# Presentation: 297653

## Event Generators 1

- A Practical Introduction to the Structure of High Energy Collisions

- Aachen, November 2007

## Disclaimer

- 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 Ions
- Topics Specific to
- B Mesons
- Higgs Discovery
- SUSY and other BSM phenomenology
- Luminosity, Total cross sections, Diffractive, and Elastic Scattering
- All = Important Topics, on which this particular lecturer is worthless 

- Event Generators 1

## Disposition

- Fundamental Topics (1st class)
- Beyond Fixed-Order Perturbation Theory
- Parton Showers
- Hadronisation
- Monte Carlo generators
- HERWIG and PYTHIA
- He who wishes to do everything ...

- Advanced Topics (2nd and 3rd classes)
- Focus on Hadron Collisions
- What we know and don’t know about hadron collisions
- The Underlying Event
- Matching

| Wed | Thu | Fri |
| --- | --- | --- |
| 10-12 : Fundamental Topics | 10-12: Advanced Topics 1 | 10-12: Advanced Topics 2 + Q&A |
|  |  |  |
|  | 13-15:30: Hands-on Session: Pythia and Alpgen |  |

- Event Generators 1

## Fundamental Topics

-  Beyond Fixed-Order Perturbation Theory:
-  Parton Showers
-  Hadronisation
-  The HERWIG and PYTHIA Generators

## Classical 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
- It is not possible to ‘tune’ better than the underlying physics model allows
- The failure of a physical model usually indicates deeper physics (more than you get from a fit that stops working).

- Event Generators 1

## Prerequisites / Discussion

- You know (a little) about
- Perturbative 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 expansion
- Through the hoops: Legs and loops
- Computer Physics
- Monte Carlo integration as a numerical tool
- Markov Chains, e.g., as describing nuclear decay
- Like me, you know (almost) nothing about
- Non-perturbative quantum field theory
- Reggeons, Pomerons, Strings (incl AdS/CFT), OPE, EFT’s, χPT, HQET, ...
- And you hate talks with C++ class diagrams (or F77 common blocks ...)

- Event Generators 1

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

Example:

- Example:

- QuantumChromoDynamics

- Reality is more complicated

- High-transverse momentum interaction

- Event Generators 1

## Monte Carlo at Fixed Order

**High-dimensional problem (phase space)**
- d≥5  Monte Carlo integration

- Principal virtues
- Stochastic error O(N-1/2)  independent of dimension
- Full (perturbative) quantum treatment at each order
- (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

- Event Generators 1

## Parton Showers

**High-dimensional problem (phase space)**
- d≥5  Monte Carlo integration

**+ Formulation of fragmentation as a “Markov Chain”:**

**Parton Showers:**
- 	iterative application of perturbatively calculable splitting kernels for n  n+1 partons

**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*

- Event Generators 1

## Traditional Generators

- Generator philosophy:
- Improve Born-level perturbation theory, by including the ‘most significant’ corrections       _complete events_

*Parton Showers *
*Hadronisation*
*The Underlying Event*

*Soft/Collinear Logarithms*
*Power Corrections*
*All of the above (+ more?)*

- roughly

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

- Asking for fully exclusive events is asking for quite a lot ...

- Event Generators 1

## Be 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

- Event Generators 1

## Collider Energy Scales

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

- Soft Jets and Jet Structure
- Soft/collinear radiation (brems), underlying event (multiple perturbative 22 interactions + ... ?), semi-hard brems jets, ...

- Resonance Masses...

- Hard Jet Tail
- High-pT jets at large angles

-  & Widths

- + Un-Physical Scales:
-  QF , QR : Factorization(s) & Renormalization(s)

- s

**Inclusive**

**Exclusive**

- Hadron Decays

- Event Generators 1

## The Bottom Line 

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

- Event Generators 1

## The Monte Carlo Method

- Want 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 *P*tot, hard process  final state
- where *P*tot = *P*res *P*ISR *P*FSR *P*MI *P*Remnants *P*Hadronization *P*decays
- With *P**i* = Π*j* *P**ij** = *Π*j* Π*k* *P**ijk** = ...*in its turn
-  Divide and conquer

- Hard Part
- Up to Ecm

- Parton
- Showers      + Multiple Interactions
- Multi-GeV

- Hadron Decays

- Hadronization
- + Remnants
- ~ 1 GeV ~ 10-15 m

- σhard process, *P*res

*P*ISR,* P*FSR,* P*MI

*P*remnants,* P*hadronization

*P*decays

- = the *S* operator from before

- Event Generators 1

## Beyond Fixed Order

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

**e****+****e****-**** ******** 3 jets**

- Event Generators 1

## Diagrammatical Explanation 1

- dσX =  ...
- dσX+1 ~ dσX g2 sab /(sa1s1b) dsa1ds1b
- dσX+2 ~ dσX+1 g2 sab/(sa2s2b) dsa2ds2b
- dσX+3 ~ dσX+2 g2 sab/(sa3s3b) dsa3ds3b

- 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
- saisib

- dσX+1

- dσX+2

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

- Event Generators 1

## Diagrammatical Explanation 2

- dσX =  ...
- dσX+1 ~ dσX g2 sab /(sa1s1b) dsa1ds1b
- dσX+2 ~ dσX+1 g2 sab/(sa2s2b) dsa2ds2b
- dσX+3 ~ dσX+2 g2 sab/(sa3s3b) dsa3ds3b
**+** 	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 events
- At 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
- saisib

- dσX+1

- dσX+2

- Given a jet definition, an event has *either*  0, 1, 2, or ... jets

- Event Generators 1

## Observation: the collinear limit is universal
If 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 shower
For 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
Limitations
Missing terms (quantum interference)
Kinematic ambiguities and “double counting” between fixed-order and resummation (see matching later ...)

- If 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 shower
- For 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
- Limitations
- Missing terms (quantum interference)
- Kinematic ambiguities and “double counting” between fixed-order and resummation (see matching later ...)

- Parton Showers

- Event Generators 1

## Bremsstrahlung - Example: SUSY @ LHC

- Problem: Necessary
- to describe both the
**hard and soft regions **
-  “Matching”

- Comparisons:
- Matrix Elements with 0,1,2 jets.
- Parton Showers ~ resommation

- Event Generators 1

## Note 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

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

- LHC - sps1a - m~600 GeV

- Plehn, Rainwater, PS (2005)

- Event Generators 1

## (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

- Event Generators 1

## Coherence

- From T. Sjöstrand

- Event Generators 1

## Ordering Variables

- From T. Sjöstrand

- Event Generators 1

## Data Comparisons

- Showers 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

- Event Generators 1

## Initial vs Final

- FSR and ISR : almost the same evolution

- From T. Sjöstrand

- Event Generators 1

## 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 quarks
PDF suppression  weaker constraints on ISR off b quarks  Z/W+b
Corrections from the underlying event
Few 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

- 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 quarks
- PDF suppression  weaker constraints on ISR off b quarks  Z/W+b
- Corrections from the underlying event
- Few 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: studies

- FSR

- ME

- HAD

- + DIS

- Event Generators 1

## Drell-Yan: physics with a muon chamber

- Muons = 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

- Event Generators 1

## Summary – Parton Showers

- Parton Showers are very useful
- Applicable to any final state
- Parton Showers are limited
- So far, they only contain the “first orders” of logarithms
- Agreement with data is desirable but can also be deceptive; not always guaranteed to be universal
- Today, it is a field full of activity
- Many new ideas in the last ~ 5 years
- Many 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, ... )?

- Event Generators 1

## Hadronisation

- Ptot = PRes PISR PFSR PUE PNP PDecays

- σfinal state = σhard process Ptot,hard process  final state

- factorisation

- factorisation

## QuantumChromoDynamics

- to Landau Pole

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

**Resummed**

**e****+****e****- ******** 3 jets**

- QuantumChromoDynamics

- Event Generators 1

## Hadronization / 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)

- Event Generators 1

## The 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

- Event Generators 1

## QCD on the Lattice

- Linear confinement in “quenched” QCD

- Event Generators 1

## Gluons = Transverse Excitations

- From T. Sjöstrand

- Event Generators 1

## Partons  Hadrons

- Hadron production arises from string breaks
- String breaks modeled by tunneling
-  Most fundamental : **THE AREA LAW**
- But also depends on spins, hadronic wave functions, phase space, baryon production, ...  more complicated

- Event Generators 1

## The Iterative Ansatz

- From T. Sjöstrand

- Event Generators 1

## Hadronization – 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 state**
- And there was a quite small total **density of strings**
- How well do we (need to) understand fragmentation at LHC?

- Event Generators 1

## The (QCD) Landscape

- D. B. Leinweber, hep-lat/0004025

- In reality, all of this takes place in the same space-time interval.
- (except maybe: long-lived resonances)

- Event Generators 1

## Questions

- 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 proton
- Is the Cronin effect important? (rescattering)
- Is fragmentation affected by the “color wakefields” generated by the beam protons?
- Are there new coherence phenomena?

- Event Generators 1

## Recent Example: Colour Annealing

- D. Wicke + PS, EPJC52(2007)133

- Δ(mtop) ~ 0.5 GeV from infrared effects
- Early 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:

- Event Generators 1

## Next Lecture: Advanced Topics