Peter Skands Theoretical Physics, CERN / Fermilab Event Generators 1 A Practical Introduction to the Structure of High Energy Collisions Aachen, November

Peter SkandsTheoretical Physics, CERN / FermilabPeter SkandsTheoretical Physics, CERN / Fermilab

Event Generators 1Event Generators 1A Practical Introduction to the Structure of High Energy Collisions

Aachen, November 2007

Event Generators 1 - 2Peter Skands

DisclaimerDisclaimer

Ask about … whatever !If I become too incomprehensible, don’t hesitate (!) to ask, I assure you it’s very difficult to make me embarrassed: try!

Focus on LHC. Even so, we will not cover:

Heavy IonsTopics Specific to

B MesonsHiggs DiscoverySUSY and other BSM phenomenology

Luminosity, Total cross sections, Diffractive, and Elastic ScatteringAll = Important Topics, on which this particular lecturer is worthless


DispositionDisposition

Fundamental Topics (1st class)

Beyond Fixed-Order Perturbation Theory

Parton Showers Hadronisation

Monte Carlo generatorsHERWIG and PYTHIAHe who wishes to do everything …

Advanced Topics (2nd and 3rd classes) Focus on Hadron Collisions

What we know and don’t know about hadron collisionsThe Underlying Event

Matching

Wed Thu Fri10-12 : Fundamental Topics

10-12: Advanced Topics 1

10-12: Advanced Topics 2 + Q&A

13-15:30: Hands-on Session: Pythia and Alpgen


Fundamental TopicsFundamental Topics

• Beyond Fixed-Order Perturbation Theory:– Parton Showers – Hadronisation

• The HERWIG and PYTHIA Generators


Classical Example: counting tracksClassical Example: counting tracks

Simple Models ~ Poisson

Can ‘tune’ to describe average,

but not the fluctuations insufficient hypothesis

More Physics:

Models with multiple parton-

parton interactions

Once upon a time … UA5, pp (546 GeV), charged track multiplicity in minimum-bias events

Low-pT only

Low-pT + Hard int

Low-pT + Hard int + ISR + FSR

The point of this story

1) It is not possible to ‘tune’ better than the underlying physics model allows

2) The failure of a physical model usually indicates deeper physics (more than you

get from a fit that stops working).


Prerequisites / DiscussionPrerequisites / Discussion

You know (a little) aboutPerturbative Quantum Field Theory

Matrix Elements Not how to calculate them necessarily, but what they represent physically and which general features they contain: propagators, phase space integrals, how to go from matrix elements to cross sections, etc

The role of the observable The difference between exclusive and inclusive observables

The perturbative expansionThrough the hoops: Legs and loops

Computer PhysicsMonte Carlo integration as a numerical toolMarkov Chains, e.g., as describing nuclear decay

Like me, you know (almost) nothing aboutNon-perturbative quantum field theoryReggeons, Pomerons, Strings (incl AdS/CFT), OPE, EFT’s, χPT, HQET, … And you hate talks with C++ class diagrams (or F77 common blocks …)


Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory

Example:

QuantumChromoDynamics

Reality is more complicated

High-transverse momentum interaction


Fixed Order (all orders)

“Experimental” distribution of observable O in production of X:

k : legs ℓ : loops {p} : momenta

Monte Carlo at Fixed Order

High-dimensional problem (phase space)

d≥5 Monte Carlo integration

Principal virtues

1. Stochastic error O(N-1/2) independent of dimension

2. Full (perturbative) quantum treatment at each order

3. (KLN theorem: finite answer at each (complete) order)

Note 1: For k larger than a few, need to be quite clever in phase space sampling

Note 2: For ℓ > 0, need to be careful in arranging for real-virtual cancellations

“Monte Carlo”: N. Metropolis, first Monte Carlo calcultion on ENIAC (1948), basic idea goes back to Enrico Fermi


Parton Showers

High-dimensional problem (phase space)

d≥5 Monte Carlo integration

+ Formulation of fragmentation as a “Markov Chain”:

1. Parton Showers:

iterative application of perturbatively calculable splitting kernels for n n+1 partons

2. Hadronization:

iteration of X X’ + hadron, according to phenomenological models (based on known properties of QCD, on lattice, and on fits to data).

A. A. Markov: Izvestiia Fiz.-Matem. Obsch. Kazan Univ., (2nd Ser.), 15(94):135 (1906)

S: Evolution operator. Generates event, starting from {p}X


Traditional GeneratorsTraditional Generators

• Generator philosophy: • Improve Born-level perturbation theory, by including the ‘most

significant’ corrections complete events

1. Parton Showers 2. Hadronisation3. The Underlying Event

1. Soft/Collinear Logarithms2. Power Corrections3. All of the above (+ more?)

roughlyroughly

(+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …)

Asking for fully exclusive events is asking for quite a lot …


Be wary of oraclesBe wary of oracles

PYTHIA Manual, Sjöstrand et al, JHEP 05(2006)026

Be even more wary if you are not told to be wary!

We are really only operating at the first few orders (fixed + logs + twists + powers) of a full quantum expansion


Non-perturbativehadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton ratio, kaon/pion ratio, ...

Soft Jets and Jet StructureSoft/collinear radiation (brems), underlying event (multiple perturbative 22 interactions + … ?), semi-hard brems jets, …

Resonance Masses…

Hard Jet TailHigh-pT jets at large angles

& W

idths

+ Un-Physical Scales:+ Un-Physical Scales:

• QF , QR : Factorization(s) & Renormalization(s)

sInclusive

Exclusive

Hadron Decays

Collider Energy ScalesCollider Energy Scales


TThe he BBottom ottom LLine ine

The S matrix is expressible as a series in gi, gin/Qm, gi

n/xm, gin/mm, gi

n/fπm

, …

To do precision physics:

Solve more of QCD

Combine approximations which work in different regions: matching

Control it

Good to have comprehensive understanding of uncertainties

Even better to have a way to systematically improve

Non-perturbative effects

don’t care whether we know how to calculate them

FO DGLAP

BFKL

HQET

χPT


The Monte Carlo MethodThe Monte Carlo MethodWant to generate events in as much detail as Mother Nature

Get average and fluctuations right Make random choices, ~ as in nature

σfinal state = σhard process Ptot, hard process final state

where Ptot = Pres PISR PFSR PMI PRemnants PHadronization Pdecays

With Pi = Πj Pij = Πj Πk Pijk = …in its turn Divide and conquer

Hard Part

Up to Ecm

Parton Showers + Multiple

InteractionsMulti-GeV

Hadron D

ecays

Hadronization+ Remnants~ 1 GeV ~ 10-15 m

σhard process, Pres PISR, PFSR, PMI Premnants, PhadronizationPdecays

= the S operator from before


Problem 1: bremsstrahlung corrections are singular for soft/collinear configurations spoils fixed-order truncation

e+e- 3 jets

Beyond Fixed OrderBeyond Fixed Order


Diagrammatical Explanation 1Diagrammatical Explanation 1dσX = …

dσX+1 ~ dσX g2 sab /(sa1s1b) dsa1ds1b

dσX+2 ~ dσX+1 g2 sab/(sa2s2b) dsa2ds2b


But it’s not yet an “evolution”What’s the total cross section we would calculate from this?

σX;tot = int(dσX) + int(dσX+1) + int(dσX+2) + ...

Probability not conserved, events “multiply” with nasty singularities! Just an approximation of a sum of trees.

But wait, what happened to the virtual corrections? KLN?

dσX

α sab

saisibdσX+1 dσ

X+2

dσX+2

This is an approximation of inifinite-order tree-level cross sections


Diagrammatical Explanation 2Diagrammatical Explanation 2dσX = …

dσX+1 ~ dσX g2 sab /(sa1s1b) dsa1ds1b



+ Unitarisation: σtot = int(dσX)

σX;PS = σX - σX+1 - σX+2 - …

Interpretation: the structure evolves! (example: X = 2-jets)Take a jet algorithm, with resolution measure “Q”, apply it to your eventsAt a very crude resolution, you find that everything is 2-jets At finer resolutions some 2-jets migrate 3-jets = σX+1(Q) = σX;incl– σX;excl(Q)Later, some 3-jets migrate further, etc σX+n(Q) = σX;incl– ∑σX+m<n;excl(Q)This evolution takes place between two scales, Qin and Qfin = QF;ME and Qhad

σX;PS = int(dσX) - int(dσX+1) - int(dσX+2) + ... = int(dσX) EXP[ - int(α sab /(sa1s1b) dsa1 ds1b ) ]

dσX

α sab

saisibdσX+1 dσ

X+2

dσX+2

Given a jet definition, an

event has either 0, 1, 2, or … jets


Observation: the collinear limit is universalIf Nature was perfectly described by this limit calculate all corrections for all reactions in one fell swoop!

Exponentiated integration kernels (Altarelli-Parisi) (resummation)

Iterative formulation = parton showerFor any reaction, for any observable, generate all the most singular corrections of QCD (& QED)

Ordered in a measure of resolution (Q ~ 1/time) a series of successive factorisations; the last one non-perturbative

LimitationsMissing terms (quantum interference)

Kinematic ambiguities and “double counting” between fixed-order and resummation (see matching later …)

Parton ShowersParton Showers


ME

PS 1

PS 2

Problem: Necessary Problem: Necessary

to describe both theto describe both the

hard and soft regions hard and soft regions

“ “Matching” Matching”

Bremsstrahlung - Example: SUSY @ LHCBremsstrahlung - Example: SUSY @ LHC

Comparisons:

1. Matrix Elements with 0,1,2 jets.

2. Parton Showers ~ resommation

FIXED ORDER pQCD

inclusive X + 1 “jet”

inclusive X + 2 “jets”

LHC - sps1a - m~600 GeV Plehn, Rainwater, PS (2005)


Note on FactorisationNote on Factorisation

Parton showers are not “soft”, here is proof:

Correction: Parton Showers are correct in the soft/collinear limit, but the neglected terms can be negative (the usual case?) splitting kernels = over-estimate

ME

PS 1

PS 2

Sjöstrand et al, PLB185(1987)435, NPB289(1987)810, PLB449(1999)313, NPB603(2001)297

LHC - sps1a - m~600 GeV Plehn, Rainwater, PS (2005)


(Note on Factorisation)(Note on Factorisation)The problem of showers that “die” then?

Caused by “cuts” in the phase space, not by the kernels

Proposition: this is not intimately related to the “softness” of showers!One possibility: choose the factorisation scale such that “everything looks like 2-jets” in the beginning, that is choose the largest possible scale s instead of s-hat “power showers” (or something inbetween?)

Have to admit that this is still somewhat controversial

Plehn, Rainwater, PS: PLB645(2007)217 & hep-ph/0511306

hep-ph/0511306

Top pair + jet

Tevatron

Top pair + jet

LHC


CoherenceCoherenceFrom T. Sjöstrand


Ordering VariablesOrdering Variables

From T. Sjöstrand


Data ComparisonsData ComparisonsShowers describe LEP data fairly well …

• Now: a renaissance in this field! August-October ‘07: 4 new cascades, 1 based on “antennae”, 2 on “Catani-Seymour dipoles”, 1 on a hybrid scheme

• Important to keep power to constrain, event after the experiments are finished


Initial vs FinalInitial vs FinalFSR and ISR : almost the same evolution

From T. Sjöstrand


For FSR, LEP allowed studies “in isolation”Especially for quark jets very good constraints

b-jets could be studied separately

Gluons 3-jet events, weaker constraints + Not always easy to separate non-perturbative perturbative

For ISR, our preferred lab is Drell-Yan (hadroproduction of dileptons)

“Crossing of LEP”: direct constraints on ISR off light quarksPDF suppression weaker constraints on ISR off b quarks Z/W+b

Corrections from the underlying eventFew constraints on ISR off gluons and b quarks:

Important to better know the environnement of Higgs Higgs is an interesting theoretical lab, but hard to isolate

The power to control Q2 in Drell-Yan should be used to the max

ISR / FSR: studiesISR / FSR: studies

FSR

ME

HAD

ME

ISR

F/I

BR

+ DIS


Drell-Yan: physics with a muon chamberDrell-Yan: physics with a muon chamberMuons = a direct light into the heart of the process A very clean, highly controllable “probe” of Initial-State Radiation (ISR)

Feed back into photon + jet improve jet calibration

Muons + tracking can also study Underlying Event here (minijets, fragmentation, …)

Evolution of UE and ISR as function of Q2 good model constraints

In preparation: PS, Les Houches ‘Physics at TeV colliders’ 2007


Summary – Parton ShowersSummary – Parton Showers

Parton Showers are very usefulApplicable to any final state

Parton Showers are limitedSo far, they only contain the “first orders” of logarithmsAgreement with data is desirable but can also be deceptive; not always guaranteed to be universal

Today, it is a field full of activityMany new ideas in the last ~ 5 yearsMany limitations are already lifted (cf. matching), but others remain … for you?

Beyond leading logs? Subleading colour?Matching to higher orders? To other expansions (HQET, BFKL, … )?


HadronisationHadronisation

Ptot = PRes PISR PFSR PUE PNP

PDecays

σfinal state = σhard process Ptot,hard process

final state

factorisation

factorisation


to Landau Pole

Probleme 2: QCD becomes non-perturbative below ~ 1 GeV (or more generally, in the resonance region)

Resumm

e

d

e+e- 3 jets

QuantumChromoDynamics


Hadronization / FragmentationHadronization / Fragmentation

Perturbative nonperturbative: not calculable from first principles!

How to model?Ideology + “cookbook”

Common Approaches:String fragmentation

(most ideological)

Cluster fragmentation (simplest?)

Independent fragmentation (most cookbook)


The Lund String ModelThe 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


QCD on the LatticeQCD on the Lattice

Linear confinement in “quenched” QCD


Gluons = Transverse ExcitationsGluons = Transverse Excitations

From T. Sjöstrand


Partons Partons Hadrons Hadrons

Hadron production arises from string breaks

String breaks modeled by tunneling

Most fundamental : THE AREA LAWBut also depends on spins, hadronic wave functions, phase space, baryon production, … more complicated


The Iterative AnsatzThe Iterative Ansatz

From T. Sjöstrand


Hadronization – Final RemarksHadronization – 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)

However, much remains uncertain for hadron collisions … At LEP, there was no colour in the initial stateAnd there was a quite small total density of stringsHow well do we (need to) understand fragmentation at LHC?


D. B. Leinweber, hep-lat/0004025

Anti-Triplet

Triplet

pbar beam remnant

p beam remnant

bbar

from

tbar

deca

y

b from

t d

ecay

qbar fro

m W

q from W

hadroniza

tion

?

q from W

In reality, all of this takes place in the same space-time interval.

(except maybe: long-lived resonances)

The (QCD) LandscapeThe (QCD) Landscape


QuestionsQuestions

At LEP, we didn’t have UE (multiple interactions) generating a large density of strings

Should new phenomena appear string interactions?Is there a critical density?

Is it related to the physics of heavy ions?

At LEP, we didn’t have the background of the protonIs the Cronin effect important? (rescattering)Is fragmentation affected by the “color wakefields” generated by the beam protons?Are there new coherence phenomena?


Recent Example: Colour AnnealingRecent Example: Colour Annealing

D. Wicke + PS, EPJC52(2007)133

Δ(mtop) ~ 0.5 GeV from infrared effectsEarly days. May be under- or overestimated. Primitive models, mostly useful for reconnaissance and order-of-magnitude

Pole mass does have infrared sensitivity. Can we figure out some different observable which is more stable?

Infrared physics ~ universal? use complimentary samples to constrain it. Already used a few min-bias distributions, but more could be included Drell-Yan, dijets, … ?

Sep 2007

Postulate string interactions, make a simple model, just to see:


Next Lecture: Advanced TopicsNext Lecture: Advanced Topics

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Peter Skands Theoretical Physics, CERN / Fermilab Event Generators 1 A Practical Introduction to the Structure of High Energy Collisions Aachen, November