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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
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.