Centrality-dependent pt spectra of Direct photons at RHIC F.M. Liu 刘复明 Central China Normal...
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Transcript of Centrality-dependent pt spectra of Direct photons at RHIC F.M. Liu 刘复明 Central China Normal...
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
9-12/7/2008 Hefei 3
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.
9-12/7/2008 Hefei 4
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.
9-12/7/2008 Hefei 5
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
9-12/7/2008 Hefei 6
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
9-12/7/2008 Hefei 7
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:
9-12/7/2008 Hefei 8
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
9-12/7/2008 Hefei 9
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
9-12/7/2008 Hefei 10
Raa(pi0, %) at high pt gives D=0.5
A common Dfor various centralitiesshould be required!
9-12/7/2008 Hefei 11
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
9-12/7/2008 Hefei 12
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
S22
*22
2*
JPC
24ln),(
4),(
),( *JPC
42
TExdpdyd
dN
t
JPC
9-12/7/2008 Hefei 14
Centrality dependent pt-spectra(1)
PHENIX data: PRL 98, 012002 (2007) & arXiv:0801.4020
Precise data and predictions coincide with each other!
9-12/7/2008 Hefei 16
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.
9-12/7/2008 Hefei 17
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
9-12/7/2008 Hefei 18
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.
9-12/7/2008 Hefei 19
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.
9-12/7/2008 Hefei 20
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
9-12/7/2008 Hefei 21
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.
9-12/7/2008 Hefei 22
Thank you!
One more word:
v2 of direct photons is expected to offer much more Information.
Our results and experiment measurements are coming soon!