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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
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PhotonradiationinsQGP MátéCsanád, Imre Májer Eötvös University Budapest WPCF 2011, Tokyo
TheLittle Bang thermalization VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
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 • 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: nearlyperfect 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
Direct photon spectra measured @ PHENIX • Background from hgg • Idea: thermal & virtual photons and dielectrons X → e+e− X → g and X → g* → e+e− • e+e- and g related • Direct and inclusive also • Direct photons calculable • Thermal below 3 GeV! • Initial temperature? EoS? • Hydrodynamics! from same process Phys. Rev. Lett. 104, 132301 (2010) VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Method of exacthydrodynamics VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
The solution we investigate By Csörgő, Csernai, Hama, Kodama, 2004 Only available 3D relativistic and realistic solution Hubble-flow: um=xm/t In the Universe: v=Hr, Hubble constant ~ (time)-1 Ellipsoidal symmetry: Thermodynamic quantities const. on the s=const. ellipsoid X, Y, Z describe the expanding ellipsoid here Gaussian temperature profile, expanding and shrinking over time: TIME VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Momentum distribution & correlation radii • 0-30% centrality, Au+Au, PHENIXdata [PRC69 & PRL91] • T0 199 ± 3 MeV central freeze-out temp. • e 0.80 ± 0.02 momentum space ecc. • ut2/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) VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Elliptic flow • 0-92% centrality, Au+Au, PHENIXdata [PRL93] • T0 204 ± 7 MeV f.o. temperature • e 0.34 ± 0.01 eccentricity • ut2/b -0.34 ± 0.07 (b<0) transv. flow/temp. grad. Eur. Phys. J. A 44, 473–478 (2010) VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Temperature versus time • Fromhadronicobservables: • Hadronicobservablescannotdecide! • EoS & Tinifrompenetratingprobes! Eur. Phys. J. A 44, 473 (2010) Fixed fromhadronicobservables VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Direct photon spectrum • Fits to 0-92% centrality PHENIX data [PRL104] • Parameters from hadronic fit • Important new parameter: k=7.7±0.8 cs=0.36±0.02 • Average EoS, compare Lacey et al., nucl-ex/0610029 arXiv: 1101.1279, 1101.1280(2010) VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Temperature versus time • Fromhadronicobservables: • EoSfromphotonspectra: k=7.7±0.8 or cs=0.36 ± 0.02 • Initialtemperature (att=1 fm/c) Ti > 519 ± 12 MeV Determinedfromphotonspectra Eur. Phys. J. A 44, 473 (2010) Fixed fromhadronicobservables VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Photon elliptic flow • Elliptic flow from PHENIX data [arXiv:1105.4126] • Early times more important • Many models fail to describe • Non-hydro effects kick in >2 GeV • Sign change possible here! VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Photon HBT • Bose-Einstein correlations • Rout/Rside = 1 for hadrons • Rout» Rside here! • Large t! Evolutiontime VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Summary • Revival of interest in perfect hydro • Our 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 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Perfecthydropicture • No data point even near the kinematic viscosity of 4He (10/4p) • Close to AdS/CFT minimum, (1/4p) VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
How to measure direct photons? • PHENIX measurement done: PRL 104, 132301 (2010) • Problem: huge background from h → gg • Idea: thermal + virtual photon production parralel • X →e+e−, X → g and X → g* → e+e− fromthesameprocess • Dielectron and realphoton production related as: • S process dependent, dng*/dng, for p0 and he.g.: • Forpt»mee»me: L, S → 1 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Dielectron spectrum measurement • Measuredelectronpairswithpt of 1-5 GeV • Easyviaelectron ID capabilities • Comparetodielectronsfromhadroniccocktail • Excessseenabovepionmassduetovirtualg Phys. Rev. Lett. 104, 132301 (2010) VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Direct photons versus decay photons • Excess:virtualdirect photons (decayinginto e+e−pairs) • Inclusive e+e−: hadronic + dir. virtualphotoncomponents • Hadronicelectronpairs (fc), calculatedfromcocktail: p, h, w, h’, f • Electronpairsfromdirectvirtualphotons (fdir)calculatedfromfcviaprevious formula • Determine ratio r by fit for separate pt bins • Use r to scale inclusive photon spectra VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Famous solutions • Landau’s solution (1D, developed for p+p): • Accelerating, implicit, complicated, 1D • L.D. Landau, Izv. Acad. Nauk SSSR 81 (1953) 51 • I.M. Khalatnikov, Zhur. Eksp.Teor.Fiz. 27 (1954) 529 • L.D.Landau and S.Z.Belenkij, Usp. Fiz. Nauk 56 (1955) 309 • Hwa-Bjorken solution: • Non-accelerating, explicit, simple, 1D, boost-invariant • R.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 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Some known relativistic solutions VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
The solutionweinvestigate Density, temperature, pressure n(s) arbitrary, butrealisticto choose Gaussian b<0 is realistic Ellipsoidalsymmetry (thermodynamicquantitiesconst. onthe s=const. ellipsoid) Directional Hubble-flow v=Hror H=v/r, theHubble-constants: (T. Csörgő, L. P. Csernai, Y. Hama és T. Kodama, Heavy Ion Phys. A 21, 73 (2004)) VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Temperature versus time • Fromhadronicobservables: • EoSfromphotonspectra: k=7.7±0.8 • Initialtemperature (att=1 fm/c) Ti > 519 ± 12 MeV Eur. Phys. J. A 44, 473 (2010) VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Insensitivitytotheinitialtime • Initial time period: small contribution VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
EoS dependence • Sensitivetokwiththeselevel of errors VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Photon elliptic flow analysis Eccentricity dependence EoS dependence Initial time dependence VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Source functions • 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 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Hadronic results • Single particle transverse momentum spectrum • Elliptic flow (asymmetryinthetransverseplane) with , I: Bessel func. • Width of two-particlecorrelation functions: VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Photon spectra and photon v2 • Integration can be done analytically • A and B are: VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Whereweare • Revival 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 dimensional • explicit + simple + compatible with the data • Need to calculate observables! VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Correlationfunctions VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Azimuthaldependence of HBT radii VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011
Azimuthalasymmetry VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011