Direct photon interferometry D.Peressounko RRC “Kurchatov Institute”

D.Peressounko, WPCF, Kromeriz, Outlook Photons are special:  Penetrating=> Specific R(K T ) dependence  Massless => Unusual R inv and inv interpretation  Rare => Strong background Experimental review  Completed experiments TAPS,WA98  Ongoing PHENIX,STAR  Developing ALICE Conclusions

D.Peressounko, WPCF, Kromeriz, Accessing space-time dimensions of different stages of the collision 17.2 AGeV R out R side R long 3+1 hydro with first order phase transition. QGP phase includes pre-equilibrium pQCD contribution D.P. Phys.Rev.Lett.93:022301,2004 QGP mixed hadr

D.Peressounko, WPCF, Kromeriz, K T dependence of photon correlation radii RHIC 200 AGeV D.P. Phys.Rev.Lett.93:022301,2004 D.Srivastava, Phys.Rev.C71:034905,2005 T.Renk, hep-ph/

D.Peressounko, WPCF, Kromeriz, Predictions for correlation radii SystemR out (fm)R side (fm)R long (fm)R inv (fm)  D.Srivastava, Phys.Rev.C71:034905,2005  D.Peressounko, Phys.Rev.Lett.93:022301,2004 ee K T =1 GeV * 3.2 J.Alam et al., Phys.Rev.C70:054901,2004  * 3.0 J.Alam et al., Phys.Rev.C67:054902,2003  T.Renk, hep-ph/ * Not LCMS system RHIC, AGeV, K T =2GeV

D.Peressounko, WPCF, Kromeriz, Q inv parameterization for massless particles S(x) = exp( - t 2 /  2 – x 2 /R o 2 - y 2 /R s 2 - z 2 /R l 2 ), C 2 (q o,q s,q l )=1 + exp( -q o 2 (R o 2 +  2  2 ) -q s 2 R s 2 -q l 2 R l 2 ) C 2 (Q inv )= ∫d 3 q/q e C 2 (q o,q s,q l )  (Q inv 2 +q 2 ) ∫d 3 q/q e  (Q inv 2 +q 2 ) = 1/(4  ) ∫ [1+ exp{-Q inv 2 (K 0 2 /M 2 cos 2  (R o 2 +  2  2 ) + R s 2 sin 2  sin 2  + R l 2 sin 2  cos 2  ) }] d  = 1+ inv exp{-Q inv 2 R inv 2 ) R inv = (not R o !) inv = 1/(4  ) ∫ exp{ - 4K T 2 (R o 2 +  2 )cos 2  }d  For massless particles ( ,e) Q inv parameterization is very special! (integrate in CM frame of the pair)

D.Peressounko, WPCF, Kromeriz, Q inv parameterization for massless particles (MC) Set 1:R o = 6R s = 6R l = 6 Set 2:R o = 4R s = 6R l = 6 Set 3:R o = 2R s = 6R l = 6 Set 4:R o = 6R s = 4R l = 6 Set 5:R o = 6R s = 2R l = 6 Set 6:R o = 6R s = 4R l = 4 Set 7:R o = 4R s = 4R l = 4 Set 8:R o = 2R s = 4R l = 4 Set 9:R o = 6R s = 2R l = 2 inv = Erf(2K T √R o 2 +  2 )/(2K T √R o 2 +  2 ) inv =1/(2K T √R o 2 +  2 )

D.Peressounko, WPCF, Kromeriz, Background photon correlations Bose-Einstein  0 correlations Resonance decays Collective flow 00 00     } 00 00 00 } 

D.Peressounko, WPCF, Kromeriz,  0 BE residual correlations D.P. Phys.Rev.Lett.93:022301,2004 R  =4 fm R  =5 fm R  =6 fm C 2  =1+exp(-Q inv 2 R  2 )

D.Peressounko, WPCF, Kromeriz,  0 BE residual correlations A.Deloff and T.Siemiarczuk, ALICE internal note INT  =1/2(k 1 -k 2 ) C 2  (  )=1+ /(1+  2 R  2 ) 2 dN  /dp=p·epx(-p/[3GeV])

D.Peressounko, WPCF, Kromeriz,  0 BE residual correlations O.V.Utyuzh, G.Wilk, Nukleonika 49:S15 (2004), hep-ph/ Varying width (and strength) Varying strength

D.Peressounko, WPCF, Kromeriz, TAPS: detector setup BaF 2 25 cm long (12 X 0 ) prism of hexagonal cross section, the diameter of the inner circle being 5.9 cm (69% of the Moliere radius). Min angle cut between photons Distance to IP 62 cm Typical photon energy ~10 MeV

D.Peressounko, WPCF, Kromeriz, TAPS: m  distribution and C 2 Geant simulations 86 Kr+ nat 60 AMeV 181 Ta AMeV Comparison to BUU calculations

D.Peressounko, WPCF, Kromeriz, Number of events collected: Peripheral (20% min bias) Central (10% min bias) WA98 setup

D.Peressounko, WPCF, Kromeriz, Two photon correlation functions

D.Peressounko, WPCF, Kromeriz, WA98: apparatus effects L min = 20 cm (5 modules) L min = 25 cm (6 modules) L min = 30 cm (7 modules) L min = 35 cm (9 modules) 200 < K T < 300 MeV 100 < K T < 200 MeV 200 < K T < 300 MeV

D.Peressounko, WPCF, Kromeriz, Hadrons and photon conversion “Narrow” (16 + 1)% (4 + 1)% “Neutral” ( 1 + 4)% (1 + 4)% “All” (37 + 4)% (22 + 4)% “Narrow neutral” (1 + 1)% (1 + 1)% obs = = 1 (N  dir ) 2 2 (N  tot + cont) 2 Contamination, (charged + neutral) 100<K T < <K T <300 pid true (1+ cont/ N  tot ) 2

D.Peressounko, WPCF, Kromeriz, Photon background correlations  0  0 Bose-Einstein correlations: Slope: -(4.5±0.4)·10 -3 (GeV -1 ) Elliptic flow: Slope: -(3.1±0.4)·10 -3 (GeV -1 ) Decays of resonances: K 0 s →2  0 →4  K 0 L →3  0 →6   →3  0 →6   →  0  →3 

D.Peressounko, WPCF, Kromeriz, C 2 (Q inv ) =1 + /(4  ) ∫ do exp{ - Q inv 2 (R s 2 sin 2  sin 2  + R l 2 sin 2  cos 2  ) - (Q inv 2 + 4K T 2 )cos 2  R o 2 } R  R  long R  side R inv = f(R s,R l ) inv = Erf(2K T R o ) 2K T R o (for massless particles!) Invariant correlation radius

D.Peressounko, WPCF, Kromeriz, Subtraction method, upper limit Yield of direct photons Correlation method: Subtraction method Predictions hadronic gas QGP sum pQCD Predictions: S. Turbide, R. Rapp, and C. Gale, hep-ph/ N  dir = N  total √2 inv = Erf(2K T R o ) 2K T R o Most probable yield (R o =6 fm) The lowest yield (R o =0)

D.Peressounko, WPCF, Kromeriz, PHENIX setup Lead Scintillator Lead + scintillating plates of 5.5*5.5 cm 2 at a distance 510 cm from IP. Lead Glass PbGl crystals 4*4 cm 2 cross section distance 550 cm from IP

D.Peressounko, WPCF, Kromeriz, PHENIX: Comparison to data d+Au collisions at √s NN =200 GeV

D.Peressounko, WPCF, Kromeriz, STAR Use 1 gamma in TPC, 1 gamma in calorimeter. A procedure has been developed which permits the measurement of gamma-gamma HBT signals despite the large background of gammas from π 0 mesons Gamma energy > 1.0 GeV is required for the residual π 0 correlation to be “small” “No HBT” calculation may be needed but appears to be doable. Conclusions from the talk of J. Sandweiss on “RHIC-AGS users meeting”, June 21, 2005, BNL:

D.Peressounko, WPCF, Kromeriz, ALICE setup PHOS: crystals PbW0 4 2*2 cm cross section Distance to IP 460 cm

D.Peressounko, WPCF, Kromeriz, ALICE: unfolding and resolution

D.Peressounko, WPCF, Kromeriz, ALICE: photon correlations in HIJING event K t =200 MeV

D.Peressounko, WPCF, Kromeriz, Summary Direct photon and electron interferometry is rather special subject due to penetrating nature, zero mass and low yield. Two-photon correlations were observed in two experiments up to now. Photon correlations are analyzed now at PHENIX and STAR. PHOS detector at ALICE is very promising tool due to fine granularity and high spatial and energy resolutions.

D.Peressounko, WPCF, Kromeriz, PHENIX: MC simulations K t = 0.2 GeV Using measured spectra and yields for  0, kaons and  K+→K+→ K0S→K0S→ K0L→30K0L→30 →30→30 c  =4.7 m c  =15. m c  =0.02 m

D.Peressounko, WPCF, Kromeriz, Jan-e Alam et al., ee correlations J.Alam et al., Phys.Rev.C70:054901,2004 K T =1 GeV Not LCMS

D.Peressounko, WPCF, Kromeriz, T.Renk Side Long side out T.Renk, hep-ph/

D.Peressounko, WPCF, Kromeriz, Penetrating probes: probe all stages? RHIC 200 AGeV D.P. Phys.Rev.Lett.93:022301,2004

D.Peressounko, WPCF, Kromeriz, Possible sources of distortion of correlation function Apparatus effects (cluster splitting and merging) Hadron misidentification Photon conversion Photon background correlations:  Bose-Einstein correlations of parent  0 ;  Collective (elliptic) flow;  Residual correlations due to decays of resonances;