Phantom Jets: the puzzle and v 2 without hydrodynamics
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Phantom Jets: the puzzle and v2 without hydrodynamics
Rudolph C. HwaUniversity of Oregon
Early Time Dynamics in Heavy Ion Collisions
Montreal, July 2007
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Jets
Conventional jet structure
Phantom jet
?
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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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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.
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Jet structure
Putschke, QM06
J+R
R
J
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Ridge
Putschke, QM06
Jet
Dependence on pT(trig) and pT(assoc)
3 - 4
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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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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.