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Jajati Nayak

ATHIC-2010(18 oct-20 oct) , WUHAN, CHINA. Measuring radial flow in partonic and hadronic phases. Outline of the talk………. Heavy ion collisions and electromagnetic probes. Ratio of thermal photons to dileptons. Flow from the ratio of photons to dileptons.

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Jajati Nayak

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  1. ATHIC-2010(18 oct-20 oct) , WUHAN, CHINA Measuring radial flow in partonic and hadronic phases Outline of the talk……… • Heavy ion collisions and electromagnetic probes • Ratio of thermal photons to dileptons • Flow from the ratio of photons to dileptons • Summary and out look Jajati Nayak Variable Energy Cyclotron Center, Kolkata Thursday, October 9, 2014

  2. Mixed phase Continuous/ crossover time Hadron gas 1st order QGP fluid collision axis 0 Variable Energy Cyclotron Center, Kolkata ATHIC-2010, WUHAN, CHINA Evolution of the system formed after collision Hadron gas time Initial singularity Glasma and unstable Longitudinal fields Growth of instabilities Quark Gluon Plasma QGP fluid Hadronisation Hadronic rescatterings collision axis Freeze out 0 0 fm 0.1 fm 1 fm 10 fm Introduction… Thursday, October 9, 2014

  3. 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. Probe the entire space time history The production rate is a function of local intensive quantities. EM radiations provide crucial information of the medium properties of hadrons. Variable Energy Cyclotron Center, Kolkata ATHIC-2010, WUHAN, CHINA Thermal Photon and dilepton productions Feinberg,1976 McLerran & Toimela, 1985 Weldon,1990 Gale & Kapusta 1991 Thursday, October 9, 2014

  4. B.E. distribution function =for a static system are 4-velocity and momentum =for an expanding system Imaginary part of self energy Variable Energy Cyclotron Center, Kolkata ATHIC-2010, WUHAN, CHINA Thermal Photon and dilepton productions The photon and dilepton emission rate per unit 4-momentum from a system is given by Photon Production rate M=0 For photon Thursday, October 9, 2014

  5. = Static rate of photon production 2 d R g The production of low mass dileptons in Quark Matter phase has been calculated from self energy, considered up to 2 d p dy T Sources: QM photons Compton, Annihilation of quarks and gluons up to order~ HM Decay of mesons are the major sources of dilepton production in hadronic matter phase. Following parameterization has been used Reaction between mesons like etc.. Alam etal., 2000 Shuryak, 1993 Rapp etal., 2000 Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Thermal Photon productions For dilepton Invariant yield of photons and dileptons photon M: invariant mass Q,M,H : QGP,MIX and Hadronic phase Static rate is convoluted over a dynamical evolution and with an assumption of 1st order phase transition. Thoma&Traxler, 1999 Ruskanen & Altherr, 1992 dilepton Thursday, October 9, 2014

  6. Variable Energy Cyclotron Center, Kolkata Sources of Thermal Photon and dilepton • Continuum part of the vector meson spectral function constrained to experimental data has been included in the present work. • No Thermal effect of spectral function has been considered. • 4 pions annihilations are excluded to avoid double counting E. Shuryak , Rev Mod. Phys. 65 (1993) 1 J. Alam et al. Ann. Phys. 286(2000)159 • A set of all hadronic reactions with all possible isospin combinations are taken in Hadronic phase. Thursday, October 9, 2014

  7. 7 AHIC-2010, WUHAN, CHINA Hydrodynamics • Based on Energy -Momentum & baryon no. conservation laws: • μTμν= 0 ,  μ(nu μ)= μnμ= 0 • For ideal fluid: Tμν= (ε+P) uμ uν - P gμν • Equation of StateP=f(ε) Hadron gas Hadron Multiplicity, time Mixed phase • Assumes local thermal equilibrium . QGP fluid • Initial conditions (Ti,ti) required for calculation • Initial condition are given through energy density and velocity profile collision axis 0 • Freeze out criteria Thursday, October 9, 2014

  8. Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Thermal Photon productions PT spectra of photons Photon : RHIC (Au+Au) Photon : SPS (Pb+Pb) (J. Phys. G,34,871, 2007) Phys. ReV. C,63,021901,2001, Alam etal. With Ti=400 and Tf=120 MeV With Ti=200 ,Tf=120 MeV Pb+Pb Collision at 158A GeV Au+Au collision at c.m energy=200 GeV/A Thursday, October 9, 2014

  9. 0 RHIC Photons & Dileptons: • PHENIX ( Au + Au ) √s= 200 GeV T. Hirano, PRC 66(2002)054905 Chemical potential is included. Min Bias 0 Mohanty, Nayak &Alam. PRC 82 (2010) 034901 Thermal+Ncollpp data A. Adare et al.(PHENIX collaboration) PRL 104, 132301, PRC 81 (2010) 034911 9 Thursday, October 9, 2014

  10. 10 SPS Photons & Dilepton: • NA60dilepton( In +In) : SPS √s= 17.3 GeV • WA98 photon (Pb+Pb) : SPS √s= 17.3 GeV • Chemical potential is included. 0 Mohanty, Nayak & Alam et al. PRC 82 (2010) 034901 Dilepton In-In 0 Thermal+Ncollpp data M. M Aggarwal et al.(WA98 Collaboration)PRL 85 (2000) 3595 R. Arnaldi et al. (NA60 Collaboration) PRL 100, (2008) 022302 Thursday, October 9, 2014

  11. Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA PT spectra of Dileptons Thermal Dilepton productions… NA60 data on 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. 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 Thursday, October 9, 2014

  12. What about Ratio ? Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Focus of the present work : Thermal radiation Slope parameter versus M for In+In collision at SPS energy. For SPS energy Teff increases with M up to M ~Mρ and then decreases. ETot= ETh+ Eflow Teff= Tav +mvr2 J. Alam, T. Hirano, J. Nayak, B. Sinha et al. , e-Print :arXiv :0902.0446 ; R. Arnaldi et al. (NA60 Collaboration) PRL 100, (2008) 022302 ; Ghosh et al. e-Print :arXiv :0902.0446 Calculation of these thermal spectra involves certain uncertainties • EOS • Initial temperature (Ti) • Nature of phase transition • Transition temperature (TC) • Freeze-out temperature (TF) To get rid of these uncertainties of model parameters Thursday, October 9, 2014

  13. Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Ratio of thermal photon to dilepton.. Phys. ReV. C,2008, J. K. Nayak etal. Ratio at SPS, RHIC and LHC energies The ratio Rem vs pT for various invariant mass. The ratio Rem reaches a plateau beyond pT~2 GeV. Thursday, October 9, 2014

  14. 14 AHIC-2010, WUHAN, CHINA Ratio of thermal photon to dilepton …… Thursday, October 9, 2014 PHOTON: For specific M and pT RATIO: Effective temp of Massless particle Effective temp of Massive particle DILEPTON:

  15. 15 Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Vr with Average Temperature @ RHIC and LHC energies . Thursday, October 9, 2014 For specific M and pT Jajati K. Nayak & Jan-e Alam PRC 80 (2009) 064906 Thursday, October 9, 2014

  16. 16 Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Is Teff vs M a good measure of flow @ LHC energy ? Jajati K. Nayak & jan-e Alam PRC 80 (2009) 064906 C3-1=Teff No fall of Teff beyond rho-mass at LHC energy Thursday, October 9, 2014

  17. Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA From the calculation of another group….. Jian Deng, Qun Wang, Nu Xu, Pengfei Zhuang arxiv:1009.3091(2010)

  18. 18 Variable Energy Cyclotron Center, Kolkata Variation of Radial velocity with Invariant Mass @ RHIC and LHC energy. Eliminating Tav from both the spectra we get a relation between vr and M Nayak & Alam PRC 80 (2009) 064906 Mohanty, Nayak and Alam, PRC 82 (2010)034901 vr increases with M up to M=Mρ Better measure of radial flow Thursday, October 9, 2014

  19. Variable Energy Cyclotron Center, Kolkata AHIC-2010(oct, 18-20), WUHAN, CHINA Ratio with pT for diff. ti RHIC energy Summary and outlook………. • Information of radial flow can be drawn from the slope at low pT which tells about the transition of the mediumformed in the collision • The simultaneous measurement of photonand dilepton spectra can quantify the evolution of flow Thank you....

  20. AHIC-2010, WUHAN, CHINA BACK UP SLIDES

  21. Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA

  22. Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Ratio of thermal photon to dilepton.. Sensitivity of TC and EOS to ratio Rem For RHIC energy at c.m energy=200 GeV Shows the dominance of HM over QM even in a high mass window

  23. Origin of plateau and its disappearance • Case 1. pT>M , at high pT, mT~pT, so the exponential momentum • dependence become same for photon and dilepton, hence plateau is achieved • Case 2. M is Large, If the large M pairs originate from early time (when • the flow is small then the ratio which includes space-time dynamics will • be close to static case hence will show plateau. • Case 3. M ~pT, here the effect of flow on dileptons is larger than photons • hence Plateau disappear. Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Ratio of thermal photon to dilepton.. What is the behavior of ratio with pT ? The pTdependence of ratio for a dynamically expanding system is Predominantly determined by the thermal factor fBE. Staticrate of dilepton

  24. Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Radial Flow Ratio vs pT is plotted for (1+1) dimensional Bjorken expansion and (2+1) dimensional expansion for different invariant mass window. The difference in slope of the pT spectra is because of the radial flow. RHIC energy, TC=192 MeV, BAG-HRG EOS

  25. For (1+1) dimensional Bjorken type of expansion. where Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Radial Flow From the previous explanation we know that plateau disappearsbecause of the effect of radial flow. Here try to extract the effect of radial flow from the ratio. We know, For (2+1) dimensional expansion. , which contains the effect of radial flow Effective temperature also contains the effect of flow.

  26. Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Ratio of thermal photon to dilepton.. Slope versus invariant mass at pT=0.5 GeV

  27. Variable Energy Cyclotron Center, Kolkata AHIC-2010, WUHAN, CHINA Flow from thermal photon to dilepton ratio

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