Introduction to Heavy Ion Collisions Rainer J. Fries Texas A&M University SERC School, VECC, Kolkata January 7-11, 2013

I.Quark Gluon Plasma 1.Quantum Chromodynamics 2.Basic Properties of QCD 3.Free the Quarks! 4.The Cosmic Connection II.Ultra-Relativistic Heavy Ion Collisions – An Introduction 1.Preliminaries: Kinematics, Geometry and all that 2.Basic Observations 3.Time Evolution of Heavy Ion Collisions 4.Highlights of Recent Results III.Hard Probes IV.Quark Recombination V.Electromagnetic Probes VI.Heavy Flavor Probes Rainer Fries 2SERC 2012 Overview

Some Books used:  YHM = Yagi, Hatsuda and Miake, Quark Gluon Plasma (Cambridge 2005)  LR = Letessier and Rafelski, Hadrons and Quark Gluon Plasma (Cambridge, 2002) Many other excellent literature available Rainer Fries 3SERC 2012 Literature

Introduction to Heavy Ion Collisions Part I: Quark Gluon Plasma

Rainer Fries 5SERC 2012 I.1 Quantum Chromodynamics

Rainer Fries 6SERC 2012 Start with Electrodynamics Maxwell: Field strength: Vector potential: Covariant derivative: U(1) gauge invariance: Lagrangian: Gauge group determined by Commutator!

SERC A Strange New Electrodynamics C N Yang & R L Mills (1954) worked out the math for a generalization to “gauge fields” with more cimplicates symmetry groups.  Most important example: SU ( N ) = unitary N x N matrices with determinant 1. From now on where is a function that takes values in the space of N x N matrices. Rainer Fries

8SERC 2012 SU(N) Yang-Mills Fields Maxwell: Field strength: Vector potential: Covariant derivative: U(1) gauge invariance: Lagrangian: Yang-Mills: Field strength: Vector potential: Covariant derivative: SU ( N ) gauge invariance: Lagrangian:

Rainer Fries 9SERC 2012 SU(N) Yang-Mills Fields Yang-Mills: Field strength: Vector potential: Covariant derivative: SU ( N ) gauge invariance: Lagrangian: All fields A and F and the current J are now N x N matrices. g = coupling constant of the theory. Non-abelian symmetry group  “non-abelian gauge field” One immediate consequence: quadratic and cubic terms in the equations of motion! The field theory is non-linear.

1940 only 5 elementary particles were known: proton, neutron, electron, muon and positron. With the advent of accelerators at the end of the decade a big zoo of hadrons (hundreds!) was discovered. Who ordered that? Gell-Mann & Zweig (1964): the zoo of hadrons could be understood if hadrons consisted of combinations of more fundamental spin-1/2 fermions with SU( N f ) flavor symmetry. Gell-Mann called them quarks. A crazy idea at the time! Rainer Fries 10SERC 2012 Hadron Zoology Gell-Mann: ‘Such particles [quarks] presumably are not real but we may use them in our field theory anyway.’

An new Rutherford experiment at higher energy:  See lecture by P. Mathews Cross section for inelastic e+p scattering: extract two “structure functions” F 1 and F 2.  Simply given by leading order (one-photon exchange) QED and Lorentz invariance. Two independent kinematic variables:  is the virtuality of the exchanged photon  x is the momentum fraction of the object inside the proton struck by the photon (elastic scattering: x = 1)  They can be related to the observables: the deflection angle and the energy loss of the electron. Rainer Fries 11SERC 2012 Dissecting Hadrons  pepe pepe q

Different predictions had been made. Suppose the proton consists of point-like spin-½ fermions (as in the quark model). Then:  F 1, F 2 don’t depend on Q 2 (Bjorken scaling)  F 1, F 2 are not independent: (Callan-Gross relation) SLAC, 1968 (Friedman, Kendall and Taylor): Quarks it is! Rainer Fries 12SERC 2012 Quarks Bjorken scaling (shown here for HERA data) Callan-Gross

The complete quark family: What are their interactions? e+e- collisions: each quark comes in triplicate! New quantum number: color! Rainer Fries 13SERC 2012 Quarks

Fritsch, Gell-Mann, Leutwyler (1972): Quarks couple to a SU( N c ) Yang- Mills field. N c = number of colors.  Quanta of the Yang-Mills/gauge field: gluons  Color plays the role of the “charge” of the quark field. Quantum chromodynamics is born! QCD Lagrangian:  q = N f quark fields of masses m f. F = gluon field strength. Quantization: non-linearity  self-interaction of the gluon field  Gluon itself carries N c 2 -1 colors.  3-gluon vertex  4-gluon vertex Rainer Fries 14SERC 2012 Quantum Chromodynamics

Rainer Fries 15SERC 2012 I.2 Basic Properties of QCD

Analytically: No! Numerically: Yes, in certain situations  Lattice QCD.  Discretize space-time and use euclidean time.  Extremely costly in terms of CPU time, very smart algorithms needed.  See lectures by R. Gavai Perturbation theory: only works at large energy scales / short distances (see asymptotic freedom below).  Lectures by P. Pal, S. Mallik, A. Srivastava Effective theories: Based on certain approximations of QCD or general principles and symmetries of QCD (e.g. chiral perturbation theory, Nambu- Jona Lasinio (NJL) model, classical QCD etc.)  Lectures by A. Srivastava, R. Venugopalan Rainer Fries 16SERC 2012 Can We Solve QCD? QCDOC at Brookhaven National Lab

Running coupling in perturbative QCD (pQCD):  Perturbative  -function known up to 4 loops. Leading term in pQCD   For any reasonable number of active flavors N f = 3 … 6.  E.g. from pQCD “potential” (cf. Handbook of Perturbative QCD) In QED: Rainer Fries 17SERC 2012 Asymptotic Freedom  -function QED: e larger at higher energies/smaller distances: screening through electron-positron cloud QCD: g smaller at higher energies/smaller distances: anti-screening through gluon loops

Leading order running of the coupling:   QCD here: integration constant; “typical scale of QCD”   QCD  200 MeV Vanishing coupling at large energies = Asymptotic Freedom  This permits, e.g., the application of pQCD in DIS.  Large coupling at small energy scales = “infrared slavery”  Bound states can not be treated perturbatively Rainer Fries 18SERC 2012 Asymptotic Freedom Gross, Wilczek, Politzer (1974)

Experimental fact: no free quarks or fractional charges found. Confinement property of QCD:  Only color singlet configurations allowed to propagate over large distances.  Energy required to remove a quark larger than 2-particle creation threshold. Heuristic picture:  At large distances the Coulomb-like gluon field between quarks becomes a flux tube with string-like properties.  String breaks once enough work is done for pair creation.  Flux tubes can be understood as gluon flux expelled from the QCD vacuum. Rainer Fries 19SERC 2012 Confinement Confinement is non-perturbative. It has not yet been fully understood. It has been named one of the outstanding mathematical problems of our time. The Clay Foundation will pay you $1,000,000 if you solve it!

Why gluon flux tubes?  Anti-screening of color charges from perturbative running coupling: Dielectric constant of QCD vacuum  < 0.  Dual Meissner Effect:   0 for long distances, expelling (color) electric flux lines.  Usual Meissner Effect in superconductors: perfect diamagnetism expels magnetic flux. Potential between (heavy) quarks can be modeled successfully with a Coulomb plus linear term:  String tension K  0.9 GeV/fm.  Successful in quarkonium spectroscopy.  Can be calculated in lattice QCD (later). Rainer Fries 20SERC 2012 Confinement

Classical QCD has several gobal symmetries. Chiral symmetry SU( N f ) L  SU( N f ) R :  acting on 2 N f -tuple of left/right-handed quarks  Obvious when QCD Lagrangian rewritten with right/left-handed quarks :  Chiral symmetry slightly broken explicitly by finite quark masses of a few MeV. Scale invariance: massless classical QCD does not have a dimensionful parameter. Both symmetries are broken:  Chiral symmetry is spontanteously broken in the ground state of QCD by a chiral condensate.  Quantum effects break scale invariance:  QCD is scale intrinsic to QCD. Rainer Fries 21SERC 2012 Global Symmetries

Pions are the Goldstone bosons from the spontaneous breaking of chiral symmetry. Gell-Man-Oaks-Renner relation: Infer value of chiral condensate at T =0:  Chiral perturbation theory: decreasing with increasing temperature. There is also a gluon condensate in the QCD vacuum Dilation current   from scale invariance:  Conserved for scale-invariant QCD (Noether Theorem).  Through quantum effects:  Gluon condensate implies a non-vanishing energy momentum tensor of the QCD vacuum! Rainer Fries 22SERC 2012 QCD Vacuum

Assuming for vacuum from Lorentz invariance. Energy density of the vacuum: This is also called the Bag Constant for a successful model for hadrons: vacuum exerts a positive pressure P = B onto a cavity with quark modes. Summary: QCD vacuum is an ideal (color) dielectric medium with quark and gluon condensates, enforcing confinement for all but color singlet configurations. Rainer Fries 23SERC 2012 QCD Vacuum

Collins and Perry, 1975: Due to asymptotic Freedom coupling becomes arbitrarily weak for large energies i.e. also for large temperatures. Therefore quarks and gluons should be asymptotically free at very large temperatures T. This hypothetical state without confinement at high T would be called Quark Gluon Plasma (QGP). Expect vacuum condensates to melt as well  chiral symmetry restoration at large T. How can confinement be broken? Rainer Fries 24SERC 2012 Why Quark Gluon Plasma?