1. Measuring initial temperature through Photon to dilepton ratio Collaborators: Jan-e Alam, Sourav Sarkar & Bikash Sinha Variable Energy Cyclotron Centre, Kolkata, India. QM-2008 VECC Jajati K Nayak

2. Outline of the talk……………… Introduction & motivation Photon and Dilepton productions Ratio of thermal photons to dileptons Summary and outlook Variable Energy Cyclotron Center, Kolkata Quark Matter-2008

3. Introduction… The production rate is a function of local intensive quantities. Probe the entire space time history EM radiations provide crucial information of the medium properties of hadrons. Variable Energy Cyclotron Center, Kolkata Feinberg,1976 McLerran & Toimela, 1985 Weldon,1990 Gale & Kapusta 1991 Photons and dileptons are efficient probes for the hot and dense matter. Mean free path is large compared to system size. Hence suffer less interaction after their production. Quark Matter-2008

4. Motivation Focus of the present work : Thermal radiation Thermal yield depends on the input parameters like; EOS, Initial temperature (T i ), Freeze-out condition (T f ), Nature of phase transition, Transition temperature (T C ), Not known unambiguously What about Ratio ? Variable Energy Cyclotron Center, Kolkata Quark Matter-2008 To get rid of these uncertainties of model parameters

5. Photon productions at SPS, RHIC and LHC Thermal Photon and Dilepton productions Controlled by pQCD Subtracted from data Experiment measures Hence estimation of thermal contribution is vital Again, Big Challenge Variable Energy Cyclotron Center, Kolkata Quark Matter-2008 Dominated by hard photons Dominated by Photons from hadronic decays Thermal window

6. Thermal Photon productions Invariant yield of thermal photons Where Q,M,H are the QGP,MIX and Hadronic phase respectively. Static rate is convoluted over a dynamical evolution and with an assumption of 1 st order phase transition. = Static rate of photon production dypd Rd T 2 2  1 st order phase transition The sources of photons from Quark matter and Hadronic matter Phases Q U A MATTER R K Annihilation and Compton Bremsstrahlung and annihilation with scatterings. Variable Energy Cyclotron Center, Kolkata Kapusta et. al,1991 Bair et. al, 1992 Aurenche et. al,1998 Arnold et. al 2001 Quark Matter-2008

7. Thermal Photon productions Similarly, H A D R MATTER O N I C Non-strange sector Strange sector Variable Energy Cyclotron Center, Kolkata Kapusta et. al,1991 Sarkar et. al. 1992 Alam et. al,2003,2005 Turbide et. al 2004 Neglected since contribution is less Quark Matter-2008

8. Hydro and initial conditions The production rate of photons and dileptons are evoluted through ideal and isentropic expansion. Hydrodynamic equations are The Initial energy density and velocity profiles are given Variable Energy Cyclotron Center, Kolkata From Isentropic expansion Quark Matter-2008

9. Hadron spectra J Phys.G,34,871-882,2007 RHIC hadron spectra at c.m energy 200 GeV/A measured by PHENIX expt. T i =400 MeV, T f =120 MeV. Phys. ReV.C,67,054901 2003 SPS pion spectra at 158A GeV energy measured by NA49. T i =200 MeV, T f =120 MeV. Variable Energy Cyclotron Center, Kolkata Thermal Photon productions Quark Matter-2008

10. (J. Phys. G 2007) Photon : RHIC (Au+Au) With T i =400 and T f =120 MeV Au+Au collision at c.m energy=200 GeV/A Photon : SPS (Pb+Pb) With T i =200,T f =120 MeV Phys. ReV. C,2001 Pb+Pb Collision at 158A GeV Variable Energy Cyclotron Center, Kolkata Thermal Photon productions P T spectra of photons Quark Matter-2008

11. Thermal Dilepton productions Invariant yield of thermal dileptons Similar to photons dileptons also do not suffer the final state interactions and retains the maximum information of the initial state of the hot fire ball. Measured dileptons contain the contributions from all stages of the evolution and from all possible interactions. For thermal contribution 1. Drell-Yan processess. 2. Decays of the vector mesons. 3. Hadronic decays after freezeout. Transverse momentum distribution is given as Variable Energy Cyclotron Center, Kolkata Thoma&Traxler,199 9 Ruskanen & Altherr, 1992 Quark Matter-2008

12. Thermal Dilepton productions f V (V) : coupling of electromagnetic current to vector meson fields m V and  V are the mass and width of the vector V and w 0 are the continuum threshold above which the asymptotic freedom is restored. Variable Energy Cyclotron Center, Kolkata Quark Matter-2008 Dilepton production from Quark & Hadronic Matter The production of low mass dileptons in Quark Matter phase has been calculated from photon self energy, considered up to HADRONIC MATTER QUARK MATTER

13. NA60 data on low mass dilepton Invariant mass spectra of muon pairs in 158 A GeV In+In collisions at CERN SPS experiment is explained with this set of parameters. Variable Energy Cyclotron Center, Kolkata Thermal Dilepton productions P T spectra of Dileptons Quark Matter-2008

14. Also the same experimental data can be explained by another set of input parameters. Hence the model dependence of the input parameters needs to be removed Variable Energy Cyclotron Center, Kolkata Thermal Dilepton productions P T spectra of Dileptons Quark Matter-2008 GeV

15. GeV GeV QGP 0.195 0.0005 MIX 0.1920.01 HAD 0.1663 0.3656 From hydro calculation the information we get is tabularized QGP HADRONIC M (GeV) 0.5 0.75 1.2 Slope -1 (GeV) 0.2330.2660.326 0.195 With flow developed at earlier stage (I.e, QGP) These slope -1 shows a fall like the slope -1 extracted by NA60 from the data. Variable Energy Cyclotron Center, Kolkata Quark Matter-2008

16. Photon and dilepton at SPS, RHIC and LHC energies Photon p T spectra Dilepton p T spectra Variable Energy Cyclotron Center, Kolkata Quark Matter-2008

17. Photon p T spectra Dilepton p T spectra Photon and dilepton at SPS, RHIC and LHC energies Variable Energy Cyclotron Center, Kolkata Quark Matter-2008

18. Ratio of thermal Photon to Dilepton Studied the variation ratio R em over p T for SPS, RHIC and LHC energies. The ratio R em reaches a plateau after p T ~1 GeV. R em is of the order of few hundred. Total Value increases if we move from low initial temp. to high initial temp. Variable Energy Cyclotron Center, Kolkata Quark Matter-2008

19. Ratio of thermal Photon to Dilepton Sensitivity of T C to the Ratio Sensitivity of In-medium effect Variable Energy Cyclotron Center, Kolkata Quark Matter-2008 RHIC energy density

20. Ratio of thermal Photon to Dilepton Sensitivity of EOS to the Ratio Sensitivity of flow to the Ratio Variable Energy Cyclotron Center, Kolkata Quark Matter-2008 RHIC energy density

21. Sensitivity of T i to the Ratio Ratio of thermal Photon to Dilepton Since it is sensitive to the initial temperature we plot here, the R em vs T i for p T =2 GeV. Variable Energy Cyclotron Center, Kolkata Ratio, R em vs T i Quark Matter-2008 RHIC energy density

22. Variable Energy Cyclotron Center, Kolkata T C =192 MeVT C =170 MeV Sensitivity of the input parameters to individual p T spectra and ratio, R em Photon less by 8.5 % dilepton less by 13 % Ratio, more by 5.0 % BAG-HRG EOSLattice EOS Photon increases by 81 times Dilepton increases by 96 times Ratio, more by 16 % only. Individual spectra by ~4-5 % but Ratio by ~1% Quark Matter-2008 Sensitivity of T C Sensitivity of EOS Sensitivity of medium effects Mass modification and width modification

23. Photons : 1. WA98 Pb+Pb data. 2. RHIC Au+Au data. Dileptons : SPS In-In data. Explained Study the ratio of thermal photon to dilepton for different energy densities with different initial parameters and showed following the results for RHIC experiment (c.m=200 GeV/A) Insensitive to transition temp (Tc) Insensitive to medium effects. Insensitive to effect of flow. The Ratio is constant after ~ p T =1 GeV. Insensitive to EOS. Variable Energy Cyclotron Center, Kolkata Quark Matter-2008 But……

24. ..It is sensitive to initial temperature Ti of the strongly interacting System produced in the Heavy-Ion experiment. The ratio for different Ti is found as follows; So we do hope for a experimental photon to dilepton ratio data in the coming experiments so that some hydro initial parameters can be constrained and the theory can be experimented. Measure of Initial temperature Sensitive to T i Variable Energy Cyclotron Center, Kolkata Summary and outlook Quark Matter-2008

25. Back up. Lagrangian for the photon emission rates in Hadronic sector. We have taken the following dipole form factor for the photon production from Hadronic channels at each vertex. The average of the 4-momentum transfer in a given t-channel exchange of meson X The QGP phase calculation is done Resuming ladder diagrams in the effective field theory for both photons and dileptons. Quark Matter-2008

26. Consistent with e + e - V(  ) data Dilepton from hadronic vectors Integration over mass range Dilepton from Quarkmatter Up to order Quark Matter-2008

29. From lowest order naïve calculation for QM phase, ratio at temperature T Largely independent of some model parameters. The contribution to R em in QM phase is from all temperatures (i.e, from T i -T c ). So ratio in QM depends the square of the effective temperature. M max and M min are the range of invariant mass of lepton pairs.

30. Quark Matter-2008 Variable Energy Cyclotron Center, Kolkata Ratio of thermal Photon to Dilepton How the ratio is sensitive to invariant mass range ?