In collaboration with Rupa Chatterjee

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

Rate

Fries, Mueller, & DKS, PRL 90 (2003)

FMS Results: Comparison to Data

r1r1 r2r2 x1x1 k1k1 k2k2 ΔRΔR x2x2 Quantum statistical correlation

q out q side q long k1k1 k2k2 q

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.

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

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

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

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, (2004)

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

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)

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.)

DKS and R. Chatterjee arXiv: 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.

RHIC

LHC

T C dependence of the outward correlation

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

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

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

Quark Matter 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/ STAR DATA STAR DATA - prelim.)

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

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

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) 

 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) 

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).

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 I d I t cos(q  r) The correlation function F. M. Marques et al., Phys. Rept. 284, 91 (1997)

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