photon radiation in sqgp
DESCRIPTION
Photon radiation in sQGP. Máté Csanád , Imre Májer Eötvös University Budapest WPCF 2011, Tokyo. The Little Bang. thermalization. Milestones @ RHIC. Jet suppression in Au+Au : new phenomenon Phys. Rev. Lett . 88, 022301 (2002) No jet suppression in d+Au : new form of matter - PowerPoint PPT PresentationTRANSCRIPT
Photon radiation in sQGPMáté Csanád, Imre Májer
Eötvös University BudapestWPCF 2011, Tokyo
2VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
The Little Bang
freeze-outexpansion, cooling
Photon spectrum: information on the time development of the sQGP
Thermalization time
Equation of state
Initial temperature
•Freeze-out time•Freeze-out
temperature•Expansion at freeze-
out
Hadronic spectrum
information on the final state
thermalization
3VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Milestones @ RHICJet suppression in Au+Au: new phenomenon
Phys. Rev. Lett. 88, 022301 (2002)No jet suppression in d+Au: new form of matter
Phys. Rev. Lett. 91, 072303 (2003)Summary of the results: matter is a liquid
Nucl. Phys. A 757, 184-283 (2005)Elliptic flow scaling: quark degrees of freedom
Phys. Rev. Lett. 98, 162301 (2007)Heavy quark flow: nearly perfect fluid
Phys. Rev. Lett. 98, 172301 (2007)Direct photon spectrum: high initial temperature
Phys. Rev. Lett. 104, 132301 (2010)
VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 4
Direct photon spectra measured @ PHENIXBackground from hggIdea: thermal & virtual
photons and dielectronsX → e+e−
X → g and X → g* → e+e−
e+e- and g relatedDirect and inclusive alsoDirect photons calculableThermal below 3 GeV!Initial temperature? EoS?Hydrodynamics! Phys. Rev. Lett. 104, 132301 (2010)
from same process
5VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
1.•Hydrodynamics gives um(x), T(x), p(x) etc.•Famous: Landau, Hwa-Bjorken (1D); few 3D
known
2.•Source function S(x,p) based on flow,
temperature etc.•E.g. a Bose-Einstein or a simple thermal
distribution
3. •Calculate observables•N1(pt), v2(pt) etc. come from integrals of S(x,p)
4.•Compare to data: determine model
parameters•Final state: hadrons; Initial state, EoS:
photons
Method of exact hydrodynamics
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The solution we investigateBy Csörgő, Csernai, Hama, Kodama, 2004
Only available 3D relativistic and realistic solutionHubble-flow: um=xm/t
In the Universe: v=Hr, Hubble constant ~ (time)-1
Ellipsoidal symmetry:
Thermodynamic quantities const. on the s=const. ellipsoidX, Y, Z describe the expanding ellipsoid here
Gaussian temperatureprofile, expanding andshrinking over time:
2 2 2
2 2 2( ) ( ) ( )
x y zsX t Y t Z t
TIME
7VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Momentum distribution & correlation radii0-30% centrality, Au+Au, PHENIX data [PRC69 &
PRL91]
T0 199 ± 3 MeV central freeze-out temp.
e 0.80 ± 0.02 momentum space ecc. ut
2/b -0.84± 0.1 (b<0)transv. flow/temp. grad
t0 7.7 ± 0.1 freeze-out proper time
Eur. Phys. J. A 44,473–478 (2010)
Eur. Phys. J. A 44,473–478 (2010)
8VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Elliptic flow0-92% centrality, Au+Au, PHENIX data [PRL93]
T0 204 ± 7 MeV f.o. temperature e 0.34 ± 0.01 eccentricity ut
2/b -0.34 ± 0.07 (b<0) transv. flow/temp. grad.
Eur. Phys. J. A 44, 473–478 (2010)
9VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Temperature versus timeFrom hadronic observables:
Hadronic observables cannot decide!EoS & Tini from penetrating probes!
Eur. Phys. J. A 44, 473 (2010) Fixed from hadronic
observables
10VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Direct photon spectrumFits to 0-92% centrality PHENIX data
[PRL104]Parameters from hadronic fitImportant new parameter: k=7.7±0.8
cs=0.36±0.02Average EoS, compare Lacey et al.,
nucl-ex/0610029
arXiv: 1101.1279, 1101.1280(2010)
11VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Temperature versus timeFrom hadronic observables:
EoS from photon spectra: k=7.7±0.8 orcs=0.36 ± 0.02
Initial temperature (at t=1 fm/c)Ti > 519 ± 12 MeV
Eur. Phys. J. A 44, 473 (2010) Fixed from hadronic
observables
Determined from photon spectra
12VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Elliptic flow from PHENIX data [arXiv:1105.4126]Early times more importantMany models fail to describeNon-hydro effects kick in >2 GeVSign change possible here!
Photon elliptic flow
13VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Bose-Einstein correlationsRout/Rside = 1 for hadronsRout» Rside here!Large t!
Photon HBT
Evol
utio
n tim
e
14VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
SummaryRevival of interest in perfect hydroOur model: 3+1d relativistic model w/o
acceleration
Calculated hadronic source → N1, v2, HBT
Calculated photon source → N1, v2, HBT
Compared successfully to data, cs=0.36±0.02
Ti≈520 MeV
Compared to fresh photon v2 data
Prediction on Bose-Einstein correlations
Thank you for your attention
VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 16
Perfect hydro pictureNo data
point even near the kinematic viscosity of 4He (10/4p)
Close to AdS/CFT minimum, (1/4p)
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How to measure direct photons?PHENIX measurement done: PRL 104, 132301
(2010)Problem: huge background from h → ggIdea: thermal + virtual photon production parralel
X → e+e−, X → g and X → g* → e+e−
from the same processDielectron and real photon production related as:
S process dependent, dng*/dng , for p0 and h e.g.:
For pt » mee » me: L, S → 1
2 2 2
2 2
4 22 1 ( ) ( ) , ( ) 1 13
ee e e
ee ee eeee t ee t ee ee
dnd n m mL m S m L mdm dp m dp m m
gp
322 2 2( ) ( ) 1 , ( ) 0 for ee ee ee h ee ee hS m F m m M S m m M
Phys. Rev. Lett. 104, 132301 (2010)
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Dielectron spectrum measurementMeasured electron pairs with pt of 1-5 GeVEasy via electron ID capabilitiesCompare to dielectrons from hadronic
cocktail
Excess seen above pion mass due to virtual g
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Direct photons versus decay photons
Excess: virtual direct photons (decaying into e+e− pairs)
Inclusive e+e−: hadronic + dir. virtual photon componentsHadronic electron pairs (fc), calculated from cocktail: p, h, w, h’, f
Electron pairs from direct virtual photons (fdir) calculated from fc via previous formula
Determine ratio r by fit for separate pt binsUse r to scale inclusive photon spectra
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Famous solutionsLandau’s solution (1D, developed for p+p):
Accelerating, implicit, complicated, 1DL.D. Landau, Izv. Acad. Nauk SSSR 81 (1953) 51 I.M. Khalatnikov, Zhur. Eksp.Teor.Fiz. 27 (1954) 529L.D.Landau and S.Z.Belenkij, Usp. Fiz. Nauk 56 (1955)
309Hwa-Bjorken solution:
Non-accelerating, explicit, simple, 1D, boost-invariantR.C. Hwa, Phys. Rev. D10, 2260 (1974) J.D. Bjorken, Phys. Rev. D27, 40(1983)
Others Chiu, Sudarshan and Wang Baym, Friman, Blaizot, Soyeur and Czyz Srivastava, Alam, Chakrabarty, Raha and Sinha
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Some known relativistic solutionsSolution Basic prop’s EoS Observables
Csörgő, Nagy, CsanádPhys.Lett.B 663:306-311, 2008 Phys.Rev.C77:024908,2008
Ellipsoidal, 1D accelerating
e-B=k(p+B)
dn/dy, e
LandauIzv. Acad. Nauk SSSR 81 (1953) 51
Cylindr., 1D, accelerating
e=kp none
Hwa-BjörkenR.C. Hwa, PRD10, 2260,1974J.D. Bjorken, PRD27, 40(1983)
Cylindr., 1D,non-
accelerating
e=kpdn/dy, e
Bialas et al.Phys. Rev. C76, 054901
(2007).
1D, betweend Landau and
Hwa-Björken
e=kpdn/dy
Csörgő et al.Heavy Ion Phys. A 21, 73 (2004))
Ellipsoidal, 3D, non-
accelerating
e-B=k(p+B)
pt spectra, flow,
correlations
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The solution we investigateDensity, temperature, pressure
n(s) arbitrary, but realistic to choose Gaussian b<0 is realistic
Ellipsoidal symmetry
(thermodynamic quantities const. on the s=const. ellipsoid) Directional Hubble-flow
v=Hr or H=v/r, the Hubble-constants:
(T. Csörgő, L. P. Csernai, Y. Hama és T. Kodama, Heavy Ion Phys. A 21, 73 (2004))
30
0
(3/ )0
0
330
0
( )
1( )
( ) ( ) ( )1, , ,( ) ( ) ( )
n n s
T Ts
p p
X t Y t Z tu x y zX t Y t Z t
k
k
m
t nt
tt n
tt
g2 2 2
2 2 2( ) ( ) ( )
x y zsX t Y t Z t
/2( ) bss en
( ) ( ) ( ), ,( ) ( ) ( )
X t Y t Z tX t Y t Z t ( ), ( ), ( ) : .; , ,
tX t Y t Z t const X Y u e
23VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Temperature versus timeFrom hadronic observables:
EoS from photon spectra: k=7.7±0.8Initial temperature (at t=1 fm/c)
Ti > 519 ± 12 MeV
Eur. Phys. J. A 44, 473 (2010)
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Insensitivity to the initial timeInitial time period: small contribution
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EoS dependenceSensitive to k with these level of errors
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Photon elliptic flow analysisEccentricity dependence EoS dependence
Initial time dependence
27VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
• Source function: probability particle creation
• For hadrons: Maxwell-Boltzmann type
• H(t)dt freeze-out distribution (e.g. Dirac-d)
• pmd3Sm(x) Cooper-Fry prefactor (flux
term)• Photons are continously created, but not
thermalized• Thermal emission determins source functions
Source functions
4 3( )( , ) ( ) exp ( ) ( )
( ) S
p u x
S x p d x n x p d x H dT x
mm m
m t t
4 41( , )1
p u T
S x p d x Ed xe
mm
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Hadronic resultsSingle particle transverse momentum
spectrum
Elliptic flow (asymmetry in the transverse plane)
with , I: Bessel func.
Width of two-particle correlation functions:
2 2 2eff 0
1eff eff 0 0
2 20 00 0
0 0 eff
( )( ) exp
2 2
1 1 1 1, , ( ) ( ) 2
t t t tt t
t t t
x t y tx y
p T T p p mN p N V m
mT mT mT T
T TT T m X T T mYb T E b T E T T T
12
0
( )( )
I wvI w
2 1 14
t
Kt y x eff
pw Em T T T
e
0 0 , 0,
,
( ) x y
x yt x y
T T TR
mTt 2 20.5 out side x yR R R R
29VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Photon spectra and photon v2Integration can be done analytically
A and B are:
3/
3/
/3/2
13/2 4 /31 0 /2
1/2
1
3 4 ,2 3
( ) (2 )3 1 4 ,
4 2 3
f i
f it t x y z
A A
N p p R R R AB A A
k
k
t t
kt t
k kp t
k 3/
3/
/
12 /2
1
1 4 ,2 3
2 3 4 ,2 3
f i
f i
ABvA
A
k
k
t t
t t
k
k
22
2 2
0 02 2
( 3)1 ,
2 ( 3) 2 ( 3)
t t t t
t t
b bp u p uA BT Tb b
u u
k ek k k
k k
30VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Where we areRevival of interest, new solutions
Sinyukov, Karpenko, nucl-th/0505041 Pratt, nucl-th/0612010 Bialas et al.: Phys.Rev.C76:054901,2007 Borsch, Zhdanov: SIGMA 3:116,2007 Nagy et al.: J.Phys.G35:104128,2008 and arXiv/0909.4285 Liao et al.: arXiv/09092284 and Phys.Rev.C80:034904,2009 Mizoguchi et al.: Eur.Phys.J.A40:99-108,2009 Beuf et al.:Phys.Rev.C78:064909,2008 (dS/dy as well!)
Need for solutions that are:accelerating + relativistic+ 3 dimensionalexplicit + simple + compatible with the data
Need to calculate observables!
31VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Correlation functions
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Azimuthal dependence of HBT radii
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Azimuthal asymmetry