1

Che-Ming KoTexas A&M University

Introduction: concepts and definitions

- Quark-gluon plasma (QGP)

- Heavy ion collisions (HIC)

Experiments and theory

- Signatures of QGP

- Experimental observations at RHIC

- Future experiments at LHC and FAIR

Relativistic Heavy Ion Collisions and Hot Dense Matter

References: C.Y. Wong, “Introduction to High Energy Heavy Ion Collisions”,World Scientific (1994); K. Yagi, T. Hatsuda, and Y. Miaki, “Quark-Gluon Plasma”, Cambridge University Press (2005)

2

Big Bang

3

Relativistic Heavy Ion Collisions: little bang

4A quark-gluon plasma is expected to be produced during initial stage

5

Phases of nuclear matter Courtesy of Roy Lacey

6

MeV160B37π

90Tpp 1/4

1/4

2cQGPH

3

εp,T

30

πgf(p)ppd

)(2

g QGPQGP

4QGP0

33

QGPQGP

fscqqg

qq87

gQGP

NNNgg16,g

37)g(ggg

Energy density and pressure of free massless quarks and gluons

Energy density and pressure of pion gas

B3

εp,BT

30

π3f(p)ppd

)(2

3 HH

4

0

33H

QCD phase transition at zero baryon chemical potential

Bag constantB1/4~220 MeV

7

Quantum Chromodynamics

Similar to QED butSimilar to QED but SU(3) gauge symmetry in color space → gluon self-interaction Approximate chiral symmetry in the light sector and is spontaneously broken in vacuum → → Eight goldstone bosons (π, K, η) and absence of parity doublets

fn

1i

aμν

μνaiiii

aμa

μμi FF

4

1ψψmψ

2

λgAiγψL

νc

μbabc

μa

ννa

μμνa AAgf-AAF

3MeV) (250qq

σ

a

f

P-S and V-A splittings in physical vacuum

8

Confinement at large distance → V(r) ~ k r Asymptotic freedom at short distance → αs=g2/4π decreases with momentum transfer

9

QCD can be solved in a discrete space

(n)Atigexp)μnU(n,ψ(n), aμ

a

Lattice QCD is the algorithm to evaluate Z in thespace-time → static at finite temperature via

Lattice QCD

Time dimension is thus regulated by temperature

μνμν

40aμν

22

p2

p pclosedμ2

FFxd4

1(n)FgiaexpTr

2g

1(n)UTr

2g

1S

e.g., for gluon field, the action becomes

),,(4 AxLdi

a eDDdAZ

1/Tτ0withiτt

10

Phase transition in lattice GCD

:Bμ 530 MeV

410

2100

Karsch et al., NPA 698, 199 (02)

Soft equation of state (p< e/3) ec ~ 6Tc

4 ~ 0.66 GeV/fm3

Appreciate interaction energy Tc ~ 170 MeV

303

T,

30n

221

16T

2

4

2

f4SB

11

Chiral symmetry restoration

Verified by lattice QCD at finite temperature and zero baryon chemical potential Expect either appearance of parity doublets or similarity of their spectral functions, e.g, ρ and a1

12

2CMS

2BANN E)p(ps

AGS

SPS

RHIC

QCD phase diagram probed by HIC

We do not observe hadronic systems with T > 170 MeV (Hagedon prediction)

13

STAR

Au+Au

The RHIC experiments

140 N_part 394

15 fm b 0 fm

Spectators

Participants

For a given b, Glauber model predicts Npart and Nbinary

S. Modiuswescki

Collision Geometry - “Centrality”

15

1ln

2z

z

E py

E p

Rapidity

1/ 22 2

cosh , sinh

T T

T z T

m m p

E m y p m y

z

z

p|p|

p|p|ln

2

1/2)tan(lnη

T22

T

2

T pdyd

dN

ycoshm

m1

pdηη

dN

Transverse mass

Rapidity distributions

Pseudirapidity

16

99% of particles

Transverse momentum distributions

Soft (< 2 GeV/c) - exponential spectrum - bulk particle production - described phenomenologically, e.g., string fragmentation through Schwinger mechanism

z

pmbexpz1zf(z)

2t

2a1

Hard (> 2 GeV/c) - power law spectrum - described by pQCD

with z= light-cone momentum fraction ofproduced hadron wrt that of fragmentingstring

17

)(zDpd

dNdz

pd

dNchc

c2

c

cc

h2

h ph= z pc , z <1

2.0)(

)(

zD

zD

c

pc

)utsδ(cd)(abtd

dσ

π

s

)Q,(x)fQ,(xfdxdxpd

dN 2b

2ab

ca

c2

c

Bb

Aa

High pT particle production

c

d

hadrons

a

b

Mini jet production

Hadron prodution from empirical fragmentation function determined from e+e- annihilation

18

5.0|| y

dy

dE

τπR

1

dzA

dEε T

2T

T

MeV350300TGeV/fm8~ε initial3

Particle streaming from origin

Energy Density

For Au+Au @ 200 GeV at RHIC

R~1.18 A1/3~ 7 fm, dET/dy~ 720 GeV

22

zz

ztτdy,τcoshydz

tanhyE

pv

t

z

Taking particle formation time τ~0.6 fm/c, then

19

Radial collective flow

Slope of transverse momentum spectrumis due to folding temperature with radial collective expansion <βT>

Slopes for hadrons with different masses allow to separate thermal motion from collective flow

Absence

Tf ~ (120 ± 10) MeV

<βT> ~ (0.5 ± 0.05)

T

TfslT

2

fslT

1

1TT m,p icrelativistUltra

m2

1TT m,p icrelativistNon

T

20

22

0/))((

2

2 ,12

iiTpEi mpEe

dppgn

ii

Assume thermally and chemically equilibrated system of non-interacting hadrons and resonances with density

Determine chemical freeze out temperature Tch and baryon chemical potential μB by fitting experimental data after inclusion of feed down from short lived particles and resonances decay.

Tch~Tc

Statistical model

21

Hydrodynamic Equations

Energy-momentum conservation

Charge conservations (baryon, strangeness,…)

For perfect fluids without viscosity

Hydrodynamic model

Equation is closed by the equation of state p(e)

Kolb & Heinz; Teany & Shuryak; Hirano, ……..

Cooper-Frye instantaneous freeze out

e: energy densityp: pressureuμ: four velocity

0)(

0)(

xun

xT

j

gxp

xuxuxpxexT

)(

)()()()()(

1u)exp(q

1dσq

(2π2

g

qd

dNE

3i

3i dσ is an element of

space-like hypersurface

22Initial Ti=340 MeV, ei=25 GeV/fm3 Freezeout Tf=128 MeV

Transverse momentum spectra from hydrodynamic modelKolb & Heinz, nucl-th/0305084

efo=0.45 Gev/fm-3

0.075 Gev/fm-3

Initial flow

23

21'2

'12121 ffff

d

dvvddpt)p,(x,f∂p

sss

/1

1

2

9,

)-t(2

9

dt

d22

2

22

2

Using αs=0.5 and screening mass μ=gT≈0.6 GeV at T≈0.25 GeV, then <s>1/2≈4.2T≈1 GeV, and pQCD gives σ≈2.5 mb and a transport cross section

σ=6 mb → μ≈0.44 GeV, σt≈2.7 mb σ=10 mb → μ≈0.35 GeV, σt≈3.6 mb

mb5.1cos1d

dd≡t

Parton cascade Bin Zhang, Comp. Phys. Comm. 109, 193 (1998)D. Molnar, B.H. Sa, Z. Xu & C. Greiner

24

A multiphase transport (AMPT) model

Default: Lin, Pal, Zhang, Li & Ko, PRC 61, 067901 (00); 64, 041901 (01);

72, 064901 (05); http://www-cunuke.phys.columbia.edu/OSCAR

Initial conditions: HIJING (soft strings and hard minijets) Parton evolution: ZPC Hadronization: Lund string model for default AMPT Hadronic scattering: ART

Convert hadrons from string fragmentation into quarks and antiquarks Evolve quarks and antiquarks in ZPC When partons stop interacting, combine nearest quark and antiquark to meson, and nearest three quarks to baryon (coordinate-space coalescence) Hadron flavors are determined by quarks’ invariant mass

String melting: PRC 65, 034904 (02); PRL 89, 152301 (02)

25

BRAHMS Au+Au @ 200 GeV

Transverse momentum and rapidity distribution from AMPT

26

thermalization early in time τ < 1 fm/c high initial energy density ε ~ 10 GeV/fm3

chemical equilibrium with limiting temperature Tc ~ 170 MeV final thermal equilibrium at Tth ~ 120 MeV with large radial collective flow velocity <βT> ~ 0.5

Matter formed in relativistic heavy ion collisions reaches

What have we learnt?

Is the matter a quark-gluon plasma?

27

Dilepton enhancement (Shuryak, 1978)

Strangeness enhancement (Meuller & Rafelski, 1982)

J/ψ suppression (Matsui & Satz, 1986)

Pion interferometry (Pratt; Bertsch, 1986)

Elliptic flow (Ollitrault, 1992)

Jet quenching (Gyulassy & Wang, 1992)

Net baryon and charge fluctuations (Jeon & Koch; Asakawa, Heinz & Muller, 2000)

Quark number scaling of hadron elliptic flows (Voloshin 2002)

……………

Signatures of quark-gluon plasma

28

-

MinBias Au-Au

thermal

• Low mass: thermal dominant (calculated by Rapp in kinetic model)• Inter. mass: charm decay

No signals for thermal dileptons yet

Dilepton spectrum at RHIC

29

MeV3002502mQ

ssgg

ssqq

s

In QGP

Strangeness enhancement

30

Strangeness quilibration Time

T

nmK

n

1

2π

Tmf(p)

(2π2

pdgρ 2

1n

2

3

3

eq

2s12ss21ss12

s ρσvρρσvdt

dρ

6 fm/c

Strangeness equilibration time in QGP from lowest-

order QCD teq ~6 fm/c is

comparable to lifetime tQGP

of QGP in HIC

Kinetic equation

Equilibrium density

31

Strangeness production in hadronic matter

MeV)530mmmm(QKΛπN

MeV)670mmm(QKNNN

MeV)7102m2m(QKKππ

πNKΛ

NKΛ

πK

In hadronic matter

80MeV)(QΚΛπρ

90MeV)(QNΛΛΔΔ

MeV)240(QKΛπΔ

380MeV)(QNΛΛNΔ

Strangeness equilibration time in hadronic matter teq ~ 30 fm/c is longer than hadronic life time thad ~ 15 fm/c

→ cross sections ~ a few mb

Cross sections are unknow but expected to be a few mb as well

32

dduu

ssS

2

e+e- collisions

Experimental results

Multistrange baryons are significantly enhanced andcan be accounted for by the statistical model → Strangenessequilibration

33

J/ψ suppression

Color charge is subject to screening in QGP

CTV /

CTr

Drss er

Vr

V /

112

1

fcD Tg2/3Tg

6

N

3

Nλ

One loop pQCD

34J/ψdisappears between 1.62Tc and 1.70Tc

A() 2()

Lattice result for J/ψspectral function

35

Nuclear absorption:Nuclear absorption: J/ψ+N→D+Λc; p+A data → σ~ 6 mb Absorption and regeneration in QGP: Absorption and regeneration in hadronic matter:

J/ψ absoprtion and production in HIC

ccgJ/Ψ DDπJ/Ψ

RHIC SPS

36

4 41 2 1 1 2 2 1 2

4 41 1 1 2 2 2

C(K,q)=1

d x d x S(x ,p )S(x ,p )cos[q (x -x )]+

d x S(x ,p ) d x S(x ,p )

1 2 1 2 1 2K= p +p /2, q=(p -p , E -E )

S(x,p) is the emission source function and is given by the phase space distribution at freeze out in the AMPT model C(K,q) can be evaluated using Correlation After Burner (Pratt, NPA 566, 103c (94))

with

Hanbury-Brown-Twiss interferometry

Two-particle correlation function

37

Pion interferometry

STAR Au+Au @ 130 AGeV

)exp(1

)exp(1

)(

22

222222

invinv

llssoo

Rq

RqRqRq

qC

open: without Coulombsolid: with Coulomb

Au+Au @ 130 GeV

STAR

Ro/Rs~1 smaller than expected ~1.5

qinv2=q2-(E1-E2)2

38

Source radii from hydrodynamic model

Fails to explain the extracted source sizes

39

Lin, Ko & Pal, PRL 89, 152301 (2002)

Au+Au @ 130 AGeV

Need string melting and large parton scattering cross section which may bedue to quasi bound states in QGP and/or multiparton dynamics (gg↔ggg)

Two-Pion Correlation Functions and source radii from AMPT

40

Shift in out direction (<xout> > 0) Strong positive correlation between out position and emission time Large halo due to resonance (ω) decay and explosion → non-Gaussian source

Emission Function from AMPT

41

High PT hadron suppression

Parton energy loss due toradiation

Wang & Wang, PRL 87, 142301 (01)

Gyulassy, Levai & Vitev, PRL 85, 5535 (00)

Jet quenching → initial energy density → 5-10 GeV/fm3

pi pfpfpi

k

× ×x x

Au+AuAA

AA p+p

dNR

T d

42

STAR Collaboration, PRL 97, 152301 (07)

p/π+ and pbar/π- ratios at high transverse momentum

Same p/π+ and /π- ratios in central and peripheral collisions →Same RAA for gluon and quark jets, which is not expected fromradiative energy loss as gluon jets lose more energy than quark jets.

p

43

Jet conversions in QGP

Elastic process: qg→gq

Inelastic process: ggqq

Quark jet conversion

Gluon jet conversion: similar to above via inverse reactions

Gluon is taken to have a larger momentum in the final state

44

Radiative conversion: 2→3

+ ………

45

Coalescence + jet quenching + jet conversion

46

Anisotropic flow vn

Sine terms vanish because of the symmetry in A+A collisions

Initial spatial

anisotropy

Anisotropicflows

Pressure gradient

anisotropy

x

Anisotropic flow

3

n T3n=1T T T T

d N dN 1 dNE 1 2v (p ,y)cos(n )

d p p dp d dy 2 p dp dy

47

Elliptic flow from hydrodynamic model

Ideal hydro describes very well data at low pT (mass effect) but fails at intermediate pT → viscous effect.

48

Need string melting and large parton scattering cross section Mass ordering of v2 at low pT as in hydrodynamic model

Lin & Ko, PRC 65, 034904 (2002)Elliptic flow from AMPT

σp= 6 mb

49

Surprise: quark number scaling of hadron elliptic flow

Except pions, v2,M(pT) ~ 2 v2,q(pT/2) and v2,B(pT) ~ 3 v2,q(pT/3) consistent with hadronization via quark recombination

50

Momentum-space quark coalescence model

Quark transverse momentum distribution

q T 2,q Tf (p ) 1 2v (p )cos(2 )

Meson elliptic flow

Baryon elliptic flow

)2/p(v2)2/p(v21

)2/p(2v)p(v T2,q

T22,q

T2,qTM2,

)3/p(v3)3/p(v61

)3/p(3v)p(v T2,q

T22,q

T2,qTB2,

Quark number scaling of hadron v2 (except pions):

n)/p(vn

1T2

Only quarks of same momentumcan coalescence, i.e., Δp=0

same for mesons and baryons

51

Coalescence model

qq3

3

N)p,x(fE)2(

pddp

36/1gg K Mg

ni

n i i q,i i i n 1 n 1 n3i=1 i

dpN =g p d f x ,p f (x ,...,x ;p ,...,p )

2 E

Quark distribution function

Spin-color statistical factor

e.g. 12/1gg *K

Coalescence probabilityfunction

)p,x(fq

PRL 90, 202102 (2003); PRC 68, 034904 (2003)

Number of hadrons with n quarks and/or antiquarks

54/1gg,108/1gg pp

}]/2Δ)m-(m-)p-exp{[(p×

]/2Δ)x-exp[(x=

)p-p;x-x(f=)p,p;x,(xf

2p

221

221

2x

221

212122121M

px

For baryons, Jacobi coordinates for three-body system are used.

52

Effects of hadron wave function and resonance decays

Wave function effectEffect of resonance decays

Wave fun.+ res. decays

Higher fock states → similar effect (Duke)

53

Fragmentation leads to p/π ~ 0.2 Jet quenching affects both Fragmentation is not the dominant mechanism of hadronization at pT < 4-6 GeV

PHENIX, nucl-ex/0212014PHENIX, nucl-ex/0304022

Puzzle: Large proton/meson ratio

π0 suppression: evidence of jet quenching before fragmentation

Au+AuAA

bin p+p

dNR

N dN

54

Large proton to pion ratio

DUKEOREGON

TAMU

Quark coalescence orrecombination can also explain observed large p/pi ratio at intermediate transverse momentum can be in central Au+Au collisions.

55

Higher-order parton anisotropic flows

Including 4th order quark flow

q T 2,q T 4,q Tf (p ) 1 2v (p )cos(2 ) 2v (p )cos(4 )

Meson elliptic flow

Baryon elliptic flow

v

v

3

1+

3

1=

v

v ,

v

v

2

1+

4

1=

v

v ⇒ 2

2,q

4,q2

B2,

B4,22,q

4,q2

M2,

M4,

)v+v(2+1

v+v2= v,

)v+2(v+1

vv2+v2=v 2

4,q22,q

22,q4,q

M4,24,q

22,q

4,q2,q2,q

M2,

)vv+v+6(v+1

v3+vv6+v3+v3= v,

)vv+v+v(6+1

vv6+v3+vv6+v3=v

4,q22,q

24,q

22,q

34,q4,q

22,q

22,q4,q

B4,4,q

22,q

24,q

22,q

24,q2,q

32,q4,q2,q2,q

B2,

Kolb, Chen, Greco, Ko, PRC 69 (2004) 051901

56

22,q4,q2

2

4 2v v 1.2 v

v

Data can be described by a multiphase transport (AMPT) model with largeparton cross sections.

Data Parton cascade gives v4,q~v2,q

2

Higher-order anisotropic flows

57Greco, Rapp, Ko, PLB595 (04) 202

S. Kelly,QM04

Charmed meson elliptic flow

v2 of electrons

Data consistent with thermalizedcharm quark with same v2 as lightquarks before boosted by radial flow

Smaller charm v2 than light quarkv2 at low pT due to mass effect

58

Charm RAA and elliptic flow from AMPT

Zhang, Chen & Ko, PRC 72, 024906 (05)

Need large charm scattering cross section to explain data Smaller charmed meson elliptic flow is due to use of current light quark masses

59

Resonance effect on charm scattering in QGP

Van Hees & Rapp, PRC 71, 034907 (2005)

4/m-k4

1J2

9

12D

2

D2/1

2D

2qc→qc

s

With mc≈1.5 GeV, mq≈5-10 MeV, mD≈2 GeV, ΓD≈0.3-0.5 GeV, and including scalar, pseudoscalar, vector, and axial vector D mesons gives

σcq→cq(s1/2=mD)≈6 mb

Since the cross section is isotropic, the transport cross section is 6 mb, which is about 4 times larger than that due to pQCD t-channel diagrams, leading to a charm quark drag coefficient γ ~ 0.16 c/fm in QGP at T=225 MeV.

60

Heavy quark energy loss in pQCD

a) Radiative energy loss (Amesto et al., hep-ph/0511257)

b) Radiative and elastic energy loss (Wicks et al., nucl-th/0512076)

c) Three-body elastic scattering (Liu & Ko, nucl-th/0603004)

a) +

May be important as interparton distance ~ range of parton interaction At T=300 MeV, Ng~(Nq+Nqbar)~ 5/fm3, so interparton distance ~ 0.3 fm Screening mass mD=gT~600 MeV, so range of parton interaction ~ 0.3 fm

a) +b) +

61

Reasonable agreement with data from Au+Au @ 200A GeV

after including heavy quark three-body scattering.

Spectrum and nuclear modification factor of electrons from heavy meson decay

62

2

CH

2

q

2CH

-+2

CHCH

Z-N

=Φ

N

NN4=Z

NN

Q-Q=

Z

ZCharge Conservation

Quark Coalescence

Resonance Gas

Quark-Gluon Plasma

Net charge fluctuations

Adams et al., STAR Collaboration, PRC 68, 044905 (2003)

Au+Au @ 130 GeV

Favor quark coalescencepicture for hadronization

63

Heavy ion collisions at LHC

TeV5.5s @ PbPb NN

64

Pb+Pb @ 5.5 TeV

Particle multiplicity at LHC increases by a factor of ~ 4 from that at RHIC

Rapidity distributions at LHC

σparton=10 mb

b< 3 mb

b< 3 mb

65

Transverse momentum distributions

Particle transverse momentum spectra are stiffer at LHC than at RHIC → larger transverse flow

0 < b < 3 fm

66

Quark elliptic flows

Quark elliptic flows are larger at LHC than at RHIC, reaching ~ 20%

Au+Au @ 200 GeV

67

Pion and proton Elliptic flow at LHC

Elliptic flow is larger for pions but smaller for protons at LHC than at RHIC

68

Heavy meson elliptic flows at LHC

)p)m/m((v)p)m/m((v)p(v TMqq2,TMqq2,T2M 2211

Quark coalescence model

69

Pion interferometry

Two-pion correlation functions narrower at LHC than at RHIC

70

Radii from Gaussian fit to correlation functions

3

1i

2i

2ii2 K)Q(Rexp1)K,Q(C

Source radii for pions are larger than for kaons and both are larger at LHC than at RHIC

71

Thermal charm production in QGP Zhang, Liu & Ko,PRC 77, 024901 (08)

Thermal production non-negligible Next-leading order and leading order contributions are comparable Insensitive to gluon masses Effect increases by about 2 for initial temperature T0=750 MeV but decreases by ~ 2 for mc=1.5 GeV

mc=1.3 GeV

72

Diquark in sQGP and Λc enhancement Lee, Yasui, Ohnishi, Yoo& Ko, PRL 100, 222301 (08)

Diquark mass due to color-spin interaction:

MeV450mm

1ss C-mmm

dududu[ud]

Coalescence model Statistical model

24.0e

m

m2

Dc0Dc

0

c T/mm-

2/3

D0

c

• Enhanced by a factor of 4-8• Similar for ΛB/B0

for mu=md= 300 MeV and C/mu2~195 Me V from mΔ-mN

73

Charm tetraquark mesons

- Tcc ( ) is ~ 80 MeV below D+D* according to quark model

- Coalescence model predicts a yield of ~5.5X10-6 in central Au+Au collisions at RHIC and ~9X10-5 in central Pb+Pb collisions at LHC if total charm quark numbers are 3 and 20, respectively

- Yields increase to 7.5X10-4 and 8.6X10-3, respectively, in the statistical model

ccud

Charmed pentaquark baryons

- Θcs( ) is ~ 70 MeV below D+Σ in quark model

- Yield is ~1.2X10-4 at RHIC and ~7.9X10-4 at LHC from the coalescence model for total charm quark numbers of 3 and 20, respectively

- Statistical model predicts much larger yields of ~4.5X10-3 at RHIC and ~2.7X10-2 at LHC

cudus

Charm exotics production in HIC Lee, Yasui, Liu & Ko Eur. J. Phys. C 54, 259 (08)

74

Mapping the QCD phase diagram at FAIR

Require first-order phase transition ?

75

Rapidity distributions at FAIR

76

Elliptic flow at FAIR

Partonic scattering enhanceselliptic flow

Mass ordering of hadron elliptic flows

77

Comparison of transport model predictions of elliptic flow at FAIR

78

Summary

Most proposed QGP signatures have been observed at RHIC. Strangeness production is enhanced and is consistent with formation of chemical equilibrated hadronic matter at Tc.

Large elliptic flow requires large parton cross sections in transport model or earlier equilibration and small viscosity in hydrodynamic model. HBT correlation is consistent with formation of strongly interacting partonic matter. Jet quenching due to radiation requires initial matter with energy density order of magnitude higher than that of QCD at Tc.

Quark number scaling of elliptic flow of identified hadrons is consistent with hadronization via quark coalescence or recombination. Electromagnetic probes and heavy flavor hadrons will be studied by upgrated RHIC. Experiments at LHC and future FAIR allow for probing QGP at even higher temperature and finite baryon chemical potential, respectively.