The Big Picture George Smoot

Particle Production in Heavy Ion Collisions • pQCD • Strings • Thermal models • Hydrodynamics • … • Overview of results from different approaches

Standard Model Sheldon Glashow Steven Weinberg Abdus Salam

Beta decay, Neutrino scattering d  u

Murray Gell-Mann Fathers of QCD George Zweig  biology  hedge funds

QCD • 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 , 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

s ~ e f gamma* e+ ~ charge (e) ~ charge (f) fbar 2

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 Leon Ledermann “Ups-Leon” Makoto Kobayashi, pred. bottom for CP violation 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

)

dp

4 ~ 

dx

1

dx

2

f

1 (

x

1 ,

Q

)

f

2 (

x

2 ,

Q

)

d

4  (

ab



cd

)

dp

4

partonic

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 D q  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 e q hadrons gamma* qbar e+

Micheal Creutz Lattice people

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



J rotator model of the hadron (I) • Motivated by the behaviour of angular momentum vs. mass J(M 2 )=alpha(0)+alpha’ M 2 alpha(0) = Regge intercept alpha’ = Regge slope ~ 1 GeV -2 M 2

r Rotator (II) Model hadron as two (massless) color charges moving at the speed of light on a circle

String tension estimate

Lattice results Flux tube between quarks and anti-quarks 22 lattice spacing apart color electric and magnetic

A(z) Particle production: Tunneling 0 L z I 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 Carlos Pajares Tjoerborn Sjostrand 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!!