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Saturation of E T /N ch and Freeze-out Criteria in Heavy Ion Collisions

This paper discusses the saturation behavior of ET/Nch and the freeze-out criteria in heavy ion collisions. It examines the data from different experiments and presents a theoretical model to understand the processes involved. The study focuses on the chemical and kinetic freeze-out processes and their dependence on energy and centrality. The results provide insights into the space-time evolution and physics of high-energy collisions.

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Saturation of E T /N ch and Freeze-out Criteria in Heavy Ion Collisions

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  1. Saturation of ET/Nch and Freeze-out Criteria in Heavy Ion Collisions RaghunathSahoo Institute of Physics, India SUBATECH, France Outline • Introduction Heavy Ion Collisions and Particle freeze-out • Motivation What do data say on ET/Nch? • Statistical Thermal Model & ET/Nch Studies with √sNN and centrality. • Summary

  2. Space-time evolution in HI collisions soft physics regime hard ( high - pT) probes 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. 2/14

  3. 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. 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. A series of freeze-outs corresponding to specific reaction channels. • We focus on : • Chemical freeze-out (at Tch Tc): Inelastic flavor changing collisions processes cease • Kinetic freeze-out (at Tfo Tch): End of elastic scatterings ; kinematical distributions • stop changing

  4. ET / Nch production with √sNN <dET /d>/<dNch /d>  ET/Nch II I Region I : lowest energy to SPS energy. Steep increase in the ratio with √sNN. Increase in √sNN results in increase in <mT>. Region II : SPS energy to higher energies. The ratio is very weakly dependent on √sNN. Increase in √sNN results in increase in particle production, instead of increasing <mT>. Might be, the system is equilibrated and strongly interacting in this region. ET/Nch for top 5% central events with √sNN. Extrapolation of the ratio to LHC  ET /Nch= 0.92 ± 0.06 GeV. PHENIX : PRC 71 (2005) 034908 4/14

  5. ET/Nch Vs Npart Hydrodynamic flow effect is reflected in the peripheral collisions. If the expansion is isentropic, dNch /d will remain constant, whereas dET /d will decrease due to the performance of longitudinal work due to generated pressure . ET, Nch and <pT> all show similar centrality behavior. Growth in ET is due to particle production. Let’s understand the data………….. STAR: PRC 70 (2004) 054907 5/14

  6. ET/Nch & Freeze-out STAR Preliminary Thermal model calculations (PRL 81, 5284, 1998) (Cleymans & Redlich) at chemical freeze-out.  Energy pumped into the system goes for particle production, instead of increasing energy per particle. 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. ET/Nch ~ 800 MeV from AGS to RHIC: independent of centrality of the collision and the center of mass energy. Is it related to freeze-out? 6/14

  7. What is expected ? Tch is independent of centrality and shows saturation at higher energies. Tch ~ Tc  Chemical freeze-out coincides with hadronization. Tch is a lower limit estimate for a temperature of pre-hadronic state. J. Cleymans et al. Phys. Rev. C 73 (2006) 34905 U. Heinz et al. nucl-th/0709.3366 STAR: PRL 92 (2004) 112301 Tkin is centrality dependent 7/14

  8. E=  √(p2 + m2) – m for nucleons √(p2 + m2) + m for anti-nucleons √(p2 + m2) for all others 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. J. Cleymans et al. Phys. Rev. C 73 (2006) 34905 Data: • The ET(from expt.) is related to the primordial energy E (from thermal model): • <ET> = /4 {<E> - mN <NB - NBbar>} • Final state Nch (from expt.) is also related to the primordial number of hadrons N (from thermal model). • Freeze-out Criteria: • E/N = 1.08 GeV • s/T3 = 7 • nB + nBbar = 0.12 fm-3 All FO criteria tell almost the same story !!!

  9. The Excitation Function of <m> Baryon dominance at low energy => <m> ~ nmand 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 <m> with √sNN.

  10. The Excitation Functions Ndecays /N ~1 at very low √sNN , as very few resonances are produced. It becomes independent of √sNN around SPS and higher energies with a value ~ 1.7. Nch/Ndecays starts around a value of 0.4 and shows energy independence at SPS and higher √sNN. At low √sNN,baryon dominance at mid-rapidity  Nch /Ndecays ~ Np /(Np+Nn) = 0.45 for Au + Au. The √sNN independence of the ratios is a direct consequence of saturation of Tch at high energies and B becoming very small at high √sNN.

  11. Lines of constant ET/Nch At low energy ET/Nch is almost independent of B : A consequence of taking out mN in the definition of ET, which supposed to play a role at low energy. At chemical freeze-out, T and B could be estimated from the experimentally measured ET/Nch.

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

  13. Summary • ET/Nch has been studied with centrality of the collision and with √sNN using statistical HG model . • A constant ET/Nch (~0.8 GeV) has been observed from AGS to SPS to RHIC, which is related to thefreeze-out of the fireball. • The statistical thermal model explains the centrality and CoM energy behavior of ET/Nch production quite satisfactory. • Saturations in various observables have been observed around SPS and higher energies. 13/14

  14. Acknowledgements 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. Thank you 14/14

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