The Big Picture
George Smoot
Particle Production in
Heavy Ion Collisions
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pQCD
Strings
Thermal models
Hydrodynamics
…
Overview of results from different
approaches
Standard Model
Steven Weinberg
Abdus Salam
Sheldon Glashow
Beta decay, Neutrino scattering
du
Fathers of QCD
Murray Gell-Mann
George Zweig
 biology
 hedge funds
QCD
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Psi_n: Quarks
A_mu: Gluon Field
F_mu nu: Gluon field tensor
m_n: Quark masses
t_a: Gell-Mann Matrices/2
a: Gluon Colour index (1..8)
Parts of the Lagrangian
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•
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, C are the SU(3) structure
constants
, like in QED, but with
non-commutative part
, quark couple to gluons
through color current
Invention of color:
Omega, Delta-, Delta++
Yoichiro Nambu
How do we know there are quarks
and colours?
• Deep inelastic scattering experiments:
direct observation of Rutherford scattering
off the quarks
• Measured cross section for hadron
production in e+ + e- interactions
2
ef
s~
gamma*
fbar
e+
~ charge (e)
~ charge (f)
Our prediction for the number of
quarks and colours…
Cross section e+e-  hadrons
E_CM (GeV)
Ratio R
Discovery of charm (74), bottom
(77) and top (95)
Sam Ting
(the J in J/Psi)
Luciano Maiani,
predicted charm
to avoid flavour
changing currents
Makoto
Kobayashi,
pred. bottom for
CP violation
Leon Ledermann
“Ups-Leon”
Toshihide Maskawa
pred. bottom for CP
violation
Hadron structure (I)
• To first approximation:
three quarks (baryon) or
quark--anti-quark (meson)
• Calculated as irreducible representations
of SU(n). E.g. with help of Young Tableaux
(see e.g. W. Greiner, Symmetries)
• First realized by Gell-Mann (quarks) (PRL,
Eightfold Way, Nobel prize) and Zweig (aces).
(Zweig’s paper is still pre-print and never got
accepted for publication ;-) …)
Quarks couple to hadrons
Hadron structure (II)
• Hadrons are complicated objects of many
quarks and gluons (partons)
• We know this from the momentum
distribution of the partons in the hadrons
(measurements by HERMES etc…)
• The number of partons in a hadron
depends on the resolution (i.e. momentum
transfer, usually called Q).
Parton model
He who needs not
be explained
James Bjorken
Sets of PDFs
•CTEQ, from the CTEQ Collaboration
•GRV, from M. Glück, E. Reya, and A. Vogt
•GJR, from M. Glück, P. Jimenez-Delgado, and E. Reya
•MRST, from A. D. Martin, R. G. Roberts,
W. J. Stirling, and R. S. Thorne
 new dev., generalized pdf’s
The pQCD scattering cross section
Within perturbative QCD a scattering
process can be easily described on the
basis of the parton distribution functions
and the pQCD scattering cross section
d 4 ( pp  cd  X )
d 4 (ab  cd )
~  dx1dx2 f1 (x1 , Q) f 2 ( x2 , Q)
partonic
4
4
dp
dp
Running coupling constant,
asymptotic freedom
David Gross
 Wilzcek
 Witten
 Pisarski
Frank Wilzcek
 Mark Alford
 Krishna Rajagopal
Why can we use pQCD?
The QCD coupling
constant
decreases with
increasing
momentum
transfer (i.e. at
small distances)
Typical Q for
alpha~1, is
Q~200 MeV,
i.e. 1fm
Hadronization of a quark (gluon jet)
• pQCD only describes the scattering of the
parton, not the hadronization process
• I.e. the pQCD scattering formula needs to be
supplemented with a model for the
‘fragmentation’ of the parton (the parton shower
or the jet, resp)
• This function is called the fragmentation function
Dqh(z), with z being the fraction of the total
parton momentum given to the hadron
Back to e+e• The fragmentation of a jet is easiest
understood in the simple process:
e+e-  q qbar
eq
hadrons
gamma*
qbar
e+
Lattice people
Micheal Creutz
More lattice people
Fritjof Karsch
Zoltan Fodor
Owe Philipsen
Linear potential from lattice
• If the quarks travel
away from each
other the QCD
potential leads to
particle production
in the critical field
Understanding the q-qbar system
• We expect the production of new q-qbar
pairs from the decay of the critical vacuum
between the quarks
 q….qbar-q….qbar-q….qbar-q….qbar-q…qbar 
rotator model of the hadron (I)
• Motivated by the behaviour of angular
momentum vs. mass
J(M2)=alpha(0)+alpha’ M2
J
alpha(0) = Regge intercept
alpha’ = Regge slope ~ 1 GeV-2
M2
Rotator (II)
r
Model hadron as two
(massless) color
charges moving at the
speed of light on a circle
String tension estimate
Lattice results
color electric and magnetic
Flux tube between quarks and
anti-quarks 22 lattice spacing
apart
Particle production: Tunneling
A(z)
0
I
z
L
II
III
QFT
Julian Schwinger
 Roy Glauber
 Gordon Baym
Roy Glauber
Gordon Baym
First prediction…
String models
• Currently there are two flavours of string
models around:
- colour exchange models (dual parton
model, Capella, Pajares,…)
- momentum transfer models (LUND)
String people
Tjoerborn
Sjostrand
Carlos Pajares
Bo Andersson
Klaus Werner
Thermal spectra / fluctuations
string vs. thermal…
• anti-omega enhancement
Problems
• No dynamical calculation of particle
production from first principles (QCD)
- pQCD: only parton-parton scattering at
Q>200 MeV
 hadron production is non-perturbative
- no lattice results of string break available
• Only effective models exist:
e.g. string models
• anti-omega problem!!