Heavy quark ”Energy loss" and ”Flow" in a QCD matter DongJo Kim, Jan Rak Jyväskylä University, Finland Lecture 16

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


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


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


• 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)


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


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


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)


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)


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.)


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


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


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 ]


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


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


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


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.


• 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?


• 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 ?


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)


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


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


((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


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


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


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



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)



AdS/CFT CorrespondenceAdS/CFT CorrespondenceAdS/CFT CorrespondenceAdS/CFT Correspondence

hep-th/0605158Put FD/String too here

Documents

Heavy quark ”Energy loss" and ”Flow" in a QCD matter DongJo Kim, Jan Rak Jyväskylä University, Finland Lecture 16