Photon radiation in sQGP

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)

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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

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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

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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

32VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

Azimuthal dependence of HBT radii

33VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

Azimuthal asymmetry