pppp Distribution of Charged Particles · pppp T ( ) Jet T 2 p GLV L 3 E ,C C s n d r( ) µ ∆ ∼...

Gyulassy LBL 5/25/05 1

Before and After the Flow:Initial Conditions and High p T jets

1. (strong) Quark Gluon Plasma: sQGP

2. Color Glass Condensate: CGC

M.Gyulassy and L. McLerran

Nucl.Phys.A750 (2005) 30

A Mini Course on the “Bigger Picture”

Gyulassy LBL 5/25/05 2

XN Wang, MG

BULKBULKBULKBULK

EntropyEntropyEntropyEntropyNullNullNullNull

ControlControlControlControl

PHOBOS PHOBOS PHOBOS PHOBOS

BRAHMSBRAHMSBRAHMSBRAHMS

High High High High pTpTpTpT TailTailTailTail

OpacityOpacityOpacityOpacity

3 pp

AA

2

T

T (0)d

dyd p

σ

3 pp

A

2

T

T (0)d

dyd p

σ

Shadow Shadow Shadow Shadow

QuenchQuenchQuenchQuench

p0

Gyulassy LBL 5/25/05 3

Phobos

ppppTTTT Distribution of Charged ParticlesDistribution of Charged ParticlesDistribution of Charged ParticlesDistribution of Charged Particles

G.Roland

We can use this tiny calibrated pQCD tail to probe the QGP Bulk!

Bulk

Tail

Gyulassy LBL 5/25/05 4

Nch =ρρρρs NPart + ρρρρH(s) NBC

Hard mini-jet ρρρρH with fixed scale Q s=2 GeV fails.Qs must vary with both s and N part

Evidence for saturating CGC initial conditionsEvidence for saturating CGC initial conditionsEvidence for saturating CGC initial conditionsEvidence for saturating CGC initial conditions−

≈

0.34

2 2 0.3

s

10Q (x,A) 1GeV A

x

Gyulassy LBL 5/25/05 5

QGP Opacity viaAbsolute Scale

Jet Tomography

Adil, Vitev, MG (2005)

( )kT

shad

AB /AB a/A b/B ab c cdN T f f d P( E) D∆

→π π→= ⊗ ⊗ ⊗ σ ⊗ ⊗∆

pT GeV

dNg/dy=900-1200

Collinear factorized pQCD

Gyulassy LBL 5/25/05 6

Physics Beyond the Standard ModelUniversidad de Colima, Colima, MexicoNovember 19, 2003

“The useful theoretical models that has served us so well at the AGSand SPS for heavy ion studies have now been overloaded with a largevolume of puzzling new data from RHIC.”

“We need moretheoretical helpto meet the challengeof understandingwhat is going on inthe RHIC regime.”

J.CramersJ.Cramers ’’ Summary Slide of RHIC Physics in 2003Summary Slide of RHIC Physics in 2003

p/π

ππ

v2,4

RAA

K*/K

ET

e,γ

Things are a bitup in the air.

Adapted from John Cramers, UWash

Gyulassy LBL 5/25/05 7

Experts have a hard time seeing the picture

HBT

RAA

v2,4

Adapted from John Cramers, UWash

K*/

K

e,γ

p/π

Gyulassy LBL 5/25/05 8

Theoretical tools used at RHIC are built onrigorous limits of the Standard Model

1. Asymptotic free perturbative pQCDProton Spin structure (high Q > 2 GeV)Jets and heavy quarks (high p T> 10 GeV)

2. High temperature/density thermodynamicsnonperturbative Lattice QCDLong Wavelength Collective (low p T < 1 GeV)

3. High energy light cone QCDColor Glass Condensate (small x< 0.001)

Gyulassy LBL 5/25/05 9

“Day 1 New Physics” at RHIC

STARSTARSTARSTAR

Collective Flow

10-6

10-5

10-4

10-3

10-2

10-1

1

10

10 2

0 1 2 3 4 5pt (GeV/c)

1/N

evt 1

/2π 1

/pt d

N/dp

t (GeV

/c)-2 PHENIX preliminary

10%

75-92%

UA1(130)scaled to 5% central

scaled to 80-92% central

PHENIXPHENIXPHENIXPHENIX

Jet QuenchingBaryon anomaly

Color Glass

Gyulassy LBL 5/25/05 10

sQGPsQGPsQGPsQGP

Empirical Evidence at RHIC that points to the Discovery of QGP

PQCD ���� Elliptic Flow

pQCD ���� Jet Quenching

dAdAdAdA����Control 1

CGC � Global

q3 � p / π

QGPCuCuCuCu2222 ����Control 2

QCDQGP=P + pQCD + dA 3QCD ssQGP=P + pQCD + dA + Q + q ...+

sCGC=Q (y,A)

wQGPsQGP

strongly coupled

s

sCGC=Q (y,A) +...

and CGC

Gyulassy LBL 5/25/05 11

sQGPsQGPsQGPsQGP

PPPPQCDQCDQCDQCD

Part II: Part II: Part II: Part II: pQCDpQCDpQCDpQCD

dAdAdAdA

Physics of Nuclear CollisionsPhysics of Nuclear CollisionsPhysics of Nuclear CollisionsPhysics of Nuclear Collisions

t fm/ct0~0.1 tH~10

EnergyEnergyEnergyEnergy

DensityDensityDensityDensity eHHHH

QGPQGPQGPQGP

Part I: CGCPart I: CGCPart I: CGCPart I: CGC

((((qqqqqqqqqqqq))))

HadronsHadronsHadronsHadrons

CGCCGCCGCCGC

102 eHHHH

Gyulassy LBL 5/25/05 12

Importance of controlled A+A Initial Conditions

Is a 1-to-1 map from Initial � Final

sQGP must first be created !

CGC is source of sQGP

0T µνµ∂ =

Gyulassy LBL 5/25/05 13

Ions Approach t=-15 fm/c

g g g g+ → +T s

p Q (x,A)>

g' g' g+ →T s

p Q (x,A)<Color Glass Condensate Saturation Scale

− ≈

1 13 32

2 2

s

10 AQ (x,A) 2GeV

x 200

High Energy NucleusIs equivalent to aWeizsacker-WilliamsGluon Beam

sQGPsQGP Formation via CGC Formation via CGC

Scales with A4/3

Scales with A1Until gg g g gg→ ≈ →

g gg→Higher EnergyMore gluons

Gyulassy LBL 5/25/05 14

Q vb

Equivalent Photons and Relativistic E+M

Fermi, Weizsacker-Williams, …, Jackson p724, Low p15 0

≈γ γ γ γ beam

Gyulassy LBL 5/25/05 15

Q vb

ρ

EB

E

B

z=vt tra

nsverse sheet

Q Q γ→ + Virtual Photons

, kω ⊥

����ℏ

Highly Boosted Coulomb Field

= Sheet of transverse E and B

Space-Time Fields Fourier Decomposition

Gyulassy LBL 5/25/05 16

4.6.12

4.6.14B

4.6.14C

Parseval (t ���� ωωωω)

Parseval (ρ ���� k)

Poynting

Gyulassy LBL 5/25/05 17

PartonsPartonsPartonsPartons IndependentIndependentIndependentIndependent

Only in Dilute LimitOnly in Dilute LimitOnly in Dilute LimitOnly in Dilute Limit

( )glue s 2

2

dN c QA (glue) R

dy Q⊥

α= <π

Critical Packing FractionCritical Packing FractionCritical Packing FractionCritical Packing Fraction2A (glue)/ R 1⊥κ = π =

Levin, Levin, Levin, Levin, etaletaletaletal

2

s(x,Q (x,A)) 1κ =

McLerranMcLerranMcLerranMcLerran----VenugopalanVenugopalanVenugopalanVenugopalan

Color Glass CondensateColor Glass CondensateColor Glass CondensateColor Glass Condensate

Dilute Parton gas

2 GeV2 GeV2 GeV2 GeV2222

0.010.010.010.01

2 22 1 20 s

A s s

s

x Q RxG (x,Q ) A LogQ

x (Q )

λ−δ ∝ ∝ α

Saturation momentum scale:Saturation momentum scale:Saturation momentum scale:Saturation momentum scale:

2 0.3 0.3

sQ (x,A) A x−∝ MuellerMuellerMuellerMueller----QiuQiuQiuQiu

KharzeevKharzeevKharzeevKharzeev----LevinLevinLevinLevin----NardiNardiNardiNardi

Gyulassy LBL 5/25/05 18

“Glauber” Form Factor TA(kT)

Point charge spectral function

Gyulassy LBL 5/25/05 19

Gyulassy LBL 5/25/05 20

When an ultra-relativistic charge comes to a sudden stop

Radiation “Dead” Cone

θθθθcone= 1/γ =M/E

Exactly the same distributions of real photons as in the virtual WW field The cloud is “shaken off” by sudden ac(de)celeration

Q

v

Gyulassy LBL 5/25/05 21

GribovGribovGribovGribov, Levin, , Levin, , Levin, , Levin, McLerranMcLerranMcLerranMcLerran, , , , VenugopalanVenugopalanVenugopalanVenugopalan , Mueller, Mueller, Mueller, Mueller…………

What is a CGC?What is a CGC?What is a CGC?What is a CGC?

UnitarityUnitarityUnitarityUnitarity limit of Virtual Gluon Cloudlimit of Virtual Gluon Cloudlimit of Virtual Gluon Cloudlimit of Virtual Gluon Cloud

CGCCGCCGCCGC

( ) ( )Rate gg g Rate g gg→ ≈ →

Gyulassy LBL 5/25/05 22

UnintegratedUnintegratedUnintegratedUnintegrated Gluon phase space densityGluon phase space densityGluon phase space densityGluon phase space density

2 22 2

2 22 2 s

2 2 2 22 2

s2 2

Q RxG(x,Q ) LogQ c

(Q)

1if Q Q

dn(x,k ) 1 dxG(x,k )

dyd rdk R dkif Q Q

k R

∝ α <α

∝ < α= π α∝ >

∼

2 22 /2ss

s

Q RdNxG(x,Q ) s ALogA

dy (Q )

λ∝ ∝ ∝α

PredictsPredictsPredictsPredicts

Slow growthSlow growthSlow growthSlow growth

Of multiplicityOf multiplicityOf multiplicityOf multiplicity

Phase spacePhase spacePhase spacePhase space

saturationsaturationsaturationsaturation

QQQQssss

QQQQ

1

α

Gyulassy LBL 5/25/05 23

Nch = ρρρρs(Qs) A + ρρρρH (Qs) A4/3

RHIC data prove Q s varies with s and A

Global Evidence for saturating CGC initial state at RHIC

− ≈

0.32

2 2

s

10 AQ (x,A) 2 GeV

x 200

Gluon Saturation below k T < Qs

Limits Rapid Growth of pQCD mini-jets

Corresponds to Deep Gluon Shadowingin x<0.01 region

Gyulassy LBL 5/25/05 24

−

=

=

=

=

= =

≈

⇒

→

→

→

0.32

2 2

s

T

T

T

LHC 2y 3 p 2

RHIC 2y 3

LHCy 0 p 2

p 2

210 AQ (x,A) 2 GeV

x 200

5GeV

5GeV

14GeV

CGC at RHIC

CGC at LHC

2 4

| |2

2( )2

1g

s

yss

s

QdN Q Rc

d Qe

sy α −

≈ KinematicallyLimited at y = 3

2 2

2( )g s

s s

dN Q Rc

dy Qα≈ Kinematics

Free at y ≤ 3

Nuclear Glue Structure RHIC vs LHC

RHIC is a sQGP machine with a partial view of CGC

LHC is a CGC machine with a partial view of sQGP

Gyulassy LBL 5/25/05 25

CGC at LHC

EIC ~ 2020

LHC ~2010

Nuclear Glue Structure @ LHC vs @ dream machine EIC (ELIC or eRHIC)

Gyulassy LBL 5/25/05 26

QGPQGPQGPQGP

Flow and PFlow and PFlow and PFlow and PQCDQCDQCDQCD

Part II: Jet Quenching and Part II: Jet Quenching and Part II: Jet Quenching and Part II: Jet Quenching and pQCDpQCDpQCDpQCD

dAdAdAdA

t fm/ct0~0.1 tH~10

EnergyEnergyEnergyEnergy

DensityDensityDensityDensity eHHHH

ssssQGPQGPQGPQGP

Entropy Entropy Entropy Entropy NNNNchchchch CGCCGCCGCCGC

((((qqqqqqqqqqqq))))

HadronsHadronsHadronsHadrons

CGCCGCCGCCGC

102 eHHHHJet attenuation in sQGP

Gyulassy LBL 5/25/05 27

Geometric Scaling of High pT Observables :

Centrality Selected Single Inclusive

part

h

h h, s

AB

,

X

2

N

dN

dy d p

→ +

⊥

4 /32

AB A B

AT (b) d s T (b s)T (s)

40mb= − ≈∫ Binary collision densityBinary collision densityBinary collision densityBinary collision density

Rare processes scale with Rare processes scale with Rare processes scale with Rare processes scale with NNNNcollcollcollcoll(b(b(b(b)= )= )= )= σσσσinininin TTTTABABABAB(b) ~ {N(b) ~ {N(b) ~ {N(b) ~ {Npartpartpartpart(b)}(b)}(b)}(b)}4/34/34/34/3

Nuclear Modifications Factor

part

AB h AB h

AB pp h pp h

AB coll

y, h, N , sdN 1 dN

R (p | )T d N dN

→ →

⊥ − −= =σ

bσ

∫b

A 2- T (s- )2 b

part A 2N (b)=2 d sT (s+ )(1-e )

Participating nucleonsParticipating nucleonsParticipating nucleonsParticipating nucleons

Gyulassy LBL 5/25/05 28

Ncoll scaling observed for direct photons

Vogelsang NLO

pp

collN dN

→γ×

collN ( ,pT 6)Au Au N N ( ,pp T 6)pγ γ +> ≈ × >+

Gyulassy LBL 5/25/05 29

Ncoll scaling of charm production

Gyulassy LBL 5/25/05 30

First Au+Au->e X data showed no hint of heavy quark energy

loss ! ??PHENIX Collaboration

(K. Adcox et al.) Phys.Rev.Lett.88:192303,2002

RAA(pT) for non-photonic single electrons in Au+Au

!Significant reduction at high pT suggest sizable

energy loss!

Sergey Butsyk(21st Winter Workshop on Nuclear

Dynamics)

Weird and Puzzling Preliminary Charm Suppression Data

?How could pT=4.5 be centrality indep and huge?

Gyulassy LBL 5/25/05 31

THE primary advantage of RHIC is its proven ability to perform

Dedicated Control p+p and p+A as well as B+A experiments as well as √√√√s

Required to sort the competing novel physics of sQGP from its CGC source

( ) / ( )BA ppBA BAR p dN T b dπ πσ→ →

⊥ =Nuclear Modification Factor

RAA ~ “Survival Probability”

Gyulassy LBL 5/25/05 32

High pT Tomography of the sQGP

Single Single Single Single HadronHadronHadronHadron TomographyTomographyTomographyTomography

g

g

jet

g

TTTTTTTT

pppp

( )T

2Jet T

p

GLV L

3

s n d r( )C CE ,µ

∆ ∫ τ ρ ττ τα∼ ℓ

DiDiDiDi----HadronHadronHadronHadron TomographyTomographyTomographyTomography

LLLL1111

LLLL2222pppp

pppp

2

1 dN

R dyπL( )φ

M.G., P. Levai, I.Vitev ; X.N. Wang, E.Wang, B.W.Zhang

Review nuclReview nuclReview nuclReview nucl----th/0302077th/0302077th/0302077th/0302077

Trigger

AwaySide

Gyulassy LBL 5/25/05 33

Final Result to Arbitrary Order in Opacity (L/ λλλλ)n

for M Q and mg > 0 (DG, Nucl.Phys.A 733, 265 (04))

Hard, Gunion-Bertsch, and Cascade ampl. in GLV generalized to finite M

Generalizes GLV MQ= mg =0 (NPB594(01))

Gyulassy LBL 5/25/05 34

Leading order in opacity

(M. Djordjevic, MG)

“Dead-cone” effect is moresubtle than for the 0th order

energy loss

LPM effects are smaller for heavythan

for light quarks!

Gyulassy LBL 5/25/05 35

g

g 2 n 7

dN cInitial Jet distribution (p) ~

dyd p pρ =

∼

π − −

π

ρ= = =

ρε

− ε − εn 2 n 2

AA

(p, )QuenchFactor R ( ) ( )

(pZ1 1

,0)

p

g

p

g p/

dpNomediumPion distribution (p D) (p) (z )

pπ

π

π

∞

π ππ

ρ = ρ =∫

( z)1

1 1z

Inmediump p p(p) p( )

(z) (z) (zD 'D' )

1

D −ε−ε −ε

θ −

→ − ∆ ≈→ = =

− ε

p1g ( ) p(1 1

1

)

p

/

(

g

)

dpQuenchedPions (p , ) (p) (z ' )

pD π

π

−ε −ε

−ε

∞

π ππ

πρ =ε ρ =∫

n quenched n 2

g gFor (p) 1/p : (p ) ( ) p )1 (π

−π πρ ∝ − ερ = ρ

Fluctuations reduce Eby fact 5or Z ~ 0.∆

Gyulassy LBL 5/25/05 36

Absolute ScaleJet Tomography

Adil, Vitev, MG (2005)

( )kT

shad

AB /AB a/A b/B ab c cdN T f f d P( E) D∆

→π π→= ⊗ ⊗ ⊗ σ ⊗ ⊗∆

pT GeV

dNg/dy=900-1200

Gyulassy LBL 5/25/05 37

QGP 0ˆ( ,x n )ρ τ + τ

Azimuthal v2(pt)

TomographyI. Vitev, X.N. Wang, MG, PRL86(01)

Wood Saxon Sharp Cylinder

STAR

High v 2(10 GeV) Still Open Problem

Gyulassy LBL 5/25/05 38

Four independent calibrations of Initial QGP density

1. Bjorken Backward extrapolation

2. Hydrodynamic initial condition needed for v2(pT)

3. Jet Tomography: dNg /dy = 1000

4. Gluon saturation pT<Qs predicted

dNg /dy = 1000 at Qsat = 1 GeV at y=0

T

2 3

0 0

3

Bj 0

E /N 0.5 GeV, dN /dy 1000,

1/p 0.2 fm/c, V (0.2 fm) R 30 fm

500Gev /30 fm 100

π π= =

τ = = = π =

ε = = ε

3

Hydro Bj 02 500Gev /30 fm 100ε > ε = = ε

Jets Bj 0100ε ≈ ε ≈ ε

3

0 0( ) 100 15GeV/ fmε τ ≈ ε =

KHH

TS

HN

GLV

WW

MB

McV

EKRT