2nd Biennial African School of Fundamental Physics and its Applications KNUST - Kumasi - Ghana

A tour to Monte Carlo

Monte Carlo Generators for particle physics P. Skands (CERN TH)

. . . because Einstein was wrong: God does throw dice! Quantum mechanics: amplitudes =⇒ probabilities Anything that possibly can happen, will! (but more or less often) 1

Count what is Countable

Measure what is Measurable (and keep working on the beam) G. Galilei 1564 - 1642

MC: P ar

ticle P hysics G

Amplitudes Partons Radiation Strings ... IG W R HE

,

c

ete D : C M

enera tors

Theory … , A P ER H S , IA H T Y P This lecture

on i t a l u tor Sim

Feedback Loop

Hits 0100110 B-Field ....

Experiment GEAN T 4, F A. Dotti Next Week

LUKA

,…

Theory: Need predictions for “physical observables” Experiment: Need simulated events to study detector response

From Theory to Experiment •

High-Energy Physics: Theory (see lectures by J. Govaerts)

• •

Parton-parton scattering cross sections

•

Truncate perturbative series at first non-zero term → lowest order

(parton = quark or gluon + sometimes leptons too)

Calculated by expansion of quantum field theory around zero coupling → perturbation theory

3

1

Standard “Mandelstam” variables for kinematics of 2→2 Scattering

High%transversemomentum% interac2on%

2

4

Feynman Diagram → (with time flowing horizontally) → 3

Ernest Rutherford, 1st Baron Rutherford of Nelson (1871-1937)

From Theory to Experiment

High%transversemomentum% interac2on%

Reality is more complicated 4

Monte Carlo Generators

Calculate Everything → requires compromise! Include the ‘most significant’ corrections → simulate complete events 1. Parton)Showers)) 2. Matching) 3. Hadronisa7on) 4. The)Underlying)Event)

1. So?/Collinear)Logarith

2. Finite)Terms,)“K”Ifacto roughly Simulated ‘events’ 3. Power)Correc7ons)(mor 4. ?) MC

(+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

Lecture 2

5

The structure of an event Warning: schematic only, everything simplified, nothing to scale, . . .

p p/p

Incoming beams: parton densities 6

W+ u d

g

p p/p

Hard subprocess: described by matrix elements 7

c

s W+

u d

g

p p/p

Resonance decays: correlated with hard subprocess 8

c

s W+

u d

g

p p/p

Initial-state radiation: spacelike parton showers 9

c

s W+

u d

g

p p/p

Final-state radiation: timelike parton showers 10

c

s W+

u d

g

p p/p

Multiple parton–parton interactions . . . 11

c

s W+

u d

g

p p/p

. . . with its initial- and final-state radiation 12

Beam remnants and other outgoing partons 13

Everything is connected by colour confinement strings Recall! Not to scale: strings are of hadronic widths 14

The strings fragment to produce primary hadrons 15

These are the particles that hit the detector ? s e l c i t r ? a ” p s t e c e e r f f f E e s e e v i h t , t c s e e g l r l n + A ere “Co scatteri ) ? … e h , r t s , s c e i r n a m o i a r t n c O y a r d e o t r n d i y (Re ation, h z i l a m r e th

Many hadrons are unstable and decay further 16

These are the particles that hit the detector

LHC Collision at 7 TeV ATLAS, March 2010

Vacuum Topological Charge, Data courtesy of M. McGuigan BNL-CSC, T. Izubuchi RIKEN-BNL, and S. Tomov University of Tennessee

Quantum Chromodynamics (QCD)

18

s

Colour Gauge Group (= local internal symmetry)

See lectures by J. Govaerts

ie etr m m

Sy

=C ons Cha erved rges

E. Noether (1882-1935)

Special Unitary group in 3 (complex) dimensions, SU(3) Group of 3x3 unitary complex matrices with det=1

Gluons One “gauge boson” for each linearly independent such matrix 32-1 = 8 : gluons are octets (each being a 3×3 matrix)

Quarks One quark “color” for each degree of SU(3) 3 : quarks are triplets (each being a 3-vector, on which matrices operate)

MC Lecture 2

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

19

⇤

1 Space Interactions in Colour j ⇥ ⌅ q =

2 3

)21 .p( 1 erutcel DCQ sdohtem cisaB yroeht noitabrutreP

cisyhpQuark-Gluon naem selur nainteractions mnyeF od tahW Quark Fields g1 ⇤ ⇤ µ ,A⇤ µ ,A 1 0 0 1 0 ⇥1 0 0⌅ ⇥0⌅ = ⇥1⌅ 0 0 0 0 0 qRa

b qG



g1



a

qR

µ γ A t gi−( ¯ ψ ) a bψ ab s

0 1 0 1 )0 1 0( 0   0 0 1  SU(3) : 8 “Gell-Mann” Matrices (equivalent to Pauli σ matrices in SU(2)) 0 0 0 0 #" ! $ #" #" ! !$

P.aψ S k a n d s - M o n t e 1C oψr P a r t i c l e P h y s i c s t a r l o G e n e r a t o r s bf ¯

ba

b

qG

MC Lecture 2

20

⇥ ⌅ = q 2

cisyhp naGluon em selur naself-interaction mnyeF od tahW Quark Fields g1 ⇤ ⇤ µ ,A⇤ µ ,A 1 0 0 1 0 ⇥1 0 0⌅ ⇥0⌅ = ⇥1⌅ 0 0 0 0 0 3

)21 .p( 1 erutcel DCQ sdohtem cisaB yroeht noitabrutreP

qRa

b qG

g4



g1



a

qR

b

qG

µ γ A t gi−( ¯ ψ ) a bψ ab s

0 1 0 1 ) 0 1 Absent 0 ( in QED 0  0 0 1  Twice as strong as quark-gluon interaction 0 0 0 0 #" ! $ #" #" ! !$ aψ

g6

1t ba

¯

bψ

g1

.ruoloc krauq eht stniaper noissime noulg A

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

MC Lecture 2

21

Brems Strahlung Charges Stopped Radiation

Radiation

The harder Associated they stop, the harder the field fluctations that continue tocontinues become strahlung (fluctuations) 22

Bremsstrahlung → Parton Showers Accelerated charges radiate Collider Observables

H+2

H+2

(0)

|MH |2 (0)

|MH+1 |2 (0)

|MH+2 |2 (0)

|MH+3 |2

Pa Sh rto ow n er s

Hard Process

Hadronization

h i Radiation pattern is of a universal type (e.g., (1) (0)⇤ 2Re MH MH synchrotron radiation) h i (1) (0)⇤ 2Re MH+1 Can be Mdescribed by an iterative branching H+1 h i processes : “Parton Shower” (1) (0)⇤ 2Re M M

Based on small-angle singularity of accelerated charges (synchrotron radiation, semi-classical) (Altarelli-Parisi Splitting Kernels)

e r o M r Late

Formation Time (a.k.a. Factorization Scale) P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

GEANT 4

MC Lecture 2

23

The Strong Coupling Bjorken scaling To first approximation, gauge theories are SCALE INVARIANT A quantum fluctuation inside a fluctuation inside a fluctuation … A gluon emits a gluon emits a gluon emits a gluon … If the coupling “constant” of the strong force was a constant, this would be absolutely true

24

Asymptotic Freedom The Nobel Prize in Physics 2004

Asymptotic Freedom

*1

*2

“What this year's Laureates discovered was something that, at first sight, seemed completely contradictory. The interpretation of their mathematical result was that the closer the quarks are to each other, the weaker is the 'colour charge'. When the quarks are really close to charge each other, the force is so weak that they behave almost as free particles. This phenomenon is called ‘asymptotic freedom’. The converse is true when the quarks move apart: potential the force becomes stronger when the distance increases.” αS(r)

http://www.nobelprize.org/nobel_prizes/physics/laur

2004 The Nobel Prize in Physics 2004 David J. Gross, H. David Politzer, Frank Wilczek

David J. Gross

H. David Politzer

Frank Wilczek

The Nobel Prize in Physics 2004 was awarded jointly to David J. Gross, H. David Politzer and Frank Wilczek "for the discovery of asymptotic freedom in the theory of the strong interaction". Photos: Copyright © The Nobel Foundation

TO CITE THIS PAGE: MLA style: "The Nobel Prize in Physics 2004". Nobelprize.org.29 May 2012 http://www.nobelprize.org/nobel_prizes/physics/laureates/2004/index.html.

force still goes to ∞ as r → 0 (Coulomb potential), just less slowly Copyright © Nobel Media AB 2012 *1 The

*2 The

1/r

potential grows linearly as r→∞, so the force actually becomes constant (even this is only true in “quenched” QCD. In real QCD, the force eventually vanishes for r>>1fm)

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

MC Lecture 2

25

Running Couplings QED:

QCD:

Vacuum polarization → Charge screening

Quark Loops → Also charge screening

+

+ -

-

B

B Y

+ +

Y

B -

Y +

Y

B

B

But only dominant if > 16 flavors! QED: Quantum Electrodynamics = Electromagnetism QCD: Quantum Chromodynamics = The Strong Nuclear Force P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

MC Lecture 2

26

Running Couplings QED:

QCD:

Vacuum polarization → Charge screening +

+

Gluon Loops Dominate if ≤ 16 flavors B

B

-

-

Y

-

Y

Y

Y

+ +

11CA 2nf b0 = 12⇡

B

B +

B Y

Y

B B

B

B

B

Y

Spin-1 → Opposite Sign QED: Quantum Electrodynamics = Electromagnetism QCD: Quantum Chromodynamics = The Strong Nuclear Force P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

Y

MC Lecture 2

27

or up to 0.0012. Most notably, excluding the most CD gives only a marginally different average value. ent and long-standing systematic difference between nd other determinations of similar accuracy. This the various inputs to this combination, evolved to (right) provides strongest evidence for the correct dence of the strong The coupling. Strong Coupling “Constant”

The Strong Coupling “Constant” as function of energy scale, Q From PDG Review on QCD. by Dissertori & Salam

0.5

α s(Q)

Coupling αs(Q) actually runs rather fast with Q

July 2009

???

Deep Inelastic Scattering e+e? Annihilation Heavy Quarkonia

0.4

Perturbative solution diverges at a scale ΛQCD somewhere below

0.3

≈ 1 GeV

0.2

So, to specify the strength of the strong force, we usually give the value of αs at a unique reference scale that everyone agrees on: MZ = 91.2 GeV/c

Freedo m? Unific ation?

0.1 QCD

3

Μ Z)

At low scales

1

α s (Μ Z) = 0.1184 ± 0.0007 10

Q [GeV]

100

measurements of αs (MZ2 ), used as input for the ands - Monte C G e naefunction r a t o r s f oof r Pthe article aryP.ofS kmeasurements ofa rαl os as

MC Lecture 2

Physics

28

Confinement We don’t see quarks and gluons … Mesons Quark-Antiquark Bound States

M. Gell-Mann: “Three quarks for mister Mark, …” James Joyce, Finnegans Wake

Baryons Quark-Quark-Quark Bound States

MC Lecture 2

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

29

Linear Confinement Lattice QCD: Potential between a quark and an antiquark as function of distance, R

Long Distances ~ Linear Confinement

“Quenched” Lattice QCD

Hadrons

Short Distances ~ pQCD

Partons

Question: What physical system has a linear potential?

MC Lecture 2

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

30

From Partons to Strings

Motivates a model: Model: assume the color field collapses into a (infinitely) narrow flux tube of uniform energy density κ ~ 1 GeV / fm → Relativistic 1+1 dimensional worldsheet – string Lund String Model of Hadronization MC

Pedagogical Review: B. Andersson, The Lund model. Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol., 1997. P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

Lecture 2

31

String Breaks In “unquenched” QCD g→qq → The strings would break

MC

Illustrations by T. Sjöstrand

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

Lecture 2

32

Hadronization Models The problem:

•

Given a set of partons resolved at a scale of ~ 1 GeV (~ 10-15 m), need a “mapping” from this set onto a set of on-shell (confined) hadrons.

MC models do this in three steps 1.

Map partons onto continuum of excited hadronic states (called ‘strings’ or ‘clusters’)

2.

Iteratively break strings/clusters into discrete set of primary hadrons (string breaks / cluster splittings / cluster decays)

3.

Sequential decays into secondary hadrons (e.g., ρ > π π , Λ0 > n π0, π0 > γγ, ...)

D i s t a n c e S c a l e s ~ 1 0 -15 m = 1 f e r m i

PYTHIA PYTHIA anno 1978 (then called JETSET) LU TP 78-18 November, 1978 A Monte Carlo Program for Quark Jet Generation T. Sjöstrand, B. Söderberg A Monte Carlo computer program is presented, that simulates the fragmentation of a fast parton into a jet of mesons. It uses an iterative scaling scheme and is compatible with the jet model of Field and Feynman.

Note: Field-Feynman was an early fragmentation model Now superseded by the String (in PYTHIA) and Cluster (in HERWIG & SHERPA) models.

MC Lecture 2

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

34

PYTHIA PYTHIA anno 2012

~ 80,000 lines of C++

(now called PYTHIA 8) LU TP 07-28 (CPC 178 (2008) 852) October, 2007 A Brief Introduction to PYTHIA 8.1 T. Sjöstrand, S. Mrenna, P. Skands The Pythia program is a standard tool for the generation of high-energy collisions, comprising a coherent set of physics models for the evolution from a few-body hard process to a complex multihadronic final state. It contains a library of hard processes and models for initial- and final-state parton showers, multiple parton-parton interactions, beam remnants, string fragmentation and particle decays. It also has a set of utilities and interfaces to external programs. […]

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

What a modern MC generator has inside:

•

Hard Processes (internal, semi-

• • • • • • • • • •

BSM (internal or via interfaces) PDFs (internal or via interfaces) Showers (internal or inherited) Multiple parton interactions Beam Remnants String Fragmentation Decays (internal or via interfaces) Examples and Tutorial Online HTML / PHP Manual Utilities and interfaces to external programs

internal, or via Les Houches events)

MC Lecture 2

35

Particle-Physics

Tools for Experiments ATLAS and CMS: the two largest experiments at the Large Hadron Collider (see lectures next week) 1

a6 .4

as of 2012-02-18, from ’papers’, excluding self-citations

thi AN T4

Particle Physics MC Detector Simulation MC (see lectures by A. Dotti)

GE

0.8

Py

Sorry, skipped in these lectures

Jet Clustering Algorithms (see lectures by S. Connell) alg

.

Proton Structure (parton distribution functions) Review of Particle Physics

0.2

0

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

Plot by GP Salam based on data from ATLAS, CMS and INSPIREHEP

MS

0.4

CT EQ

6P

DF s TW 20 08 CT PD EQ Fs 6.6 He PD rw Fs ig 6M RP C P2 01 0 AL PG EN LO *P DF s MC @ NL O JIM MY Ma dG rap h4 PO WH EG FE (20 WZ 07 ) NN CT LO 10 PD Fs MC @ NL O He he rw av ig+ + M y-flav Fa ou C stJ r et Z1 UE Tu ne Py thi a8 .1

ti-k

t

jet

0.6 An

fraction of ATLAS & CMS papers that cite them

MC

Papers commonly cited by ATLAS and CMS

MC Lecture 2

36

(Parton Distributions) Parton Distribution Functions

Hadrons are composite, with time-dependent structure:

For hadron to remain intact, virtualities k2 < Mh2 High-virtuality fluctuations suppresed by powers of

Partons within clouds of further partons, constantly emitted and absorbed

u d g u

p

↵s Mh2 k2 Mh : mass of hadron k2 : virtuality of fluctuation

→ Lifetime of fluctuations ~ 1/Mh 2 Hard

fi (x, Q ) = number density of partons i at momentum fraction x over and probing Q2. time incoming probe interacts much scale shorter

scale ~ 1/Q

Linguistics (example): On that timescale, partons ~ frozen ! F2(x, Q2) =

2) e2 xf (x, Q i i

Hard scattering knows nothing of ithe target hadron apart from the fact that it contained struck parton structurethe function parton distributions Illustration from T. Sjöstrand P. Skands

QCD Lecture II

37

(Factorization Theorem) Example: DIS

(Collins, Soper, 1987)

Scattered Lepton

Incoming Lepton

Deep Inelastic Scattering (DIS)

See also electron-nucleon scattering in lectures by K. Assamagan

Q2 Momentum Fraction

(By “deep”, we mean Q2>>Mh2)

Struck Hadron

xi

ˆ

f

Scattered Quark

“Beam Remnant”

fi/h

→ We really can write the cross section in factorized form : `h

=

Z XX i

f

Sum over Initial (i) and final (f) parton flavors P. Skands

dxi

Z

`i!f dˆ (xi , 2 d f fi/h (xi , QF ) dxi d f

= Final-state phase space

fi/h

= PDFs Universal Constrained by fits to data

2 , Q f F) f

Differential partonic Hard-scattering Matrix Element(s)

QCD Lecture II

38

Summary - Lecture 2 Monte Carlo Generators are used in particle physics to simulate realistic “events” in as much detail as mother nature (but with approximations)

Hard Processes → Perturbative Quantum Field Theory (based on Lagrangian of Standard Model - or BSM extensions) Hard partons emit bremsstrahlung → simulated by iterating universal radiation patterns (e.g., dipoles) in a parton shower, ordered in a measure of formation time Linear Confinement → Quarks and Gluons turn into hadrons. Hadronization modeled by color strings + string breaking via quantum mechanical tunelling (in PYTHIA) MC Lecture 2

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

39

Recommended Reading G. Dissertori, I. Knowles, S. Schmelling

Quantum Chromodynamics Oxford Science Publications, 2003 P. Skands Lecture notes from TASI, June 2012, Boulder, Colorado

Introduction to QCD

e-Print: arXiv:1207.2389

MCnet Review : A. Buckley et al.

General-purpose Event Generators for LHC Physics Phys.Rept. 504 (2011) 145

MC Lecture 2

P. S k a n d s - M o n t e C a r l o G e n e r a t o r s f o r P a r t i c l e P h y s i c s

40