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603-0060 極限量子構造汎論 Ⅱ Physics of the quark-gluon plasma. 担当:平野哲文、浜垣秀樹 Tetsufumi Hirano & Hideki Hamagaki. 4/9-5/21 (Hirano), 5/28-7/9 (Hamagaki). Thur. 16:30-18:00@Rm.207. Syllabus (planned, not confirmed).

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603 0060 physics of the quark gluon plasma

603-0060極限量子構造汎論ⅡPhysics of the quark-gluon plasma


Tetsufumi Hirano & Hideki Hamagaki

4/9-5/21 (Hirano), 5/28-7/9 (Hamagaki)

Thur. 16:30-18:00@Rm.207

syllabus planned not confirmed
Syllabus (planned, not confirmed)

[1] Introduction to hadron physics[2] Basic features of the quantum chromodynamics(QCD)[3] QCD phase transition at extreme conditions[4] Relativistic ideal/viscous hydrodynamics[5] Transport theory for QGP

[6] QGP in relativistic heavy ion collisions[7] Space-time description of the heavy ioncollisions[8] Observable and signatures of the QCD phasetransition[9] Relativistic heavy ion collider and detectorsystems[10] Recent experimental data


Q. What is the matter (in the sense

of many body system) in which

“building blocks” play

a fundamental role?

This is the question

which I would like to

address in this lecture.

building blocks
Building Blocks



physics of many bodies
Physics of Many bodies
  • “The whole is more than the sum of its parts.” (Aristotle) http://en.wikipedia.org/wiki/Holism
  • “More is different” (P.W. Anderson) http://www.sciencemag.org/cgi/pdf_extract/177/4047/393
  • “Wholism is the way to proceed science in the 21st Century.”(T.D. Lee, one of the founders of elementary particle physics)http://www.riken.jp/r-world/info/release/news/2000/dec/index.html#fro_01 (Original article in Japanese)

Elementary Particle Physics

as “Reductionism”

condensed matter physics of elementary particles
Condensed Matter Physics of Elementary Particles

Quark Gluon Plasma QGP:

Many-body system of quarks and

gluons under equilibrium

 Statistical and thermodynamical

physics of quarks and gluons

recipes for quark gluon plasma
Recipes for Quark Gluon Plasma

How are colored particles set free

from confinement?


Heat up

hadronic many body system

Figure adopted from


how high
How High?

Suppose a closed-pack massless pion system,

Or how low?


where was the qgp
Where WAS the QGP?

History of the Universe

History of the matter



Quark Gluon Plasma

(after micro seconds of Big Bang)

where is the qgp
Where IS the QGP?

Fate of Smashing Two Nuclei

Front View

Side View

Multiplicity of hadrons ~ 5000 in a

head-on collision at sqrt(sNN)=200 GeV

qgp from the 1 st principle

M.Cheng et al., PRD77,014511 (’08)

QGP from the 1st Principle
  • Equation of state from lattice QCD
  • Typical energy density scale of transition : ~1 GeV/fm3
  • Pseudo-critical temperature: ~190 MeV
  • Sound velocity is small in the vicinity of transition region
  • Lattice QCD is NOT applicable for time evolution
conjectured phase diagram of qcd
Conjectured Phase Diagram of QCD

Understanding of

phase diagram

 “Condensed matter

physics of QCD”

The region in which

we can investigate

by relativistic heavy

ion collisions


Physics of Relativistic

Heavy Ion Collisions

primary goals of heavy ion collisions at ultrarelativistic energies
Primary Goals of Heavy Ion Collisionsat Ultrarelativistic Energies
  • Understanding of QCD matter under extreme conditions (high T and low nB)
    • Confinement, chiral symmetry breaking
    • Relevant to early universe
    • Unique opportunity
  • Understanding of hadrons and nuclei at very high collision energy
    • Universal behavior (color glass condensate)
    • Not necessary unique, but give a good opportunity
big bang vs little bang
Big Bang vs. Little Bang

beam axis

Nearly 1D Hubble expansion*

+ 2D transverse expansion

3D Hubble expansion

Figure adopted from



big bang vs little bang contd
Big Bang vs. Little Bang (contd.)

Local thermalization is not trivial

in heavy ion collisions.

Collective flow is a key to see whether

local thermalization is achieved.

estimated energy density at rhic
Estimated Energy Density at RHIC

Well above ec from lattice simulations in central collision at RHIC

ec from lattice



Major Discovery at

Relativistic Heavy

Ion Collider (RHIC)

what is elliptic flow

Ollitrault (’92)

What is Elliptic Flow?

How does the system respond to spatial anisotropy?

Hydro behavior

No secondary interaction





Spatial Anisotropy


Interaction among

produced particles




Momentum Anisotropy







elliptic flow in kinetic theory
Elliptic Flow in Kinetic Theory

ideal hydro limit



: Ideal hydro

: strongly



b = 7.5fm


generated through secondary collisions

saturated in the early stage

sensitive to cross section (~1/m.f.p.~1/viscosity)

v2 is

arrival at hydrodynamic limit
Arrival at Hydrodynamic Limit



Experimental data reach hydrodynamic limit curve for the first time at RHIC.

qgp as opaque qcd matter
QGP as Opaque QCD Matter

Perfect liquid is something like

a black ink in a sense of QED.

jet tomography
Jet Tomography

1. Suppression of

inclusive yields

at high pT

2. Modification

of back-to-back


Adopted from


jet quenching
Jet Quenching
  • An energetic parton loses its energy by emitting
  • gluons during traversing medium.
  • Emitted gluons also interact with medium.
  • Interference effect (LPM effect)
  • Medium evolves dynamically.

Figure adopted from M. van Leeuwen, talk at QM2005.

high p t spectra
High pT Spectra

Proton-proton collision

Nucleus-nucleus collision





A x

















A x

A: Mass number

f’ : Parton distribution in a nucleus

D’: Modified fragmentation function

f: Parton distribution function

D: Fragmentation function

perturbative qcd
Perturbative QCD


Leading order

PHENIX data and

NLO QCD results

how to quantify jet quenching

Figure adopted from http://www.star.bnl.gov/central/focus/highPt/

How to Quantify Jet Quenching

Nuclear modification factor

Cronin peak

Yield scales with

Ncoll ?

Null case


Quenched case

Yield suppresses?

suppression of high p t hadrons
Suppression of High pT Hadrons

Large suppression in central Au+Au collisions!

Slide adopted from D.d’Enterria, talk at QM2004.

onset of jet quenching
Onset of Jet Quenching


RHIC, low E

RHIC, maximum E

D.d’Enterria, 0902.2011[nucl-ex]

(Almost) no jet quenching at SPS

Jet quenching was discovered for the first time

at RHIC.

jet accoplanarity
Jet Accoplanarity

What happens to away side peak in

azimuthal angle distribution for

associated hadrons?

Figure adopted from


disappearance of away side peak
Disappearance of Away-Side Peak

Where does the lost

energy go?

 Distributed among

soft particles?

Away-side peak:

Exists in p+p and d+Au

collisions, but disappears

in Au+Au collisions

Figure adopted from http://www.star.bnl.gov/central/focus/highPt/

split of away side peak
Split of Away-Side Peak

(trigger) x (associated)

*Background subtracted

One away-side peak  Two peaks!?

Figure adopted from H. Büsching, talk at QM2005.

mach cone in qgp
Mach-Cone in QGP?

Mach angle

(Sound velocity) < (Velocity of a high energy parton)

Information about sound velocity in the medium

Mach angle ~ 75 deg.

(Average) sound velocity cs2 < 0.1

 Very soft equation of state?

other probes
Other Probes
  • Rare particles
  • at the RHIC energies
  • heavy quarks
  • quarkonia
  • photons
  • di-leptons…

Rare probes will be

important at LHC.

Figure adopted from

D.d’Enterria, 0902.2011[nucl-ex]

See also Hamagaki-san’s lecture.



for LHC

extrapolation to lhc energy
Extrapolation to LHC energy

Naïve expectation:

More particles,

higher initial temperature,

longer lifetime of the QGP,

some predictions
Some Predictions

Elliptic flow coefficient

Nuclear modification factor

D.d’Enterria, 0902.2011[nucl-ex]

T.Hirano et al., J.Phys.G34,S879(’07)

Extrapolation of the same scenario

from RHIC to LHC…

understanding of full evolution at lhc era
Understanding of Full Evolution at LHC Era
  • After some initial time, space-time evolution of created matter is described by hydrodynamics reasonably well.
  • What happens at first contact? (Or how does the hadron/nucleus look at very high energy?)
  • If we would know the particle/entropy production at first contact, how does the QCD matter under local equilibrium form?
parton distribution in proton at small x
Parton Distribution in Proton at Small x
  • Gluons are dominant at small x.
  • Small x = High energy
  • Hadron/Nucleus as a bunch of gluons at high energy

x 20!!

Bjorken x ~ Fraction of longitudinal momentum in proton

Kinematics in gg g

interplay btw emission and recombination at small x
Interplay btw. Emission and Recombination at Small x

Linear effect (BFKL)

Non-linear effect

Figures adopted from

E.Iancu and R.Venugopalan, in Quark Gluon Plasma 3 (world scientific)

non linear evolution and color glass condensate cgc
Non-Linear Evolution and Color Glass Condensate (CGC)

Rate eq.*

small x

high energy

*More sophisticated equation (BK or JIMWLK)

based on QCD has been solved.

Figures adopted from

K.Itakura, talk at QM2005.

phase diagram of hadrons
“Phase Diagram” of hadrons
  • Onset of CGC at RHIC
    • Some evidences exist.
  • Test of CGC at LHC
    • How to describe
    • perturbative CGC to
    • non-perturbative QGP?


geometrical scaling


non-perturbative region



dilute parton



onset of cgc in d au collisions at rhic
Onset of CGC in d+Au Collisions at RHIC


forward rapidity


BRAHMS Collaboration, white paper


theory (CGC)

H.Fujii, talk at RCNP workshop(’07)

D.Kharzeev et al., PRD68,094013(’03).

  • An almost perfect fluid and opaque QCD matter is created at RHIC for the first time.
    • Concept of strongly interacting quark-gluon many body system is established.
  • Toward comprehensive understanding of the collision as a whole and the QGP at LHC
    • CGC is the key concept at ultrarelativistic energy.
  • Some exotic phenomena are anticipated.
    • Something like perfect fluidity or shock wave (Mach cone) at RHIC
syllabus planned not confirmed1
Syllabus (planned, not confirmed)

[1] Introduction to hadron physics[2] Basic features of the quantum chromodynamics(QCD)[3] QCD phase transition at extreme conditions[4] Relativistic ideal/viscous hydrodynamics[5] Transport theory for QGP

[6] QGP in relativistic heavy ion collisions[7] Space-time description of the heavy ioncollisions[8] Observable and signatures of the QCD phasetransition[9] Relativistic heavy ion collider and detectorsystems[10] Recent experimental data

2 basic features of the quantum chromodynamics qcd
[2] Basic features of the quantum chromodynamics (QCD)
  • Classical QCD Lagrangian
    • SU_c(3) Lie algebra, Equation of motion (Dirac for quarks and YM for gluons)
    • Gauge transformation, Noether's theorem
    • Global symmetry
      • Chiral symmetry, Scale invariance
  • Quantum aspects of QCD
    • Broken symmetry due to quantum effects
      • Axial anomaly, Trace anomaly, Broken chiral symmetry
      • Symmetry in vacuum < symmetry in Lagrangian --> Symmetry Breaking
    • Summary: fate of symmetry
  • Renormalization and asymptotic freedom
    • Runnning coupling alpha_s, beta function
  • Some experimental facts on N_c = 3
    • Delta^{++}, R value, pi^{0} -> 2 gamma
3 qcd phase transition at extreme conditions
[3] QCD phase transition at extreme conditions
  • Basic thermodynamics
    • Grand Partition function and thermodynamic function
    • Thermodynamic relations
    • Gibbs' phase equilibrium condition
  • Simple example: Relativistic ideal gases
    • Boson, Fermion
    • Steffen Boltzmann law
    • Resonance gas model, bag model, Hagedorn model
    • Chemically frozen resonance gas
  • Comments on recent lattice results
    • Partition function and imaginary time
    • Pseudocritical temperature
    • Equation of states
4 relativistic ideal viscous hydrodynamics
[4] Relativistic ideal/viscous hydrodynamics
  • Relativistic hydrodynamic equation
    • Tensor decomposition
    • Meaning of u^{mu}
    • Entropy conservation
    • Constitutive equation at 1st order
    • Equation of motion
    • Necessity of relaxation time
    • Constitutive equation at 2nd order
5 transport theory for qgp
[5] Transport theory for QGP
  • Kinetic interpretation of hydrodynamic equation
    • Liouville equation and BBGKY hierarchy
    • Classical and relativistic Boltzmann equation
    • H theorem
    • Equilibrium solution
    • Deviation from equilibrium
  • Phenomenological transport equation in QCD
    • Hosoya-Kajantie?
    • Danielewicz-Gyulassy?