Introduction to Relativistic Heavy Ion Collision Physics

Huan Z. Huang

黄焕中Department of Physics and Astronomy

University of California, Los Angeles

Oct 2006 @Tsinghua

http://hep.tsinghua.edu.cn/talks/Huang/

Two Puzzles of Modern Physics

• Missing Symmetry – all present theories are based on symmetry, but most symmetry quantum numbers are NOT conserved.

• Unseen Quarks – all hadrons are made of quarks, yet NO individual quark has been observed.

-- T.D.Lee

Vacuum As A Condensate

• Vacuum is everything but empty! • The complex structure of the vacuum and the

response of the vacuum to the physical world breaks the symmetry.

• Vacuum can be excited!

We do not understand vacuum at all !

A Pictorial View of Micro-Bangs at RHIC

Thin PancakesLorentz =100

Nuclei pass thru each other

< 1 fm/c

Huge StretchTransverse ExpansionHigh Temperature (?!)

The Last Epoch:Final Freezeout--

Large Volume

Au+Au Head-on Collisions 40x1012 eV ~ 6 micro-Joule

Human Ear Sensitivity ~ 10-11 erg = 10-18 Joule

A very loud Bang, indeed, if E Sound……

Vacuum Engineering !

initial state

pre-equilibrium

QGP andhydrodynamic expansion

hadronization

hadronic phaseand freeze-out

High Energy Nucleus-Nucleus Collisions

Physics: 1) Parton distributions in nuclei 2) Initial conditions of the collision 3) a new state of matter – Quark-Gluon Plasma and its properties 4) hadronization

Rapidity:

Pseudo-rapidity:

Transverse Momentum:

Transverse Mass:

Kinematic Variables

)ln(2

1

Z

Z

PE

PEy

)2

ln(tan)ln(2

1

Z

Z

PP

PP

22YXT ppp

20

2 mpm TT

Useful Expressions

Edydp

y

ymp

ymE

z

z

TZ

T

tanh

sinh

cosh

2

*

*max

*

S

LLF

p

p

px

M

Qx

EE

qQppqfi

fi

2

)(

;)(

2

2222

Feymann xF:

Bjorken x:

Light-cone x+:beamz

z

pE

pEx

)(

)(

Cross Sections

Total = Number of Reactions

Number of Beam Particles X Scattering Center / Area

Dimension [L2]

Total = inel + el

inel= SD + ND

SD: Singly Diffractive ND: Non-Diffractive

Differential Cross Section:

dddppdpdpdppd

pd

d

zyx sin23

3

3

Question: differential cross section vs total cross section?

Invariant Multiplicity Density:

E d3n/d3p

Invariant Cross Sections

dydmm

d

dydpp

d

TT

TT

2

22

2Invariant Differential Cross Section:

E d3/d3p

dydmmN

Nd

dydppN

Nd

TTev

TTev

2

22

2

Experimental Considerations: Efficiency, Acceptance, Decay Correction, Target-out Correction.

Order of Magnitude

Geometrical CS: pp r2 = (1fm)2 = 32 mb

Au+Au Collisions: Rau = 1.2 A1/3 = 6.98 fm bmax=(2R)2 = 6 barn

1 barn = 10-24 cm2

Regge Theory: total=XS0.0808 + YS-0.4525

p-pbar 21.70 98.39 mbp-p 21.70 56.08 mb

Pomeron f,a,….

HIJING: minijet production

Luminosity at Collider

L = NB

2 B v / UA

B Number of bunches per beamNB Number of particles per bunchv velocity of particlesU circumference of the ringA beam cross section at the collision

Relativistic Heavy Ion Collider:

*

2

2

3

N

Brev

NBfL

N Invariant Transverse 95% Emittance the beta function

RHIC Numbers

RHIC Design:Au Beam proton Beam

B 57 NB 109 1011

L 2x1026 1x1031 cm-2s-1

200 GeV 500 GeVNNs

Collision Rate: L x Hz 0.7 MHz

RHIC Complex

STAR

Relativistic Heavy Ion Collider --- RHIC

Au+Au 200 GeV N-N CM energyPolarized p+p up to 500 GeV CM energy

Building Blocks of Hadron World

Proton Neutron

(uud) (udd)

Mesons

(q-q)

Exotics

(qqqq-q,…)

Molecules

Atoms

Electrons

Strong interaction is due to color charges and mediated by gluons. Gluons carry color charges too.

Baryon Density: = baryon number/volumenormal nucleus 0 ~ 0.15 /fm3 ~ 0.25x1015 g/cm3

Temperature, MeV ~ 1.16 x 1010 K10-6 second after the Big Bang T~200 MeV

Nucleus

Hyperons

(s…)

Energy Scale and Phase Transition

Entity Energy Dimension Physics Bulk Property P/T

Atom 10’s eV 10-10 m Ionization e/Ion Plasma No

Nucleus 8 MeV 10-14 m Multifrag. Liquid-Gas Y(?)

QCD 200 MeV 10-15 m Deconfine. QGP Y(?)

EW 100 GeV 10-18 m P/CP Baryon Asymmetry Y(?)

GUT 1015-16 GeV Supersymmetry

TOE 1019 GeV Superstring

Salient Feature of Strong Interaction

Asymptotic Freedom: Quark Confinement:

庄子天下篇 ~ 300 B.C. 一尺之棰，日取其半，万世不竭

Take half from a foot long stick each day,You will never exhaust it in million years.

QCD q q

q qq q

Quark pairs can be produced from vacuumNo free quark can be observedMomentum Transfer

Co

up

lin

g S

tren

gth

Shorter distance

(GeV)

QCD on Lattice

Transition from quarks to hadrons – DOF !QGP – not an ideal Boltzmann gas !

Lattice: current statusLattice: current status• technical progress: finer mesh size, physical quark masses, improved

fermion actions phase-transition: smooth, rapid cross-over EoS at finite μB: in reach, but with large systematic uncertainties

critical temperature: TC180 MeV

Rajagopal & Wilczek, hep-ph/0011333

Fodor & Katz, hep-lat/0110102

Quark-Hadron Phase Transition

QGP – micro-second after the Big Bang

The Melting of Quarks and Gluons-- Quark-Gluon Plasma --

Matter Compression: Vacuum Heating:

High Baryon Density-- low energy heavy ion collisions-- neutron starquark star

High Temperature Vacuum -- high energy heavy ion collisions -- the Big Bang

Deconfinement

QCD Phase Transition

Baryonic Potential B [MeV]

Chem

ical Tem

pera

ture

Tch

[M

eV

]

0

200

250

150

100

50

0 200 400 600 800 1000 1200

AGS

SIS

SPS

RHIC quark-gluon plasma

hadron gas

neutron stars

early universe

thermal freeze-out

deconfinementchiral restoration

Lattice QCD

atomic nuclei

What do experimental data points indicate and how were these points obtained ?

Nuclear Collision Geometry

Number of Participants

Impact Parameter

Particle Production is assumed to be directlyrelated to the impact parameter or number of

participant nucleons.

a) Geometrical Interpretation of Observables A monotonic relation between the observable and collision centrality is assumed

b) Estimate from direct measurement missing energy from Zero-degree calorimeter from dn/dy of protons….

Number of Participant Nucleons

Directly Determining NPART

Best approach (for fixed target!):– Directly measure in a “zero degree calorimeter”– (for A+A collisions)

– Strongly (anti)-correlated with produced transverse energy:

PerNucleon

ZDCPART E

EAN 2

ET

ET

EZDC

NA50

Number of Participant Nucleonsc) Dynamical Model Tune to fit experimental measurement From model to convert measurement to impact parameter and number of participant nucleons ++ Fluctuations are included - - Physical picture is biased to begin with

mT spectrum: d2n/(2mT)dmTdy vs (mT-m0)pT spectrum: d2n/(2pT)dpTdy vs pT

Spectrum Fit

Boltzmann mT Fit:d2n/(2mT)dmTdy ~ mT exp(-mT/slp)

slp Slope Parameter

Why is this Boltzmann?d3n/d3p ~ exp(-E/T)

Invariant Multiplicity Density:Ed3n/d3p ~ E exp(-E/T)E = mTcosh(y-ycm)d2n/(2mT)dmTdy ~ mT cosh(y-ycm) exp(-mT cosh(y-ycm)/T)

Slp depends on rapidity for an isotropic thermal fireballslp = T/cosh(y-ycm)

dn/dy =

2

2

2

)(2

2)2

( y

cmyy

TTTT

edmmdydmm

nd

y ~ 0.7-0.8

Naïve Expectations• Thermal Isotropic Source mT Scaling

, K and proton have the same slope parameter e-E/T

T = 190 MeV

T = 300 MeV

Tp = 565 MeV

mid-rapidity

Data show a large difference among these particles Expansion

Naïve Expectation 2

Slope parameter TemperatureRapidity density dn/dy entropy or energy density

First Order Phase Transition:

dn/dy

<pT>

hadron

QGP

Mixed

Collision dynamics much more complicated !!

Collision Dynamics

Bjorken Scaling

Bjorken Ansatz: “…… at sufficient high energy there is a‘central-plateau’ structure for the particle production as a function of the rapidity variable.”

y

dn/dy

Physics must be invariant under Lorentz-boost:

1) Local thermodynamic quantity must be a function of

proper time only.

2) Longitudinal velocity

vz = z/t or y = 0.5 ln ((t+z)/(t-z))

22 zt

Bjorken Energy Density

Energy density = E x N

A x z

E average energy per particleA transverse area of the collision volumez longitudinal intervalN number of particles in z interval

vz = z/t = tanh y; z = sinh yz = cosh y yE = mT cosh y

= mT cosh y N

A cosh y ymT

Adn/dy

Initial Energy Density EstimatePRL 85, 3100 (00); 91, 052303 (03); 88, 22302 (02), 91, 052303 (03)

PHOBOS

hminus:Central Au+Au <pT>=0.508GeV/cpp: 0.390GeV/c

Pseudo-rapidityWithin ||<0.5 the total transverse momentum created is 1.5x650x0.508 ~ 500 GeV from an initial transverse overlap area of R2 ~ 153 fm2 !

Energy density ~ 5-30 0 at early time =0.2-1 fm/c !

19.6 GeV

130 GeV200 GeV

Ideas for QGP Signatures

Strangeness Production: (J.Rafelski and B. Muller PRL 48, 1066 (1982))

s-s quark pair production from gluon fusions in QGP leads to strangeness equilibration in QGP most prominent in strange hyperon production (and anti-particles).

Parton Energy Loss in a QCD Color Medium:(J.D. Bjorken Fermilab-pub-82-059 (1982) X.N. Wang and M. Gyulassy, PRL 68, 1480 (1992))

Quark/gluon

Quark/gluon dE/dx in color medium is large!

Ideas for QGP Signatures

Chiral Symmetry Restoration: T = 0, m(u,d,s) > 0 – Spontaneous symmetry breaking T> 150 MeV, m=0 – Chiral symmetry restored Mass, width and decay branching ratios of resonances may be different in dense medium .

QCD Color Screening: (T. Matsui and H. Satz, Phys. Lett. B178, 416 (1986))

A color charge in a color medium is screened similar to Debye screening in QED the melting of J/.

c c Charm quarks c-c may not bindInto J/ in high T QCD medium

The J/ yield may be increased due to charm quark coalescence at the final stage of hadronization (e.g., R.L. Thews, hep-ph/0302050)

Models of Neutron StarsF. Weber J.Phys. G27 (2001) 465

“Strangeness" of dense matter ?In-medium properties of hadrons ?Compressibility of nuclear matter ? Deconfinement at high baryon densities ?

1st year detectors

Silicon Vertex Tracker

Central Trigger Barrel

FTPCs

Time Projection Chamber

Barrel EM Calorimeter

Vertex Position Detectors

Endcap Calorimeter

Magnet

Coils

TPC Endcap & MWPC

RICH+ TOF

Silicon Strip Detector

ZDC

2nd year detectors installation in 2002 installation in 2003

ZDC

The STAR Detector