March 16-19Chunbin Yang Elliptic Flow Without Using Hydrodynamics Chunbin Yang Hua-Zhong Normal University Wuhan, China Done with R.C. Hwa University of.

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


Outline

•QGP, flow and hydrodynamics•Quark recombination and flow•V2 at low pT

•V2 at intermediate pT

•Summary


Formation of QGP at RHIC

• Strong suppression of pion spectrum in central Au+Au collisions

• Absence of opposite jets• Quark number scaling of v2


v2 scaling21 2 ( )cos(2 )T

T T

dNv p

p dp d

K


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


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).


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


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


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.


|| < = 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.


, ,..., ,...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


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 '()

()( | |)( | |)


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)


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


20 ''

1sin 2 ( )|

TET

vb

E T

'' 1.7T GeV


T’p=0.35(1-0.5c) GeV


Tp’’=2.37GeV


20 ''

1sin 2 ( )|

T

p

ET p

vb

E T


ˆ / 2b b R


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


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


0-10%

Determine parameter







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



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


Thank you!Thank you!

March 16-19Chunbin Yang Elliptic Flow Without Using Hydrodynamics Chunbin Yang Hua-Zhong Normal University Wuhan, China Done with R.C. Hwa University of.

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