UCT Seminar IV: Introduction to Hadronization

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UCT Seminar IVIntroduction to Hadronization

• Peter Steinberg
• Brookhaven National Laboratory
• Fulbright Scholar Program

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Basic Problem

• Quarks Gluons are confined
• Scattering experiments can liberate partons from
  hadrons ejection of bare color charge
• Final state must be colorless
• Partons blanch themselves by radiating hadrons!
• This process is called hadronization
• Interface between hard soft processes
• For some people, this is a problem
• Some people want to study the QCD matrix elements
  directly at hard scales (gt 1 GeV) need
  corrections
• For some people, this is a field of study unto
  itself!
• This is the central mystery of QCD!
• Heavy Ion Physics is an application
• What does it mean to hadronize a large system??

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Where to study hadronization
e
e-
g/Z
q
q
One scale ?s
Electron-positron annihilation
Best to study a simple system No color in
initial state
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Fragmentation Functions

• The first obvious thing to measure is the
  fragmentation spectrum relative to beam energy

More stuff_at_ low-x
where
Multiplicity!
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Scaling Violations

• System fragmentation functions are composed of
  parton fragmentation functions
• These evolve with scale, similarly to structure
  functions!

DGLAP functions
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QCD Predictions

• Can put the pieces together and predict
  multiplicity distributions in ee-!
• QCD ? prediction about final state hadrons

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How to Model Real Collisions

• What if we want to know more details
• Cannot calculate hadronization processes directly
  in QCD
• There is no feynman diagram for q?ppp
• Instead, we have models based on general
  properties of QCD
• Generally called fragmentation models
• Independent (ISAJET) Pure Fragmentation
• Strings (JETSET, PYTHIA) String Fragmentation
• Cluster (HERWIG) Phase Space Fragmentation
• As time goes by, more and more QCD is
  incorporated into these models
• Gluon radiation down to a soft momentum scale Qo
• Hadronization becomes less important as scale
  decreases

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Field-Feynman Picture

• Independent Fragmentation
• ISAJET model
• Jets are fragmented starting from the initial
  quark according to a fragmentation function,
  where z Eh/Eq

p
p
q
q
p
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Basic Idea of String Models
Nature of strong force confines field lines toa
narrow flux tube Potential is Coulomb Linear
V( r ) -A/r Br
p-
p
d
d
u
u
Anti-proton
proton
d
d
d
uu
uu
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Regge Trajectories

• Empirical Observation by Chew and Frautschi
• Hadron Masses Spins fall on linear trajectories
  in (J, M2) space

J
1
M2
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String Model of Hadrons

• Consider a hadron to be a rotating string of
  radius L and string tension k
• The energy stored in the string is
• The angular momentum is

vc
2L
Regge trajectories
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String Model position space

• String with massless quark endpoints

t
T
A
x
Area subtended by yo-yo string is its rest
mass. Mass is boost-invariant (can be checked!)
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String Model momentum space
V1
V0
p
p-
Boost-invariance!
Require invariance
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Lund String Model
Quark massdependence!
Correlation betw.Space Time( rapidity)of
production
Naturally givesplateau in rapidity
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Heavy Quark Fragmentaion
Heavy quarks (c b) give most of their momentum
to a leading heavy hadron (e.g. b?B)
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Comparing Functions
Light quarks (u,d) blue Fields-Feynman black
dash Lund fragmentation
dN/dz z
Heavy quarks (c,b) red Peterson function black
dash Lund fragmentation Bowler correction not
shown d(1-z) is obvious
For charm quarks, the Peterson and Lund
fragmentation roughly agree and give an average
ltzgt 0.8.
z
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Modern String Models

• Combination of QCD processes and string
  fragmentation
• Outgoing quarks radiate gluons
• Creates jet structure of event
• Can also think in terms of dipole picture
• Radiated gluons can also radiate
• Below a certain scale, string fragmentation takes
  over, as we have described

kink
g
2 boostedstrings!
q
q
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QCD Coherence

• Hard to radiate soft gluons at large angles

-
At large angle, if photon wavelengthtoo large,
sees zero net chargecant see structure of
dipole
q
QED
k

Limits photon emission to inside opening angle of
ee- Would not be the case if e and e- emitted
incoherently
Same effect in QCD, hard toemit large-angle soft
gluons!Angular Ordering
QCD
AO naturally creates angular structure of events
jet cones!
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HERWIG

• Basic idea
• Outgoing partons radiate gluons quarks
• Radiation constrained by QCD coherence
• Angular ordering is a major part of this
• At end of chain, gather partons into color
  singlet clusters
• Clusters decay by phase space
• Small clusters ? 1 hadron
• Big clusters ? 2 clusters
• Just Right ? 2 hadrons

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Details of particle production
Compilation by B. Webber(who made HERWIG!)
Shows how well modelscan be tuned
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Whats Better?

• When making measurements, you need to simulate
  real events
• Detector response
• Physics acceptance
• Fluctuations
• String Cluster fragmentation are both used
  heavily by experiments both are adequate
• Simple reason
• Models are tuned ? adjust parameters to fit
  data
• Much of the QCD-related physics is similar
• DGLAP evolution is a common feature
• More reliable at higher energies
• Not surprising, as we use more pQCD, results are
  less dependent on details of npQCD part!
• Still, there are results which favor one model
  over the other (e.g. charge-rapidity correlations)

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Statistical Models

• HERWIG is based partially on phase space, with
  some dynamics
• Interestingly models based almost completely on
  phase space can describe many details of final
  state

Thermal Model of F. Becattini
Jets are thermalized fireballswith collective
motion.Model is an efficient descriptionof
yields of particles in termsof T, gs
Strangeness suppression
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Factorization in hadron-hadron

• In hadron collisions, cross sections to produce
  high-pT hadrons expected to factorize into
  different parts

Structure Functionsof colliding beams
QCD CrossSection
FragmentationFunction
Final spectrum
EnergyConservation
PYTHIA ( HERWIG) calculate this via Monte Carlo
approach -- main differences is in fragmentation
scheme!
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Conclusions

• Hadronization is one of the central mysteries of
  QCD boundary of soft and hard physics
• However, QCD can tell us a lot already about
  high-energy reactions
• Evolution of fragmentation functions
• At soft scales, we have models that describe
  various features of data.
• Lund (JETSET, PYTHIA), HERWIG
• Statistical Models
• Factorization allows us to apply what we learn to
  hadron-hadron collisions
• Will this hold up in heavy ions? Stay tuned!