1. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo Saturation of E T /N ch and Freeze-out Criteria in Heavy Ion Collisions Raghunath Sahoo Institute of Physics, India SUBATECH, France Introduction Heavy Ion Collisions and Particle freeze-out Motivation What do data say on E T /N ch ? Statistical Thermal Model & E T /N ch Studies with √s NN and centrality. Summary Outline

2. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 2/14 hard ( high - p T ) probes soft physics regime Space-time evolution in HI collisions Theoretical description of the whole process is difficult, as different degrees of freedom (dof) are important at various stages. Thermal model uses hadronic dof at freeze-out.

3. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 3/14 FREEZE-OUT Freeze-out process depends on :  flow velocity gradient  thermal velocity (1)  expansion rate (controlled by vel. gradient)  local scattering rate (2) 1 & 2 depend on particle species  Concept of “differential freeze-out”  Different particles decouple from the fireball at different times. A series of freeze-outs corresponding to specific reaction channels. We focus on : Chemical freeze-out (at T ch  T c ): Inelastic flavor changing collisions processes cease Kinetic freeze-out (at T fo  T ch ): End of elastic scatterings ; kinematical distributions stop changing Reactions with lower cross-sections switch-off at higher densities/temp., while those with larger cross-sections last longer, e.g. charmed/strange particles decouple earlier than other hadrons.

4. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 4/14 E T / N ch production with √s NN PHENIX : PRC 71 (2005) 034908 E T /N ch for top 5% central events with √s NN. Region I : lowest energy to SPS energy. Steep increase in the ratio with √s NN. Increase in √s NN results in increase in. Region II : SPS energy to higher energies. The ratio is very weakly dependent on √s NN. Increase in √s NN results in increase in particle production, instead of increasing. Might be, the system is equilibrated and strongly interacting in this region. Extrapolation of the ratio to LHC  E T /N ch = 0.92 ± 0.06 GeV. /  E T /N ch I II

5. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 5/14 E T /N ch Vs N part Hydrodynamic flow effect is reflected in the peripheral collisions. If the expansion is isentropic, dN ch /d  will remain constant, whereas dE T /d  will decrease due to the performance of longitudinal work due to generated pressure. E T, N ch and all show similar centrality behavior. Growth in E T is due to particle production. Let’s understand the data………….. STAR: PRC 70 (2004) 054907

6. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 6/14 E T /N ch & Freeze-out E T /N ch ~ 800 MeV from AGS to RHIC: independent of centrality of the collision and the center of mass energy. If the freeze-out is assumed to occur at all energies and impact parameters in A+A collisions, on a fixed decoupling isotherm, then the energy per particle will always be the same.  Energy pumped into the system goes for particle production, instead of increasing energy per particle. Thermal model calculations (PRL 81, 5284, 1998) (Cleymans & Redlich) at chemical freeze-out. STAR Preliminary Is it related to freeze-out?

7. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 7/14 What is expected ? T ch is independent of centrality and shows saturation at higher energies. T ch ~ T c  Chemical freeze-out coincides with hadronization. T kin is centrality dependent STAR: PRL 92 (2004) 112301 J. Cleymans et al. Phys. Rev. C 73 (2006) 34905 T ch is a lower limit estimate for a temperature of pre- hadronic state. U. Heinz et al. nucl-th/0709.3366

8. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 8/14 The Statistical-Thermal Model Thermal model: particles and resonances up to m < 2 GeV B, s, Q are conserved Chemical freeze-out with no dynamics  Observables are functions of T and  B.  The E T (from expt.) is related to the primordial energy E (from thermal model): =  /4 { - m N }  Final state N ch (from expt.) is also related to the primordial number of hadrons N (from thermal model). Freeze-out Criteria:  E/N = 1.08 GeV  s/T 3 = 7  n B + n Bbar = 0.12 fm -3 √(p 2 + m 2 ) – m for nucleons √(p 2 + m 2 ) + m for anti-nucleons √(p 2 + m 2 ) for all others E =  Data: All FO criteria tell almost the same story !!! J. Cleymans et al. Phys. Rev. C 73 (2006) 34905

9. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 9/14 The Excitation Function of Baryon dominance at low energy => ~ n m and at higher energies although the dominant particles are pions, at chemical freeze-out most of the pions are hidden in the mesonic and baryonic resonances. The average thermal mass corresponds to the  -meson mass. Different freeze-out criteria show similar behavior of with √s NN.

10. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 10/14 The Excitation Functions N decays /N ~1 at very low √s NN, as very few resonances are produced. It becomes independent of √s NN around SPS and higher energies with a value ~ 1.7. N ch /N decays starts around a value of 0.4 and shows energy independence at SPS and higher √s NN. At low √s NN, baryon dominance at mid-rapidity  N ch /N decays ~ N p /(N p +N n ) = 0.45 for Au + Au. The √s NN independence of the ratios is a direct consequence of saturation of T ch at high energies and  B becoming very small at high √s NN.

11. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 11/14 Lines of constant E T /N ch At low energy E T /N ch is almost independent of  B : A consequence of taking out m N in the definition of E T, which supposed to play a role at low energy. At chemical freeze-out, T and  B could be estimated from the experimentally measured E T /N ch.

12. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 12/14 E T /N ch and Freeze-out J. Cleymans, R. Sahoo, D.P. Mahapatra, D.K. Srivastava & S. Wheaton Phys. Letts. B 660 (2008) 172 E T /N ch behaves like T ch Saturations in all discussed observables have been observed around SPS and higher energies !!!!! For different initial conditions, collisions evolve to the same freeze-out condition. Thermal model: E T /N ch is a lower limit estimate for in the pre-hadronic state.

13. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 13/14 Summary E T /N ch has been studied with centrality of the collision and with √s NN using statistical HG model. A constant E T /N ch (~0.8 GeV) has been observed from AGS to SPS to RHIC, which is related to the freeze-out of the fireball. The statistical thermal model explains the centrality and CoM energy behavior of E T /N ch production quite satisfactory. Saturations in various observables have been observed around SPS and higher energies.

14. QM08, Jaipur, 9 th February, 2008 Raghunath Sahoo 14/14 In Collaboration with: J. Cleymans, S. Wheaton CERN-UCT Research centre, Cape Town, SA D. P. Mahapatra, IoP, Bhubaneswar, India D.K. Srivastava, VECC, Kolkata, India We acknowledge the financial support of the SA-India Science & Technology agreement. I thank the organizers for giving me the opportunity to talk on our recent work in this conf. Acknowledgements