1

Theory Overview of QGP and Cold Nuclear Matter Effects at

RHIC

Ivan Vitev

GHP Satellite Workshop, October 22 – 24, 2006APS, DNP fall meeting, Nashville, Tennessee

2

Cronin Effect in p+A Reactions

Default

0d Au X

Good description at mid rapidity

I.V., Phys.Lett.B526 (2003)

• Cronin effect

A.Accardi, CERN yellow report, references therein

0Au Au X

0

21

-2

1

1- - ..( ) ( ).

!-

niel

n

in e ii

nf

l

dd qdN e d

nq

d qNp qpc s

sc¥

= =

= å Õò2( ) ( )i k kdN d

^ ^=

2

2

2

1,( )

2

k

f edN k

cmx

mp xc

^-

^= /Lc l=

Initial condition Solution Mean number of scatterings

2

2 2

2

2

For 2

med

tot vac med

k

k k k

cmx^

^ ^ ^

D =

D = D + D

The approximate solution is that of a 2D diffusion

Implemented in the PQCD approach as kT broadening of the initial state partons

Scales: 0 ~ 1 2T QCDQ p Q GeV

3Kharzeev, Kovchegov, Tuchin, hep-ph/0405045

Brahms hadron forward suppression pattern

Gluon Saturation ModelsLo

wer

x

Gribov, Levin, Rishkin, Phys. Rep. (1980)

• Nonlinear gluon evolution 2 to 1 processes

• Particle production via 2 to 1 processes (monojets)

BRAHMS collab., Phys.Rev.Lett. 93 (2004)

Note: are these monojets?

J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004)

Nuclear Shadowing

Longitudinal size: 1/ 2 Nm xIf then 0z r 0.1x

Deviation from A-scaling: A A

2

2BN

Qx

m

00

2 20

2 2

(0) ( )1

( , )2

1 ( , ) ( )

2

2i

ff

f f

x

sf

T Q Q d e px

x

p

Q

F

Q

p

O

S.Brodsky et al, Phys.Rev.D65 (2002)

• Shadowing is dynamically generated in the hadronic collision y coherent final state scattering

• Simplistic view: modification of the nuclear wave function

Alternative model: “leading twist”2~ lnQ

222 ( ) 2 ( ) 2

2

1/

2

3( 1)( , ) , = 1 ,dynLT LTA

T T T

mxF x Q F

Ax Q F x Q

QA

QA

5

Evidence for Energy Loss

something more, dE/dx? &

more?

= X1 – X2

19 GeV

39 GeV

200 GeV

J/ for different s collisions

M.Leitch et al. PHENIX,EA866 and NA3 data

1 2, 1Fx x if x

A NA Cross section scaling:B.Kopeliovich et al. hep-ph/0501260

• Energy loss is a dominnant mechanism in the forward rapidity / large xF suppression

p, x1 A, x2

xF

S.S.Adler et al., nucl-ex/0603017

6

Nuclear Effects at Forward Rapidity

• Note the different contributions to an overall suppression effect

I.V., in preparation (2006)

S.S.Adler et al., nucl-ex/0603017

• The most detailed calculation do far at forward rapidity

• Original incoherent result:

I.V., T.Goldman, M.B.Johnson, J.W.Qiu, Phys.Rve.D74 (2007)

G.Bertsch and F.Gunion, Phys.Rev.D (1982)

0

(1) lng

E L Econst

E Q

0

(2) lng

E L Econst

E Q

• Original incoherent result:

Six fold cancellation

Extreme radiation length

(2) 1

(1) 6

const

const

0 100X fm

7

Particle Production Mechanism

OK

• Excludes: all the monojet color glass phenomenology, large final state energy loss

• Compatible with: Dynamical shadowing, initial state energy loss, leading twist shadowing parameterizations

Dijets:

Monojets:

1

2

2

1

1

2 21 2 1

11/

1 2/1min

2

222

2

1

( ) (( )

) ( )( ) h c

h d

a sb

abcd aT T b

ab cdN

T T z

h hN

D zdz D z

x x

p p x

d

dydyd p d p SM

z x

ffd j p as®

D -= å ò

8

The QCD Phase Transition

J.P.Blaizot,E.Iancu,A.Rebhan, Phys.Lett.B470, (1999)

• Hard thermal loop calculations: improved resummation of the perturbation series

• Agreement between HTL and Lattice for

3 cT T

F.Karsch,E.Laermann,A.Peikert, Phys.Lett.B487, (2000)

Asymptotic freedom:

Note on LHC versus RHIC: strongly versus weaklycoupled plasmas, beware of logarithmic running

2T gT g T

Note: recent results Tc~ 190 MeV vs Tc~ 175 MeV

• Deviation from Stefan-Boltzman: the log running of s

9

Relativistic Hydrodynamics

( ) ( ) ( )

( )

( ) ( ) ( )

( ) ( )

u x

T x u x u x g

j

x

x u x

p p x

n

x

0

0

( )

( )

T x

j x

x

yz

2 2 2

11 2 (cos ) .2 ..

2

h h

T T

dN dN

dyd p dydv

d p

P.Kolb,J.Sollfrank,U.Heinz, Phys.Rev.C62, (2002)

Elliptic flow

• Favors: EoS with QCD phase transition, low viscosity, early thermalization high energy density

0 1 fm 3

0 15 /GeV fm

Ideal hydro, initial conditions

10

Plasma Instabilities. Strikland

Current filamentation

Vlasov equation:

Yang-Mills equation:

Note on time scales: t = 10 fm, still too large

11

Energy Loss in the QGP

R.Baier et al. Nucl.Phys.B (1997)

M.Gyulassy, P.Levai, I.V., Nucl.Phys.B594, (2001) Phys.Rev.Lett.85, (2000)

M.Gyulassy, X.N.Wang, Phys.Rev.Lett.68, (1992)

• The most important effect in dense nuclear matter: QGP but also cold nuclei

(1) R s

3(1)

2

2g

g

2R s

2CE Log ... ,

4

Static medium

9 C 1E Log ... ,

4 A

(L)

dNdy (L

1+1D

)

L 2E

Bjo

L

2EL

L

rken

p

k xp k

1q 1q 2q 3q 4q5q 5q 6q 6q 7q

f

LPM = Landau-Pomeranchuk-Migdal

0

raddE E

dz XQED: QCD:

12

System Size Dependence of Jet Quenching

I.V., Phys.Lett.B 639 (2006)

• In classes with the same we find numerically the same suppression

partNAAR

(For example central Cu+Cu and mid central Au+Au)

1' 2 2

/ /

0

12

/

0

(1 ),(1 )

1( , ) ,

1 1

1

( )

) + ,(

cc c c

vach q h q

vacg

h g

zp p z

zD z Q d D Q

zd D Q

P

dN

d

Identifying nuclear effects:

1

i

i

E

E E

( )P Probability density -

0A A X

TNN

TAA

collTAA dpdd

dpdd

NpR

/

/1),(

2

2

13

Jet Tomography

I.V., M.Gyulassy, Phys.Rev.Lett. 89 (2002)

F.Karsch, Nucl.Phys.A698 (2002)

SPS RHIC LHC

0 0

' / ( ') ' ( ')

0 0

( ')

( )

r r

abs absdr r dr r r

I r I e I e

Principles of jet tomography

14

Hard Processes

11

2

/1 1 2

1 1

1

2min min 1

2( )(

()

))(

a b

sa b a b

ab

h

cd a bx x

ab cT

dc

hNNd

dx dD z

zx x x

x x Sd pM

ydas

ff ®= å ò ò

5 10pT [GeV]

15

0S.Turbide et al., Phys.Rev.C72:014906,2005

V.Wogelsang et al., Phys.Rev.D Note: prompt versus fragmentation photons

qg q qg qg

/ ( )qD z

• Particle production: processes

• Direct photons: no final state interactions and no attenuation

2 2

15

• Cancellation of collinear radiation

large angle soft gluons and correspondingly more soft hadrons

• It is broad but is it dipped?

I.V., Phys.Lett.B630 (2005)

What Happens to Medium-Induced Radiation

In A+A

+2Re

2

x

2 *2 Resin *

...gmed

a b c

dNM M M

d d d

0, / 0k k

S.Pal, S.Pratt, Phys.Lett.B574 (2003)

Note: strong theoretical arguments againstStrong “dip”

16

Mach Cones and Sound Velocity

A.Chaudhuri, U.Heinz, Phys.Rev.Lett. 97 (2006)

J.Casalderrey-Solana et. al, Nucl. Phys.A774, (2006)

F. Karsch, hep-lat/0601013

<cs>~ 0.35 Soft EOS

• Hydro simulations do not confirm such mechanism

• There is no realistic simulation of the di-jet distributions yet!

17

S. Wicks et al., nucl-th/0512076

Heavy Quark Production and Modification

• Single electron measurements (presumably from heavy quarks) may be problematic

• Problem: treated in the same way as light quarks! D B

10 fm 1.0 fm 0.35 fm( 10 )f Tp GeV

2 2 2

1 (0.2 . ) 2 (1 )

(1 ) (1 )h q

GeV fm z z py

p k z m z z M

• Interactions beyond the partonic level

M.Djordgevic, M.Gyulassy, Nucl.Phys.A (2004)

11

(1 ) (1 )

2

2 22

2 2

22

2

,g

n ngm x M

m

xE

k k k

x Mx

p Ek k

• Significant interest in collisional energy loss

Note: what is important is consistent evaluation ofcollisional versus radiative E-loss

18

Diffusion and Dissociation of Heavy Mesons

• Langevin simulation of heavy quark diffusion

H.van Hees, I.V., in preparation

• B is significantly less quenched than D

Drag coefficient:1 i

ii

pA

p t

t [fm]

Su

rviv

al p

rob

ab

ilit

y

exp /s dissP t

D

B

~ 1.7B fm

~ 3.7d fm

/ 0.2, / 0.35b c

E E E E

A.Adil, I.V. in preparation

Prelim

inary

D(B) meson

• B is comparably quenched to D

Prelim

inary

• Collisional dissociation of heavy mesons

19

Conclusions

Quark-gluon plasma effects: LQCD predicts Tc=175 – 190 MeV, no colored bound states. EoS consistent between LQCD and HTL. Deviations from SB, log running of alpha Hydro simulations of v2 suggest early thermalization, e0 = 15 GeV/fm3 Non-Abelian plasma instabilities: path to isotropisation, time still too long Final state non-Abelian energy loss in the QGP is the dominant jet quenching mechanism. Tested against p+A and direct photons Jet tomography: e0 = 15 GeV/fm3 based on successful PQCD predictions Energy redistributed in soft particles. Mach cones? Strong theoretical arguments against. Lack of accurate simulations. Heavy flavor still problematic, highlights collisional E-loss. New mechanisms should be explored. Collisional dissociation of mesons, promising.

Cold nuclear matter effects: Particle production consistent with hard parton scattering, no monojets Nuclear effects arise dynamically from elastic, inelastic and coherent multiple parton scattering “Leading twist” versus “high twist” shadowing theory from final state interactions. Test at EIC. Bring a broader community to EIC Theoretical advances in understanding energy loss in cold nuclear matter. It appears to be a dominant effect at forward rapidity p+A reactions p+A program at RHIC II, vary C.M. energy. Advance theoretical models