Upload
devon-medland
View
216
Download
1
Tags:
Embed Size (px)
Citation preview
Elliptic flow of thermal photons in Au+Au collisions at 200GeV
QNP2009 Beijing, Sep 21 - 26, 2009
F.M. Liu Central China Normal University, China
T. Hirano University of Tokyo, Japan
K. Werner University of Nantes, France
Y. Zhu Central China Normal University, China
2
Outline
• Motivations• Calculation approach• Results• Conclusion
3
Motivations• The properties of the hot dense matter created in heavy ion collision are of great
interest, especially the critical behaviors.
• As penetrating probes, thermal photons can provide the inner information of the
plasma, which is a useful compensation to the signals of hadrons emitted from
the surface of the plasma.
• Questions: What can we learn from direct photon signals? How is
thermal photon signal, i.e. the elliptic flow, related to the system
evolution? …
4
Calculation approachA precise calculation of direct photon productionrequires careful treatments on
• All sources of direct photons: from primordial scatterings at early stage, thermal photons, jet photon conversion, fragmentation contribution, …
• The space-time evolution of the created hot dense matter distributions of thermal partons thermal photons, low pt hadrons
• The propagation of jets in plasma (energy loss) distribution of hard partons high pt photons and hadrons
5
thermal photon production
upETExdpdyd
dN
t
**thermal
42
thermal
),,(
2004 al,et Rapp R.
1991 al,et Kapusta:),( *HG TE
(2001) Yaffe& MooreArnold, :),( *QGP TE
Thermal parton interactions are considered in emission rate:
...effect LPM
qqg
qqg
gqq
• In the local rest frame, photons are emitted from the thermal bath isotropically.
• Thermal photons’ v2 is caused by the Lorentz boost and accumulated with the space-time integration.
• Both the strength and the asymmetry of the transverse flow are important.
6
the evolution of the matter
fm/c6.00
),,,,...(,,,, zyxBsup
Initial condition: thermalized QCD matter at
Freeze-out:
Evolution: 3D ideal hydrodynamic equation
described with 3+1D ideal hydrodynamics
0 T
MeV100~or fm/GeV08.0 3 thth T
MeV170cTEoS: 1st order phase transition at
QGP phase: 3 flavor free Q & G gas
HG phase: hadronic gas PCE
7
Initial conditions at 0Flow velocity: zero
Energy density: (two options)
Parameterized based on Glauber model—a plateau is assumed. Hirano et al. Phys. Rev. C77:044909, 2008
EPOS model: based on string overlapping. K.Werner@SQM09
Uniform distribution is assumed along longitudinal direction in 2+1D hydrodynamics
Parameters constrained with PHOBOS data
Tested with hadrons’ yields, spectra, v2 and particles correlation
%) ,(d
dn
8
Time evolution of the plasma
Energy-weighted Space-averaged
Energy density gets weaker with time.
Transverse flow gets stronger with time.
The asymmetry increases with eccentricity.22
22
2
22
yx
yxH
yxr
vv
vvv
vvv
9
FML, T.Hirano, K.Werner, Y. Zhu Phys. Rev. C 79, (2009) 014905;
J. Phys. G 36 (2009) 064072.
Results: Pt spectra of direct photons
Direct photon production from AuAu collisions at top RHIC energy is well explained in a large pt range at all centralities. The effect from jet quenching is discussed.
10
pt dependence of thermal photon v2
Elliptic flow of thermal photons decreases at high pt due to the abundant emission at early time.
FML, T.Hirano, K.Werner, Y. Zhu, Phys. Rev. C80,034905 (2009).
11
Centrality dependence of pt-int. v2
Maximum appears at 40-50% centrality. Why?
Note:
The maximum of measured hadronic v2
also appears at this centrality,
but viscosity is needed to explain it.
Both strength and asymmetry of transverse flow are important.
Thermal photons dominant the low pt contribution and become the main part in the pt-integrated v2 of direct photons.
When compared with measurements, one should be careful with minimum pt.
12
Rapidity dependence
The rapidity distribution can not identify different initial conditions;
But the elliptic flow of thermal photons “remembers” the initial conditions.
13
Thermal photons from eta_s source Parameterized initial condition
EPOS initial condition
14
Conclusion• Ideal hydro model can reproduce the measured pt spectra of direct photons at diff
erent centrality with the four sources we considered.
• Thermal photons’ v2 decreases at higher pt due to more fraction from early emissi
on.
• We predict thermal photons’ v2 reaches maximum at 40-50% centrality, due to the
interplay between the strength and asymmetry of the transverse flow. Contrary to
hadronic v2, no need of viscosity here.
• Thermal photons dominant the low pt contribution and become the main part in the
pt-integrated v2 of direct photons.
• Similar to hadronic signal, the rapidity distribution of thermal photons’ v2 can revea
l the initial longitudinal energy/entropy distribution.
15
Thank you!
16
Initial condition : Glauber model
Parameterized rapidity distribution in pp collisions
Energy density or entropy distribution in the space:
17
EPOS initial condition
Strings are constructed randomly in NN collisions. String segments overlap in the space and
form the core and corona region.
18
thermal photons v2 time evolution
Fraction emitted at earlier timeIncreases with pt.
Elliptic flow of thermal photonsincreases with time.
19
Dependence of EoS?
Elliptic flow is more sensitive to EoS than pt spectrum!
Various input of EoS
20
QGP phase and HG phase
V2 from hadronic phase is much bigger than from QGP phase.
V2 can carry different information than pt spectrum.
21
Pt spectrum from pp collisionsPRL 98, 012002 (2007)
A good test for contributions from leading order +fragmentation without Elossin AA collisions.
22
Isosping mixture and nuclear shadowing:
RAA suppression from initial effect
),()]()(
)([)( /// AxRxGA
zAxG
A
zxG EKS
aNapaAa
)ˆˆˆ()(ˆ
ˆ),(),( 2
/2
/AB2
)LO(
utscdabtd
dsMxGMxGdxdxT
pdyd
dNbBb
abaAaba
t
AB
The dominant contribution at high pt is the LO contribution from NN collisions:
The isospin mixtureand nuclear shadowing reduce Raa at high pt.
This is the initial effect, not related to QGP formation.
23
Distribution of hard partons
)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:
24
Why jets lose energy
25
Fix D with pi0 suppression • 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
26
Parton Energy Loss in a Plasma
• Energy loss of parton i=q, g,
• Energy loss per unit distance, i,e, with BDMPS
D: free parameter
• Every factor depends on the location of jet in plasma , i.e.,
0
))(,())(,,( ),,( 00 rfridrpiE QGP
is EDri / ))(,,( *2
)/8ln()233(
6)(
cfs TTN
T
upE *
)(r
fQGP: fraction of QGP at a given point
27
Fix D with pi0 suppression
A common D=1.5for various Centralities!