1. In collaboration with Rupa Chatterjee

2. Direct photons are penetrating probes for the bulk matter produced in nuclear collisions, as they do not interact strongly. They have a large mean free path. hadronic phase qgp phase mixed phase pre-equilibrium phase z t Penetrating probes: emitted at all stages then survive unscathed ( α e << α s ). “Historians” of the heavy ion collision: encode all sub-processes at all times

3. Rate

6. Fries, Mueller, & DKS, PRL 90 (2003) 132301.

7. FMS Results: Comparison to Data

8. r1r1 r2r2 x1x1 k1k1 k2k2 ΔRΔR x2x2 Quantum statistical correlation

9. q out q side q long k1k1 k2k2 q

10. q out q side q long R side R long R out k1k1 k2k2 q One can show that R out – R side is a measure of the duration of the emission.

11. 19501960198019942004   pp astronomy intermediate energies relativistic energies intermediate energies Chronology of intensity correlation experiments

12. C(q out, q side =q long =0) C(q long, q out =q side =0) C(q side, q out =q long =0) R side (K 1T ) q out =q long =0 R long (K 1T ) q out =q side =0 R out (K 1T ) q side =q long =0

13. C(q out, q side =q long =0) C(q long, q out =q side =0) C(q side, q out =q long =0) R side (K 1T ) q out =q long =0 R long (K 1T ) q out =q side =0 R out (K 1T ) q side =q long =0

14. The two-photon correlation function for average photon momenta 100 < K T < 200 MeV/c (top) and 200 < K T < 300 MeV/c (bottom). The solid line shows the fit result in the fit region used (excluding the  0 peak at Q inv  m  0 ) and the dotted line shows the extrapolation into the low Q inv region where backgrounds are large. M. M. Aggarwal et al., [WA98 collaboration] PRL 93, 022301 (2004)

15. WA98 measures R inv as 8.34 ± 1.7 fm and 8.63 ± 2.0 fm, respectively For y 1 =y 2 =0 and  1 =  2 =0, q side =q long =q inv =0, but q out =k 1T -k 2T.ne.0

20. The outward, sideward, and longitudinal correlation functions for thermal photons produced in central collision of gold nuclei at RHIC taking  0 = 0.2 fm/c. Symbols denote the results of the calculation, while the curves denote the fits. Correlation function in the two phases can be approximated as where, i=out, side, and long  = quark matter (Q) or hadronic matter (H)

21. i=out, side, and long  = quark matter (Q) or hadronic matter (H) The final correlation function can be approximated as:  R i stands for the space-time separation of the two sources. R o,Q = 2.8, R o,H = 7.0,  R o =12.3, R s,Q ≈ R s,H = 2.8,  R s ≈ 0., R ℓ,Q = 0.3, R ℓ,H = 1.8,  R ℓ ≈ 0. (all values are in fm.)

22. DKS and R. Chatterjee arXiv: 0907.1360 The outward, sideward, and longitudinal correlation functions for thermal photons produced in central collision of lead nuclei at LHC taking  0 = 0.2 fm/c. Symbols denote the results of the calculation, while the curves denote the fits.

23. RHIC

26. LHC

29. T C dependence of the outward correlation function @RHIC

30. The side-ward correlation is only marginally affected and is not shown.

33. reaction plane q out q side q long   = 0°  = 90° R side (large)‏ R side (small)‏

34. Elliptic Flow of Thermal Photons: Measure Evolution of Flow ! Chatterjee, Frodermann, Heinz, and DKS, PRL 96 (2006) 202302. Early times Late times Adult life

37. Quark Matter 2005 - Zbigniew Chajęcki for the STAR Collaboration 37 Typical results for pion intensity interferometry Pion HBT radii from different systems and at different energies scale with (dN ch /dη) 1/3 RHIC/AGS/SPS Systematics ≈ 400 MeV (RHIC) ≈ 390 MeV (SPS) Lisa, Pratt, Soltz, Wiedemann, nucl-ex/0505014 STAR DATA STAR DATA (pp,dAu,CuCu,AuAu@62GeV - prelim.)

40. phase of source real function, characterizes the source strength bosons / fermions x 1 -x 2 Incoherent emission  

41. k 1 -k 2 Correlation function r1r1 r2r2 x1x1 k1k1 k2k2 ΔRΔR x2x2 

42. Spatial evolution of a central collision in the nucleus-nucleus centre of mass frame obtained with BUU calculation for the system 181 Ta+ 197 Au at 40A MeV. x (fm)  z (fm) 

43.  production rate (a.u.)  Production rate of photons with an energy of 30 MeV as a function of the incompressibility K  of nuclear matter obtained with BUU calculations for the system 181 Ta+ 197 Au at 40A MeV and b= 5 fm. Time (fm/c) 

44. Inclusive hard photons at  lab =90 0. Thermal (solid squares) and direct (sold circles). E  (MeV)  (counts/MeV)  G. Martinez et al.; Physics Letters B 349, 23 (1995).

45. IdId ItIt rr Initial compression 2 nd compression r Intensity  (r)   (q)  (r -  r)   (q) X e iq  r  d  (r) +  t  (r -  r)   (q) X ( I d +I t e iq  r ) C 12 (q) = 1 + exp(- q 2 R 2 - q 0 2  2 ) I  (q) I  (q) = I d 2 + I t 2 + 2 I d I t cos(q  r) The correlation function F. M. Marques et al., Phys. Rept. 284, 91 (1997)

46. Fits to the interferometry data; showing interference between two sources. Fits to the interferometry data; showing interference between two sources. Q (MeV) C 12