Heavy quark ”Energy loss" and ”Flow" Heavy quark ”Energy loss" and ”Flow" in a QCD matterin a QCD matter
Heavy quark ”Energy loss" and ”Flow" Heavy quark ”Energy loss" and ”Flow" in a QCD matterin a QCD matter
DongJo Kim, Jan Rak Jyväskylä University, Finland
Lecture 16
Oct-18-2007 DongJo Kim, KPS 2007 Fall 2
HI collision - Nuclear Modification Factor HI collision - Nuclear Modification Factor RRAAAAHI collision - Nuclear Modification Factor HI collision - Nuclear Modification Factor RRAAAA
RAA (pT ) =d2NAA / dpTdη
Nbinary d2Npp / dpTdηRAA (pT ) =
d2NAA / dpTdηNbinary d2Npp / dpTdη
A+AA+A
n x m Nbinaryvaries with impact parameter b
p+pp+p
Oct-18-2007 DongJo Kim, KPS 2007 Fall 3
Nuclear Geometry and Hydrodynamic flowNuclear Geometry and Hydrodynamic flowNuclear Geometry and Hydrodynamic flowNuclear Geometry and Hydrodynamic flow
RP
multiple scattering
larger pressure gradient in plane
d 3N
pT dpT dyd∝ [1+ 2v2 (pT )cos2( −φRP ) + ...]
d 3N
pT dpT dyd∝ [1+ 2v2 (pT )cos2( −φRP ) + ...]
less yield out
more in plane
less yield out
more in plane
Coordinate
space
Momentum
space
Initial
Later
€
ε=< y 2 − x 2 >
< y 2 + x 2 >
€
v2 =< px
2 − py2 >
< px2 + py
2 >
PRL 91, 182301
Oct-18-2007 DongJo Kim, KPS 2007 Fall 4
v 2
0.1
0.05
0
v2 /n
qThe “Flow” Knows QuarksThe “Flow” Knows QuarksThe “Flow” Knows QuarksThe “Flow” Knows Quarks
v2 (pT ) → nq ⋅v2
KET
nq
⎛
⎝⎜
⎞
⎠⎟
v2 (pT ) → nq ⋅v2
KET
nq
⎛
⎝⎜
⎞
⎠⎟
Assumption:
all bulk particles are coming from recombination of flowing partons
Discovery of universal scaling:
flow parameters scaled by quark content nq resolves meson-baryon separation of final state hadrons. Works for strange and even charm quarks. strongly suggests the early thermalization and quark degree of freedom.
v 2
baryons
mesons
Oct-18-2007 DongJo Kim, KPS 2007 Fall 5
• PHENIX– Single electron measurements in p+p,
d+Au, Au+Au , y~0sNN = 130,200,62.4 GeV
– Single muon measurements in p+p, d+Au ,1<|y|<2 sNN = 200 GeV
• STAR– Direct D mesons hadronic decay
channels in d+Au• D0Kπ• D±Kππ• D*±D0 π
– Single electron measurements in p+p, d+Au
Phys. Rev. Lett. 88, 192303 (2002)
How to measure Heavy Flavor ?How to measure Heavy Flavor ?How to measure Heavy Flavor ?How to measure Heavy Flavor ? Experimentally observe the decay products of Heavy Flavor particles (e.g. D-
mesons)
– Hadronic decay channels DK D0 0
– Semi-leptonic decays De() K e
Meson D±,D0
Mass 1869(1865) GeV
BR D0 --> K+- (3.85 ± 0.10) %
BR D --> e+ +X 17.2(6.7) %
BR D --> + +X 6.6 %
PHENIX Preliminary
(η = 0)
Oct-18-2007 DongJo Kim, KPS 2007 Fall 6
S/B > 1 for pT > 1 GeV/c
Run04: X=0.4%, Radiation length
Run02: X=1.3%
Signal/Background
We use two different methods to determine the non-photonic electron contribution (Inclusive = photonic + non-photonic )
• Cocktail subtraction – calculation of “photonic” electron background from all known sources• Converter subtraction– extraction of “photonic” electron background by special run with additional converter (X = 1.7%)
• Cocktail subtraction – calculation of “photonic” electron background from all known sources• Converter subtraction– extraction of “photonic” electron background by special run with additional converter (X = 1.7%)
How to measure Heavy Flavor?How to measure Heavy Flavor?
C
harm/B
ottom
electrons
Oct-18-2007 DongJo Kim, KPS 2007 Fall 7
Systematic on the measurementSystematic on the measurementSystematic on the measurementSystematic on the measurement
• Cocktail and converter analysis agrees very well
• Low pT : Converter • High pT : Cocktail
• S/B > 1 for pT > 2 GeV/c
PRL 97(2006) 252002
eID @ RICH
Hadronic background
Electrons
E/p
Signal/Background
Oct-18-2007 DongJo Kim, KPS 2007 Fall 8
Heavy Flavor in Au+Au 200GeVHeavy Flavor in Au+Au 200GeVHeavy Flavor in Au+Au 200GeVHeavy Flavor in Au+Au 200GeV
No suppression at low pT
• consistent with N<coll> scaling of total charm yield
Suppression observed for pT>3.0 GeV/c,
smaller than for light quarks( RAA ~ Rcharm
AA).
PRL. 98, 172301 (2007)
Oct-18-2007 DongJo Kim, KPS 2007 Fall 9
Non-photonic electron vNon-photonic electron v22 measurement measurementNon-photonic electron vNon-photonic electron v22 measurement measurement
Non photonic electron v2 is given as;
v2 γ.e ; Photonic electron v2
Cocktail method (simulation) stat. advantage Converter method (experimentally)
v2e ; Inclusive electron v2
=> Measure RNP = (Non-γ e) / (γ e)=> Measure
NP
eeNPenon
enonee
R
vvRv
d
dN
d
dN
d
dN
.22.
2
..
)1( γγ
γγ
−+=
Φ+
Φ=
Φ
−
−(1)
(2)
Oct-18-2007 DongJo Kim, KPS 2007 Fall 10
Photonic e vPhotonic e v22 determination determinationPhotonic e vPhotonic e v22 determination determination
decaye vRv 2.
2 ×∑=γ
good agreement converter method (experimentally determined)
photonic electron v2
=> cocktail of photonic e v2
R = N X->e/ Nγe
photonic e v2 (Cocktail)
decay
v2 (π0)
pT<3 ; π (nucl-ex/0608033)pT>3 ; π0 (PHENIX run4 prelim.)
Oct-18-2007 DongJo Kim, KPS 2007 Fall 11
Non-zero charm vNon-zero charm v22 ? (1) ? (1)Non-zero charm vNon-zero charm v22 ? (1) ? (1)
Apply recombination model Assume universal v2 (pT) for quark
simultaneous fit to v2π, v2
K and v2non-γe
eT
D
cqT
D
uqT
D vpm
mbvp
m
mavpv 2222 )()()( →+=
[PRC 68 044901 Zi-wei & Denes]
charm
Shape is determinedwith measured identifiedparticle v2
universal v2 (pT) for quark
a,b ; fitting parameters
Oct-18-2007 DongJo Kim, KPS 2007 Fall 12
Non-zero charm vNon-zero charm v22 ? (2) ? (2) Non-zero charm vNon-zero charm v22 ? (2) ? (2)
χ2 minimum ; a = 1, b = 0.96 (χ2/ndf = 21.85/27) Based on this recombination model, the data suggest non-zero v2 of charm quark.
2σ
4σ
1σ
b ;
ch
arm
a ; u
χ2 minimum resultD->e
Oct-18-2007 DongJo Kim, KPS 2007 Fall 13
Compare with modelsCompare with modelsCompare with modelsCompare with models
[PRB637,362]
(1) Charm quark thermal + flow(2) large cross section ; ~10 mb (3) Resonance state of D & B in sQGP (4) pQCD
[PRC72,024906]
[PRC73,034913]
[Phys.Lett. B595 202-208 ]
Oct-18-2007 DongJo Kim, KPS 2007 Fall 14
Overview of Theoretical FrameworkOverview of Theoretical FrameworkOverview of Theoretical FrameworkOverview of Theoretical Framework
pQCD (1) Radiative energy loss ( GLV, light quarks ) Collisional(elastic) energy loss ( additional 2x2 process ) Still pending issues not solved ( only RAA, Charm/Bottom Ratio )
Relative magnitude of elastic vs radiative loss channels
Non-perturbative pQCD (2) Adding nonperturbative hadronic final state interaction effects
I.van Vite and A. Adil( Collisional dissociation, RAA )
Van Hees ( recombination , RAA and v2 )
AdS/CFT Related (3) Partonic radiative transport coeff ( ) : H.Liu, K.Rajagopal,U.A. Wiedemann Diffusion coefficient(DHQ) , RAA and v2 ) : G.D. Moore, D.Teany
W. Horowitz ( more like direct calculation according to ads/CFT ) Double ratio ( RAA(charm)/RAA(bottom) )
Comparison with pQCD€
ˆ q
Oct-18-2007 DongJo Kim, KPS 2007 Fall 15
Shear Viscosity( Shear Viscosity( ηη ) to Entropy density( s ) ratio ) to Entropy density( s ) ratioShear Viscosity( Shear Viscosity( ηη ) to Entropy density( s ) ratio ) to Entropy density( s ) ratio
Shear Viscosity( η ) to Entropy density( s ) ratio
η/s ~ 1/4 (4) Diffusion coefficient(DHQ) , RAA and v2 ) : G.D. Moore, D.Teany
Elastic scattering and resonance excitation : Van Hees Ads/CFT itself Hydrodynamics
Oct-18-2007 DongJo Kim, KPS 2007 Fall 16
2003 CTEQ SS - Cacciari Heavy quark mass
Suppress radiation in acone of Θ < mQ/E
Dead cone effectNo collinear divergence
Heavy quarks as a probe Heavy quarks as a probe
parton
hot and dense medium
light
M.Djordjevic PRL 94 (2004)
ENERGY LOSS
Oct-18-2007 DongJo Kim, KPS 2007 Fall 17
Elastic energy lossElastic energy lossElastic energy lossElastic energy lossS. Wicks et al., nucl-th/0512076
Partonic Energy Loss
Radiative 2N processes. Final state QCD radiation as in vacuum (p+p coll) - enhanced by QCD medium.
Elastic 22 LO processes
8 LO subprocesses
q ′q → q ′q 49
s2 +u2
t2
qq→ qq 49
s2 +u2
t2+
s2 + t2
u2
⎡
⎣⎢
⎤
⎦⎥
qq→ q ′q 49
t2 +u2
s2
......
8 LO subprocesses
q ′q → q ′q 49
s2 +u2
t2
qq→ qq 49
s2 +u2
t2+
s2 + t2
u2
⎡
⎣⎢
⎤
⎦⎥
qq→ q ′q 49
t2 +u2
s2
......
Elastic E models predict significant broadening of away-side correlation peak - not seen in the data. Also various models differ significantly in radiative/elastic fraction.
Oct-18-2007 DongJo Kim, KPS 2007 Fall 18
• Electrons • Pionss = .3
First results indicate that the elastic energy loss may be importantM. G. Mustafa, Phys.Rev.C72:014905,2005
(1)PHENIX ,PRL. 98, 172301 (2007)
(2) M. G. Mustafa, Phys.Rev.C72:014905,2005
Elastic energy loss is becoming important?Elastic energy loss is becoming important?Elastic energy loss is becoming important?Elastic energy loss is becoming important?
Oct-18-2007 DongJo Kim, KPS 2007 Fall 19
• Fragmentation and dissociation of hadrons from heavy quarks inside the QGP
D B
25 fm 1.6 fm 0.4 fmform ( 10 )Tp GeVτ =
B
D
QGP extent
(3)I. Vitev (A.Adil, I.V., hep-ph/0611109), Phys Lett B649 139-146 2007
Collisional dissociation ?Collisional dissociation ?Collisional dissociation ?Collisional dissociation ?
Oct-18-2007 DongJo Kim, KPS 2007 Fall 20
HQ Energy Loss and FlowHQ Energy Loss and FlowHQ Energy Loss and FlowHQ Energy Loss and Flow
Two models describes strong suppression and large v2
simultaneously Rapp and Van Hees Phys.Rev.C71:034907,2005
Elastic scattering : small τ DHQ × 2πT ~ 4 - 6
Moore and Teaney Phys.Rev.C71:064904,2005
DHQ × 2πT = 3~12
Recall ε+p = T s at B=0
• This then gives η/s ~(1.5-3)/4
• Within factor of 2 of conjectured boundPhys.Rev.D74,0850012,2006
PRL. 98, 172301 (2007)
Oct-18-2007 DongJo Kim, KPS 2007 Fall 21
Is the quark matter really perfect fluid? Is the quark matter really perfect fluid? Is the quark matter really perfect fluid? Is the quark matter really perfect fluid?
Viscosity η then defined as . In the standard picture
reflects the transport properties of multi-particle system. Small viscosity → Large cross sections Large cross sections → Strong couplings Strong couplings → perturbation theory difficult !
Fx
Area=η
∂vx
∂y
Ideal(perfect, inviscid) fluid η=0Ideal(perfect, inviscid) fluid η=0
String theory approach:
Strongly interacting matter AdS/CFT duality
(Phys. Rev. Lett., 2005, 94, 111601)
What can we learn from the data ?
ηs
≥1
4π
Oct-18-2007 DongJo Kim, KPS 2007 Fall 22
Universal Universal ηη/s/sUniversal Universal ηη/s/s
P.Kovtun, D.Son, A.S., hep-th/0309213, hep-th/0405231
Minimum of in units of
Oct-18-2007 DongJo Kim, KPS 2007 Fall 23
((ηη/s)/s)min min in units ofin units of ((ηη/s)/s)min min in units ofin units of
T.Schafer, cond-mat/0701251 Chernai, Kapusta, McLerran, nucl-th/0604032
~23 ~8.8
a trapped Fermi gas
~25
~ 4.2
€
h4πkB
QCD
Oct-18-2007 DongJo Kim, KPS 2007 Fall 24
Viscosity from the data at RHICViscosity from the data at RHICViscosity from the data at RHICViscosity from the data at RHIC
Phys. Rev., 2003, C68, 034913 Phys. Rev. Lett., 2007, 98, 092301
ηs
/1
4π: 1.13 ± 0.18
ηs
/1
4π: 1.13 ± 0.18
Temperature
T=160 MeV
Mean free path (transport sim.)
f=0.30.03 fm
Speed of sound
cs=0.350.05
ηs
= T λ f cs
ηs
= T λ f cs
Oct-18-2007 DongJo Kim, KPS 2007 Fall 25
AdS/CFT AdS/CFT and and pQCD at LHCpQCD at LHCAdS/CFT AdS/CFT and and pQCD at LHCpQCD at LHC
Double ratio of charm and bottom quark suppression
promising window for AdS/CFT models. ε pQCD ≈ Cα S3 dNg
dy
L
A⊥
log(p⊥ / MQ )
p⊥
ε pQCD ≈ Cα S3 dNg
dy
L
A⊥
log(p⊥ / MQ )
p⊥
εAdS ≈ 1 − exp μ (τ )τ 0
L
∫⎡⎣⎢⎤⎦⎥
εAdS ≈ 1− exp μ (τ )τ 0
L
∫⎡⎣⎢⎤⎦⎥
€
RAdScb ≈
Mc
Mb
nb ( pT )
n c ( pT )≈
Mc
Mb
≈0.26
€
RpQCDcb ≈1−
pcb
pT
W.Horowitz Gyulassy arXiv:0706.2336
Oct-18-2007 DongJo Kim, KPS 2007 Fall 26
RHIC RRHIC Rcbcb Ratio RatioRHIC RRHIC Rcbcb Ratio Ratio
• Wider distribution of AdS/CFT curves due to large n: increased sensitivity to input parameters
• Advantage of RHIC: lower T => higher AdS speed limits
pQCD
AdS/CFT
pQCD
AdS/CFT
WH, M. Gyulassy, to be publishedSQM07
W.Horowitz Gyulassy arXiv:0706.2336
Oct-18-2007 DongJo Kim, KPS 2007 Fall 27
Model InputsModel InputsModel InputsModel Inputs
AdS/CFT Drag: nontrivial mapping of QCD to SYM
Mapping QCD Nc to SYM is easy, but coupling is hardS runs whereas SYM does not: SYM is something of an unknown constant “Obvious”: s = SYM = const., TSYM = TQCD
D/2T = 3 inspired: s = .05 pQCD/Hydro inspired: s = .3 (D/2T ~ 1)
“Alternative”: = 5.5, TSYM = TQCD/31/4
Start loss at thermalization time τ0; end loss at Tc
WHDG convolved radiative and elastic energy loss s = .3
WHDG radiative energy loss (similar to ASW) = 40, 100
Use realistic, diffuse medium with Bjorken expansionPHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900)
W.Horowitz Gyulassy arXiv:0706.2336
Oct-18-2007 DongJo Kim, KPS 2007 Fall 28
AdS/CFT CorrespondenceAdS/CFT CorrespondenceAdS/CFT CorrespondenceAdS/CFT Correspondence
hep-th/0605158Put FD/String too here