Ridges and v2 without hydrodynamics

Rudolph C. HwaUniversity of Oregon

Int’nal Symposium on Multiparticle Dynamics

Berkeley, August 2007

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Prevailing paradigm on azimuthal asymmetry in heavy-ion collisions at low pT is hydrodynamical flow.

Calling v2 “elliptic flow” is a distinctive mark of that paradigm.

Are there any alternatives?

Why bother?

What if hydrodynamics is found invalid at early times?

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Results on single-particle distributions from hydro

Kolb & Heinz, QGP3

0=0.6 fm/c (RHIC 130, 200), 0=0.8 fm/c (SPS

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RHIC 130 GeV

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“Elliptic flow” -- v2

Agree with data for pT<1.5GeV/c possible only if

0~0.6 fm/c

dN

pTdpTdφ∝1+ 2v2 (pT )cos(2φ) +L

Huovinen, Kolb, Heinz, Ruuskanen, Voloshin Phys. Lett. B 503 58, (2001).

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Conventional wisdomAzimuthal anisotropy can be understood in terms of hydrodynamical flow for pT<1.5 GeV/c

It requires fast thermalization. 0=0.6 fm/c

high pressure gradient

leads to momentum space asymmetry: v2>0

px > py

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Conventional wisdom BNL-PR strongly interacting QGP perfect liquid

What is the direct experimental evidence that either verifies or falsifies the conclusion on perfect liquid?

Based on a crucial assumption in theoretical calculation: fast thermalizationNot expected nor

understood in QCD.

What if 0=1-1.5 fm/c? If so, then the hydro results would disagree with data.

How much of sQGP and perfect liquid can still be retained?

Instability?

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Alternative approach

• must be sensitive to the initial configuration (hard)

• must be able to describe the bulk behavior (soft)For pT<1.5 GeV/c (the region that hydro claims success)

we consider semi-hard scattering:

Semi-hard parton qT ~ 2-3 GeV/c (0.1 fm/c) can have significant effect on thermal partons for pT<1.5 GeV/c.

Ridges

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Ridgeology

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Jet structure

Putschke, QM06

J+R

R

J

ridge R Jet J

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In a high pT jet, a hard- scattered parton near the surface loses energy to the medium.

Recombination of enhanced thermal partons gives rise to the ridge, elongated along

The peak is due to thermal-shower recombination in both and

Chiu & Hwa, PRC 72, 034903 (2005)

ridge

bg R

J

pT

Power-law behavior is a sign of Jet production

peak

It generates shower partons outside.

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puzzle

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distribution of associated particles shows what seems like jet structure.

pT distribution is exponential; thus no contribution from jets

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Bielcikova (STAR) 0701047Blyth (STAR) SQM 06

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STAR data nucl-ex/0701047 2.5<pTtrig<4.5

1.5<pTassoc<pT

trig

Chiu & Hwa, 0704.2616

All ridge !

The puzzle is solved by recognizing that the trigger and its associated particles are all produced by the thermal partons in the ridge.

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Jet

3 - 4

Ridge

Putschke, QM06

J

R= 0.1

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The ridge would not be there without a semi-hard scattering, but it does not appear as a usual jet.

Ridges of low pT hadrons are there, with or without triggers, so long as there are semi-hard partons near the surface to generate enhanced thermal partons.

Phantom jet

It is a Jet-less jet.

Summary of ridgeology

• Ridges are the recombination products of enhanced thermal partons stimulated by semi-hard scattering near the surface.• At low pT there can be ridges without Jets (peaks).

A ridge without any significant peak on top.

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Azimuthal Asymmetry

Now to

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Relevant physics must be sensitive to the initial configuration.

Phantom jets are produced at early times, if hard enough, but should be soft enough so that there are many of them produced in each collision.

At low x (~0.03) there are many ‘soft’ partons to create phantom jets at ~0.

Semi-hard partons: qT~2-3GeV/c, (<0.1 fm/c),

(That is not true at large forward .)

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|| < = cos-1(b/2R)

At any given

Each scattering sends semi-hard partons in random directions.

on average, the jet direction is normal to the surface.

If the phantom jets are soft enough, there are many of them, all restricted to || < .

Recoil partons thermalize the bulk medium.

Initial configuration

Thermalization of partons takes time, but the average direction of each ridge is determined at initial time.

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Bulk partons q0

dNqB

dqTdφ=CqTe−qT /T

pions B(pT ) =dNπ

B

pTdpTdφ=

C2

6e−pT /T

pions

B(pT )+ R(pT ,φ)=C2

6e−pT /T 'Θ(φ)

Bulk+Ridge

partons q0

dNqB+R

dqTdφ=CqTe−qT /T 'Θ(φ)

Θ(φ) = θ (Φ− |φ |) +θ (Φ− | π −φ |)

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v2

dN

pTdpTdφ=B(pT ) + R(pT ,φ)

v2 (pT ,b) = cos2φ =dφcos2φ dN

pTdpTdφ0

2π

∫dφ dN

pTdpTdφ0

2π

∫

v2 (pT ,b) =dφcos2φR(pT ,φ)0

2π

∫dφ[B(pT ) + R(pT ,φ)]0

2π

∫=

R(pT )sin2(b)πB(pT ) + 2R(pT )

R(pT ,φ) =R(pT )Θ(φ)

v2 (pT ,b) =sin2(b)

π B(pT )R(pT )

+ 2(b)

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R(pT ) =C2

6[e−pT /T ' −e−pT /T ] =

C2

6e−pT /T (epT /T " −1)

B+R B

B(pT )

R(pT )=

1(epT /T " −1)

v2π (pT ,b) =

sin2(b)π

(epT /T " −1)+ 2(b)

Thermal pions only

pT<1.5 GeV/c

Small pT region (b) = cos−1 b

2R⎛⎝⎜

⎞⎠⎟v2

π (pT ,b) ≈pT

πT "sin2(b)

1

T ''=1T−

1T '

=TTT '

T = T '−T

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ridge spectrum harder than inclusive h+,-

(~ 40-50 MeV in slope parameter)

“Jet”/ridge yield vs. pt,assoc. in central Au+Au

preliminaryAu+Au 0-10%preliminarySTAR preliminaryRidgeJet

Rid

ge/

Jet

yiel

d

STAR preliminary“jet” sloperidge slopeinclusive slope€

dN /dpt ∝ pte−p t /T

Putschke HP06

T

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v2π (pT ,b) ≈

pT

πT "sin2(b) T "=

TT 'T

T = T '−T

Use T=45 MeVT=0.29 GeV

Get T”=2.12 GeV

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dNπ / pTdpT

pT

PHENIX 40-50%

Max of sin2(b) at =π/4

b=√2 R=10 fm

centrality 50%

v

2

π (pT ,10) ; 0.15pT

At small pT

The first time that a connection is made between ridge and v2.

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40-50%

30-40%

20-30%

10-20%

5-10%

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40-50%

30-40%

20-30%

10-20%

5-10%

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Centrality dependence

v2

b

sin2(b)

(b)=cos-1 b/2R

v2π (pT ,b) ≈

pT

πT "sin2(b)

at pT=0.5 GeV/c

Max[v2]=pT/πT’’=0.075

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STAR: Au-Au at 130 GeV PRC 66, 034904 (2002)

(what pT range not indicated)

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Normalized impact parameter

=b/2R

sin2(b) f() = sin(2cos-

1)

f() is universal, so it should be the same for Cu-Cu and at other √s.

STAR data on v2 for Au-Au at 130GeV, normalized to 1 at max: =1/√2

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∂v2

∂pT= 0.12(GeV / c)−1∂v2

∂pT= 0.05(GeV / c)−1

Nouicer (PHOBOS) QM06

∂v2

∂pTπT '' = sin 2Φ(b) = f (β )

f () =0.33 f () =0.8

f()

0-20% 20-40%

describes universal centrality behavior, independent of: Au or Cu, for √s=200 or 62.4 GeV

f ()

1/0.15

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Proton

exp(−pT /T )

exp[−(mT −mp) /T ] 40-50%

at small pT

v2

p =pT2

2πmpT "sin2(b)

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Transverse kinetic energy EK

pT for pion

mT-mp for proton

Initial slope ∂v2h (pT ,b)

∂EK pT <0.5

=1

πT ''f (β )

A property that is independent of the hadron species h. T’’ is a property of the partons that recombine.

It trivially satisfies the constituent quark scaling:

∂v2h (pT ,b) / nq∂EK / nq pT <0.5

=1

πT ''f (β )

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PHENIX preliminary

KEKETT Scaling Scaling KEKETT Scaling Scaling

Mesons

Baryons

R.Lacey, ETD-HIC 07

Jet contribution

f ()πT ''

Property of partons in the ridge before hadronization

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Forward rapidity

=0

>0

Mid-rapidity region

• Semi-hard scattering involve small x partons

• more phantom jets

• many ridges

• larger x partons, thus lower multiplicity

• fewer phantom jets

• ridge effect reduced

v2 (pT ,b) =sin2(b)

π B(pT )R(pT )

+ 2(b)v2 decreases with increasing

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Au+AuAu+Au

Au+Au:PHOBOS CollaborationPRL. 94, 122303 (2005)

Cu+Cu:PHOBOS CollaborationPRL: nucl-ex/0610037

Cu+CuCu+CuPreliminary

v2 measured:

- broad range

- several energies

Observations on

v2 of Cu+Cu :

- large

- similar in

shape

to Au+Au

Nouicer QM06 (PHOBOS)

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Conclusion

• Azimuthal anisotropy is mainly a ridge effect. No fast thermalization or hydrodynamical flow are needed.

• Hydrodynamics may still be applicable after some time, but it is not needed for v2, for which the relevant physics at <1 fm/c is crucial --- semi-hard scattering at qT<3.

• For pT<1.5 GeV/c, the analysis is simple, and the result can be expressed in analytic form that agrees with data.

• For pT>1.5 GeV/c, shower partons must be considered. Jet dominance (>3GeV/c) will saturate v2.

• No part of the study suggests that the medium behaves like a perfect fluid.

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EXTRA SLIDES

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In peripheral collisions there are some complications. It is harder to produce protons in the bulk because of lower density of soft partons. (remember pp collisions) Thermal parton distributions in Fuud are not factorizable. T in B(pT) is lower.Thus phantom jets are relatively more effective in enhancing the thermal partons for p production at large b.So B(pT)/R(pT) for proton is smaller than for pion

v2 (pT ,b) =sin2(b)

π B(pT )R(pT )

+ 2(b)

Hence, v2(pT,b) continues to increase for (b) smaller than π/4.

not negligible

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How universal is ? 1

πT ''=0.15GeV−1

Ridge phenomenology is rudimentary, and theoretical calculation at low pT unreliable.

Enhanced thermal partons in the ridge: T’/T=1+?

Since the bulk T encapsules the dependences on: energy, system size, thermalization,

then T’-T=aT2+…, compared to T=TT’/T’’,

a=1/T’’ to first order.

Thus T’’=2.12 GeV is universal to first order.

T’/T=1+aT+…expand

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QuickTime™ and aTIFF (LZW) decompressor

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PHOBOS PRL 94, 122303 (2005)

v2 at all and various s

v2 = 0.014 - 0.0075 ’

’ ~ ln x for some <mT>

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BRAHMS has pT dependence at =3.2 nucl-ex/0602018

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Theoretical treatment of forward production is not simple.Hwa & Yang, PRC (2007).

pT =1GeV / cs =62.4GeV =3.2

xπ =0.4 xp =0.54 xq ; 0.2

Recombination of thermal partons in comoving frame at . Exponential

Ridge due to semi-hard parton at ’> of bulk. R/B decreases with increasing x as a function of F(x).v2 R/B decreases with increasing ’ as a function of F(x), thus exhibiting a scaling behavior.