Phantom Jets: the puzzle and v2 without hydrodynamics

Rudolph C. HwaUniversity of Oregon

Early Time Dynamics in Heavy Ion Collisions

Montreal, July 2007

2

Jets

Conventional jet structure

Phantom jet

?

3

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

4

The specific problem Phantom jet

How phantom jets solve the puzzle

The more general problem

v2 without hydrodynamics

Do not assume fast thermalization. There is no need to conjecture sQGP; no basis for concluding perfect liquid.

5

Jet structure

Putschke, QM06

J+R

R

J

6

Ridge

Putschke, QM06

Jet

Dependence on pT(trig) and pT(assoc)

3 - 4

7

Bielcikova, QM06

Dependence on particle species

J

R= 0.1

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Thus we have a ridge without any significant peak on top. The ridge would not be there without a hard scattering, but it does not appear as a usual jet.

is formed by the s quarks in the ridge, since s quark in the shower is suppressed.

But phantom jets of intermediate pT are there with or without trigger.

Triggering on is the experimental way to select events to exhibit the properties of phantom jets.

Phantom Jet

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In the case of usual jets, 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 TS recombination

peak

It generates shower partons outside.

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and spectra

Exponential thermal

Phantom jets ridges

→ ss →φ

→ sss→ Ω

→ qq → π

has associated particles above background.

puzzle can thus be resolved.

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Hadronization by recombination

e−q1 /T e−q2 /T (ggg)δ(q1 +q2 −pT )

∝ e− pT /T

Hwa&Yang,PRC(2004)

dNπth

pTdpT

=1

p0 pT

dq1

q1∫

dq2

q2

T (q1)T (q2 )R(q1,q2 , pT )

p0 dNMdp

=dq1

q1

dq2

q2∫ Fqq'(q1,q2 )RM (q1,q2 , p)

p0 dNBdp

=dq1

q1

dq2

q2∫

dq3

q3

Fqq'q"(q1,q2 ,q3)RB(q1,q2 ,q3, p)

Fsss =T sT sT s +T sT sSs +T s{SsSs} + {SsSsSs}p0 dN

dp

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Hwa & Yang , PRC(2007) nucl-th/0602024

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dist. dN R

dφ∝ H(φ) dpT

trig f(pTtrig,T ')

dN

dpTtrig∫

⎡

⎣⎢

⎤

⎦⎥−

dNbg

dφ

yield Y (pTtrig ) ∝ d

−1

1

∫ φH(φ)⎡⎣⎢

⎤⎦⎥

f(pTtrig,T ')−bg

H0 our only free parameter.

6.9

trigger (thermal s quarks in ridge)dN

pTdpT

∝pT2

p0

e−pT /T '

T’=0.33 GeV

Associated particles (thermal q quarks in ridge)

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QuickTime™ and aTIFF (LZW) decompressor

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STAR data nucl-ex/0701047

(a) H0=0.795

(b) H0=0.790

2.5<pTtrig<4.5

1.5<pTassoc<pT

trig

<1% variation

Chiu & Hwa, 0704.2616

It leads to 20% change in dN/d and yield.

All ridge !

The problem is not a puzzle any more.

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Predictions

• Ridge height: dNR/d~0.06

• p/π ratio >1 in the ridge for pT>2 GeV/c

• similar behavior for -triggered events

Implications

• Even for pT up to 6 GeV/c, one should not think of as a product of fragmentation of hard partons. • Phantom jets and ridges are present, irrespective of trigger, so long as there are semi-hard partons near the surface to generate enhanced thermal partons.

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hydrodynamical results

It is an assumption. What if it is regarded as unacceptable?

Azimuthal AnisotropyConventional approach: hydrodynamical flow

high pressure gradient

requires fast thermalization. 0=0.6 fm/c

sQGP

perfect liquid

leads to momentum space asymmetry: v2>0

px > py

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Relevant physics must be sensitive to the initial configuration

(a) Soft physics --- hydrodynamics

No commonly accepted mechanism for fast development of pressure gradient

(b) Hard physics --- high-pT jet quenchingProcess too rare at high pT

(c) Medium hard physics --- semi-hard scatteringSoft enough to have frequent

occurrences, hard enough to create intermediate-pT jets at early times.

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Phantom jets --- ridges

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

At any given

Each scattering sends semi-hard partons in random directions

on average, jet direction is normal to the surface.If the phantom jets are soft enough, there are many of them, all restricted to || < .

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Bulk partons q0

dNqB

dqTdφ=CqTe−qT /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 |)

pions B(pT ) =dNπ

B

pTdpTdφ=

C2

6e−pT /T

Hwa&Yang,PRC(2004)

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v2v2 (pT ,b) = cos2φ =

dφcos2φ dNpTdpTdφ0

2π

∫dφ dN

pTdpTdφ0

2π

∫

=dφcos2φR(pT ,φ)

0

2π

∫dφ[B(pT ) + R(pT ,φ)]

0

2π

∫=

R(pT )sin2Φ(b)

π B(pT ) + 2ΦR(pT )

T "=TT 'T

T = T '−T

Small pT region v2π (pT ,b) ≈

pT

πT "sin2(b) (b) = cos−1 b

2R⎛⎝⎜

⎞⎠⎟

R(pT ) =C2

6[e−pT /T ' −e−pT /T ] =

C2

6e−pT /T (epT /T " −1)

R(pT ,φ) =R(pT )Θ(φ)

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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 MeV

Get T”=2.12 GeV

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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dNπ / pTdpT

pT

PHENIX 40-50%T=0.28 GeV

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40-50%

30-40%

20-30%

10-20%

5-10%

STAR

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40-50%

30-40%

20-30%

10-20%

5-10%

STAR

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Centrality dependence

v2

b

v2

Npart

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v2

% centrality

pT=0.5 GeV/c

sin2(b)

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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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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.

So B(pT)/R(pT) for proton is smaller than in 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.

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For pT>1.5 GeV/c, shower partons must be considered for both π and p spectra. Jet dominance (>3GeV/c) will saturate v2.

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

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

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Conclusion

• Phantom jets produced by semi-hard parton scattering create ridges that are important in low and intermediate pT physics.

• up to 6 GeV/c is produced by thermal partons in the ridge and can have associated particles.

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

Calling v2 “elliptic flow” may be misleading.