]

⇥dP(parton shower) [TeV ! Q0]

⇥dP(hadronisation) [⇠ Q0]

⇥dP(hadronic decays) [O(MeV)]

Stefan Gieseke · CTEQ School 2013 11/91

Divide and conquerPartonic cross section from Feynman diagrams

ds = dsharddP(partons ! hadrons)

Note, that ZdP(partons ! hadrons) = 1 ,

I s remains unchangedI introduce realistic fluctuations into distributions.

Simulation steps governed by different scales�! separation into (Q0 ⇡ 1GeV > LQCD)

dP(partons ! hadrons) = dP(resonance decays) [G > Q0]

⇥dP(parton shower) [TeV ! Q0]

⇥dP(hadronisation) [⇠ Q0]

⇥dP(hadronic decays) [O(MeV)]


Mini event generator

I We generate pairs (~xi,wi).I Use immediately to book weighted histogram of arbitrary

observable (possibly with additional cuts!)I Keep event~xi with probability

Pi =wi

wmax.

Generate events with same frequency as in nature!



Radiation Factorization PDFs Jets

PDFs: parametrisations and results

Example below: CT14NNLO, at Q = 2 GeV and Q = 100 GeV

g!x,Q"#5u

d

u!bard!bar

s!bar

0.001 0.003 0.01 0.03 0.1 0.3 10.

0.2

0.4

0.6

0.8

x

xf!

x,Q"

at Q

= 2

GeV

CT14 NNLO

g!x,Q"#5

u

d

u!bard!bars!bar

0.001 0.003 0.01 0.03 0.1 0.3 10.

0.2

0.4

0.6

0.8

x

xf!

x,Q"

at Q

= 1

00 G

eV

CT14 NNLO

F. Krauss IPPP

QCD at Colliders

Radiation Factorization PDFs Jets

Q2

1/x

F. Krauss IPPP

QCD at Colliders

Fluctuations - Example: PDFs - Proton has 3 valence quarks (uud) - But also gluons and sea quarks - This Dirac sea is pretty flat from

the outside - But tested with large scale/ small

times the structure changes dramatically.


HadronisationPhysical input

Self coupling of gluons$ “attractive field lines” Linear static potential V(r)⇡ kr.

Supported by lattice QCD,hadron spectroscopy.


- Colors not visible (to strong to separate/Confinement)

- Colors are pulled back similar to rubber band / string

- Pair creation / string break!

Physical input

Self coupling of gluons$ “attractive field lines” Linear static potential V(r)⇡ kr.

Supported by lattice QCD,hadron spectroscopy.


Lund string model

Ajacent breaks form hadrons.

Works in both directions (symmetry).Lund symmetric fragmentation function

f (z,p?)⇠1z(1� z)a exp

�

b(m2h+p

2?)

z

!

a,b,m2h

main adjustable parameters.Note: diquarks ! baryons.


Johannes Bellm, Lund University , 28.-30.5.2018Lecture 6

Modelled as ColorlinesIn PS usually color is treated in large color limit SU(3)×SU(2)×U(1). Generators keep track of colors and build colorless objects.


Cluster (Herwig) or Lund Strings (Pythia)

Several models in different generators (cluster and strings). Cluster models in Herwig and Sherpa. Lund Strings in Pythia and Vincia.


Lecture 6

Multi Parton Interactions

One needs to care about the rest of the proton parsons and colors.

Various MPI models implemented. Needed for interpretation of cross section.


Lecture 6

Resummation


Introductory example (courtesy of Gavin Salam)

Why resummation is needed

0.1

1

10

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

1/s

ds/d

B T

Total Broadening (BT)

OPAL 91 GeV

Resummation () WebberFest 22/ 09/ 2010 3 / 20


ResummationIntroductory example (courtesy of Gavin Salam)


0.1

1

10

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

1/s

ds/d

B T


OPAL 91 GeVLO


ddB(α s ln2 B)




0.1

1

10

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

1/s

ds/d

B T


OPAL 91 GeVLO

NLO


ddB(α s ln2 B + α 2s ln

4 B)




0.1

1

10

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

1/s

ds/d

B T


OPAL 91 GeVLO

NLONLL + NLO



4 B + · · · )




0.1

1

10

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

1/s

ds/d

B T


OPAL 91 GeVNLO + NLL

+ hadronisation



4 B + · · · )

• Resummation probes high-order structure of perturbation theory: leads to non-perturbative structure


General Purpose Event Generators

http://mcplots.cern.chGo to:

Find large set of measured observables and the corresponding predictions from generators.


General Purpose Event Generators

Z-boson transverse momentum (recoil against emission)

Number of jets in W-boson production (in this plot: merging only in Sherpa)


Matching and Merging7.1. Parton Production in e

+e� Annihilation 89

qq(0,1,2)qqV (0)qqV

C (1) ⇥ -1qqV (1)qqV

C (2) ⇥ -1qq(2)

10 3

10 4

10 5

10 6

10 7

10 8

ds/d

y 34

[pb]

10�4 10�3 10�2 10�1

0.6

0.8

1

1.2

1.4

y34

Rat

io

qq(0,1,2)qq(0,-,-)qq(-,1,-)qq(-,-,2)

10 3

10 4

10 5

10 6

10 7

10 8

ds/d

y 34

[pb]

10�4 10�3 10�2 10�1

0.6

0.8

1

1.2

1.4

y34

Rat

io

Figure 7.2.: Di↵erential cross section as a function of y34, which separates three jet eventsfrom four jet events in a Durham jet algorithm. The cross section is split up into the di↵erentcontributions leading to the combined qq(0, 1, 2) merged sample. The blue contributions inthe left picture are compensated by the red, clustered subtraction terms. The red lines aremultiplied by a factor minus one. In the right picture the blue contributions are the sum ofthe red and blue lines in the left plot, e.g. qq(0,�,�) = qqV (0) + qqV

C (1).

qq(0)qq(0,1)qq(0,1,2)qq(0,1,2,3)

10�2

10�1

1

10 1

10 2

10 3

10 4

1/s i

jds

/dy 2

3,..,

67

10�4 10�3 10�2 10�1

0.6

0.8

1

1.2

1.4

y23,..,67

vs.y

45

qq(0)qq(0,1)qq(0,1,2)qq(0,1,2,3)

10 4

ÂN i=

2s i

,exc

l.[p

b]

0 5 10 15 200.9

0.95

1.0

1.05

incl. N-partons

Rat

io

Figure 7.3.: Left: Di↵erential jet rates as a function of the various Durham ya,a+1 parameter,where a particular event changes the multiplicity from an a-jet to an a+1-jet configurationwithin the Durham jet algorithm. The di↵erential cross sections have been normalized to theirindividual integrated cross section and the ratio is with respect to y45 of qq(0). Right: Thecross section as a function of inclusive N -parton states.

three to four jet events. The di↵erent distributions are plotted leading to qq(0, 1, 2). Here, wesplit the distribution according to Eqs. (4.35) and (4.36). On the left hand side of Fig. 7.2,the dashed lines correspond to configurations entering the vetoed shower with no additionalemission. These are (before the vetoed showering) the pure e

+e�! qq events (blue dashed),

which are compensated by the clustered events with one additional emission (red dashed)

Lecture 5

Good Description

Collider Tools

Hard Processes and Higher Orders

At the LHC: ATLAS Z+jets) [

pb]

jets

*+N

γ(Z

/σ

-210

-110

1

10

210

310

410

510

610 ATLAS Preliminary1−13 TeV, 3.16 fb

jets, R = 0.4tanti-k < 2.5⎜

jet y⎜ > 30 GeV, jet

Tp

) + jets−l+ l→*(γZ/ Data

HERPAS + ATHLACK B 2.2HERPA S

6YP + LPGEN A8 CKKWLYP + MG5_aMC8 FxFxYP + MG5_aMC

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

Pred

./Dat

a

0.5

1

1.5

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

Pred

./Dat

a

0.5

1

1.5

jetsN0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

Pred

./Dat

a

0.5

1

1.5

100 200 300 400 500 600 700

[pb/

GeV

]je

t

T/d

pσd

-410

-310

-210

-110

1

10

210

310 ATLAS Preliminary1−13 TeV, 3.16 fb

jets, R = 0.4tanti-k < 2.5⎜

jet y⎜ > 30 GeV, jet

Tp

1 jet≥) + −l+ l→*(γZ/ Data

NNLOjetti

1 jet N≥ Z + HERPAS + ATHLACK B

2.2HERPA S6YP + LPGEN A

8 CKKWLYP + MG5_aMC8 FxFxYP + MG5_aMC

100 200 300 400 500 600 700

Pred

./Dat

a

0.5

1

1.5

100 200 300 400 500 600 700

Pred

./Dat

a 0.5

1

1.5

(leading jet) [GeV]jetT

p

100 200 300 400 500 600 700

Pred

./Dat

a

0.5

1

1.5

ATLAS-CONF-2016-046

Peter Richardson Collider Tools


MCnet projectsPythia+Vincia

HerwigSherpa

MadGraph“Plugin” – Ariadne+HEJ

CEDAR – Rivet+Professor+Contur+hepforge+…

Thank you!


Documents

Introduction to Monte-Carlo Event Generatorshome.thep.lu.se/~jbellm/VSOP/MONTE_CARLO_1_BELLM... · 2018. 8. 30. · Introduction to Monte-Carlo Event Generators — 24th Vietnam School