Centrality-dependent pt spectra of Direct photons at RHIC

F.M. Liu 刘复明 Central China Normal University, China

T. Hirano University of Tokyo, Japan

K.Werner University of Nantes, France

Y. Zhu 朱燕 Central China Normal University, China

liufm@iopp.ccnu.edu.cn

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Outline

• Motivations• Calculation approach• Results• Discussion and conclusion

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Motivations• Heavy ion collisions at various centralitis offer us various bulks of

hot dense matter.

• The interaction between jets ( hard partons) and the bulk has receiv

ed notable interest, i.e. jet quenching is one of the most exciting obs

ervables at RHIC.

• The interaction of partons inside the bulk and the properties of the b

ulk are of great interest, which may offer us some insight to quark c

onfinement.

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direct photons, jets and plasmaPRL94,232301(2005), PRL96,202301(2006)

1. Jet queching gives different effects to direct photons?

2. Thermal photons and JPC photons are penetrating probes for the inter

action of partons inside the bulk and the interaction between jet and bu

lk. We can make cross check of the properties of the medium.

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Calculation approachA precise calculation requires

• A realistic description of the space-time evolution of plasma

• A good jet topology

• A reasonable treatment of jet energy loss

( interaction between jet + plasma)

• A careful consideration of all sources of direct photons

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Space-time evolution of Plasma

),,,,...(,,, zyxBsu

%) ,(ddn

Described with ideal hydrodynamics in full 3D spaceConstrained with PHOBOS data

Tested with hadrons’ yields, spectra, v2 and particles correlation

For more details, read T. Hirano

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Jet (hard parton) Topology

)ˆˆˆ()(ˆ

ˆ),(),( 2

/2

/AB2

jet

utscdabtd

dsMxGMxGdxdxTK

pdyd

dNbBb

abcdaAaba

t

AB

),()()()( /// AxRxGA

ZxG

A

NxG EKS

apaNaAa

MRST 2001 LO pDIS and EKS98 nuclear modification are employed

)(),2

(),2

(),(30 zy

bxTy

bxT

pd

dNrpf BA

Jet phase space distribution at τ=0:

)(),(),,(),( 00003 Evpptvrpfpdrpfxpf

at τ>0:

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Parton Energy Loss in a Plasma

• Energy loss of parton i=q, g, D: free parameter

• Energy loss per unit distance, by BDMPS

• Every factor depends on the location of jet in plasma , i.e.,

0

))(,())(,,( ),,( 00 rfridrpiE QGP

is EDri / ))(,,( *2

)/8ln()233(

6)(

cfs TTNT

upE *

)(r

fQGP: fraction of QGP at a given point

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Fix parton energy loss parameter D• From pp collisions:

• From AA collisions, parton energy loss is considered

via modified fragmentation function

),(1 20

/2t

2,t

2

0

QzDzpdyd

dNdz

pdyd

dNcc

c

cpp

gqcc

pp

Factorization scale and renormalization scale to be tpQM

functionion fragmentat KKP :),( 20/ QzD cc

),,( 2/ ccc EQzD X.N.Wang’s formula

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Raa(pi0, %) at high pt gives D=0.5

A common Dfor various centralitiesshould be required!

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Sources of direct photons• Leading Order contr. from primordial NN scatterings

(does not depend on the plasma)

• Thermal contribution

upETExd

pdyd

dN

t

**thermal

42

thermal

),,(

qqg

gqq

)ˆˆˆ()(ˆ

ˆ),(

),(

2/

2/AB2

)LO(

utscdabtd

dsMxG

MxGdxdxTpdyd

dN

bBb

abaAaba

t

AB

Rapp Kapusta,:),( *HG TE

AMY/

22

*QGP

1

1

2

)(

9

6),( * C

eT

TTE

TEs

Interactions of thermal partonsare inside the rate!

...effect LPM

qqg

qq

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Sources of direct photons• Jet photon conversion

• Fragmentation contribution: similar to pi0 production, modified fragmentation function is used.

Ignored contributions: Induced radiation (higher order)

radiation from pre-equilibrium phase (short time)

qqg

gqq

C

Tg

TETxpfeTE q

qq

S22

*22

2*

JPC

24ln),(

4),(

),( *JPC

42

TExdpdyd

dN

t

JPC

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Results

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Centrality dependent pt-spectra(1)

PHENIX data: PRL 98, 012002 (2007) & arXiv:0801.4020

Precise data and predictions coincide with each other!

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Centrality dependent pt-spectra(2)PRL94,232302(2005)

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Pt spectrum from pp collisions

The PHENIX fit of pp spectrum is used by us to calculated the nuclear modification factor of direct photons, Raa.

PRL 98, 012002 (2007)

Side proof for our results ofLO + Frag_w/o_E loss in AA.

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Raa: scale, centrality & energy loss

• Data is reproduced within theory uncertainty.

• Almost independent of centrality for pt > 6 GeV/c, why?

• Visible, but not sensitive to energy loss, why?

PRL94,232302(2005);J.Phys.G34, S1015-1018,2007

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Jet quenching & bulk volume

• Parton energy loss does play a role in fragmentation contribution and JPC.

• This is centrality-dependent, similar to the suppression to pi0 production.

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Competition btw different sources

Raa is not sensitive to E loss at high pt, due to the dominance of LO.

Raa is almost independent to centrality at high pt, due to the compensation btw the two sources, JPC & frag. when collisions move from central to peripheral.

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Information from Thermal photonsEnergy density at plasma center

• The slope of pt spectrum at low pt region (dominant by thermal photons)

can reflect the temperature (energy density, …) of the bulk.

• The yields of photons (mainly low pt ) is roughly proportional to Ncoll., which reflect the bulk volume.

Raa due to thermal source

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Discussion and Conclusion• Parton energy loss does make a visible but not so significant effect in Raa

(γ) compared to Raa (π). D=0.5 is to understand.

• The modification of Raa(γ) by jet quenching is at the same degree of that

by theory scales, which is quite different from the case of Raa (π) .

• Raa(γ) is weakly dependent on centrality for pt> 6GeV/c, due to

1) the dominance of leading order contribution

2) the compensation btw JPC and fragmentation contribution.

• As a penetrate probe, thermal photons can reflect the properties of bulk, i.

e., temperature and volume via the slope of pt spectrum and the yields.

The interaction between thermal partons gives a cross check to the infor

mation offered by parton energy loss.

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Thank you!

One more word:

v2 of direct photons is expected to offer much more Information.

Our results and experiment measurements are coming soon!

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purely leading order calculation:

Isosping mixture and nuclear shadowing make an evident decrease.

Why RAA decreases at high pt?

),()]()(

)([)( /// AxRxfA

zAxf

A

zxf EKS

aNapaAa