march 16-19chunbin yang elliptic flow without using hydrodynamics chunbin yang hua-zhong normal...
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March 16-19 Chunbin Yang
Elliptic Flow Without Using Hydrodynamics
Chunbin YangHua-Zhong Normal University
Wuhan, ChinaDone with R.C. Hwa
University of Oregon, USA
March 17,2008,Hungary
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Outline
•QGP, flow and hydrodynamics•Quark recombination and flow•V2 at low pT
•V2 at intermediate pT
•Summary
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Formation of QGP at RHIC
• Strong suppression of pion spectrum in central Au+Au collisions
• Absence of opposite jets• Quark number scaling of v2
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v2 scaling21 2 ( )cos(2 )T
T T
dNv p
p dp d
K
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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
17)
RHIC 130 GeV
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Agree with data for pT<1.5GeV/c possible only if
0~0.6 fm/c
Huovinen, Kolb, Heinz, Ruuskanen, Voloshin Phys. Lett. B 503 58, (2001).
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Conventional wisdom
Azimuthal 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 at early time before the spatial asymmetry disappearsleads to momentum space asymmetry: v2>0
px py
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Alternative approach• must be sensitive to the initial configuration
• must be able to describe the bulk behavior
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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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.
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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|| < = cos-1(b/2R)
Each scattering sends semi-hard partons in random directions.
At any given on average, the jet direction is normal to the surface.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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, ,..., ,...3 31 2 1 2
1 2 31 2 3
( , , ) ( , , )p
pdx xdx dx x xdNx F x x x R
dx x x x x x x
Recombination model
Distributions depend on b and v2
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Bulk partons q0dNq
B
dqTdCqTe
qT /T
pions B(pT )dN
B
pTdpTdC 2
6e pT /T
pions
B(pT ) R(pT ,)C 2
6e pT /T '()
Bulk+Ridge
partons q0dNq
BR
dqTdCqTe
qT /T '()
()( | |)( | |)
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v2
dN
pTdpTdB(pT ) R(pT ,)
v2 (pT ,b) cos2 d cos2 dN
pTdpTd0
2
d dN
pTdpTd0
2
v2 (pT ,b)d cos2R(pT ,)0
2
d[B(pT ) R(pT ,)]0
2
R(pT )sin2(b)B(pT ) 2R(pT )
R(pT ,)R(pT )()
v2 (pT ,b)sin2(b)
B(pT )R(pT )
2(b)
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B(pT )
R(pT )
1
(epT /T " 1)
v2 (pT ,b)
sin2(b)
(epT /T " 1) 2(b)
Thermal pions only
pT<1.5 GeV/c
Small pT region (b)cos 1b
2R
v2
(pT ,b)pT
T "sin2(b)
1
T ''1
T1
T '
TTT '
T T ' T
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20 ''
1sin 2 ( )|
TET
vb
E T
'' 1.7T GeV
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T’p=0.35(1-0.5c) GeV
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Tp’’=2.37GeV
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20 ''
1sin 2 ( )|
T
p
ET p
vb
E T
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ˆ / 2b b R
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At intermediate PT
• Soft partons• Hard partons• Energy loss proportional to L• L depends on azimuthal angle• Fit spectra to fixed parameter• Thermal-shower recombination
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0 2
( , , ) ( ) ( , , )
( , , ) ( , ) 2 ( , ) cos(2 )i iF k b f k G k b
G k b g k b g k b
Hard parton with momentumK originated with higher
k’=k+Δk
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0-10%
Determine parameter
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2 2 2
2 2 2
2 2
2
( ) ( )
T S
p T S
T S
v v v
v v v
v q v q
;
;
2
2
( ) 2
(3 / 2) 3T
pT
v E
v E
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Summary
• Ridge plays an important role in flow• Features of elliptic flow can be reproduc
ed by the recombination model• Quark number scaling violation of v2 is d
ue to the difference between flows of thermal and shower partons
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Thank you!Thank you!