Saturation of ET/Nch and Freeze-out

1
Saturation of ET/Nch and Freeze-out Criteria in
Heavy Ion Collisions
Raghunath Sahoo 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 vsNN 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 vsNN
ltdET /d?gt/ltdNch /d?gt ? ET/Nch
II
I
Region I lowest energy to SPS energy. Steep
increase in the ratio with vsNN. Increase in vsNN
results in increase in ltmTgt. Region II SPS
energy to higher energies. The ratio is very
weakly dependent on vsNN. Increase in vsNN
results in increase in particle production,
instead of increasing ltmTgt. Might be, the system
is equilibrated and strongly interacting in this
region.
ET/Nch for top 5 central events with vsNN.
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 ltpTgt all show similar centrality
behavior.
Growth in ET is due to particle production.
Lets 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 AA 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
The Statistical-Thermal Model

• Thermal model
• particles and resonances up to m lt 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)
• ltETgt ?/4 ltEgt - mN ltNB - NBbargt
• 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 ltmgt
Baryon dominance at low energy gt ltmgt nm 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 ltmgt with vsNN.
10
The Excitation Functions
Ndecays /N 1 at very low vsNN , as very few
resonances are produced. It becomes independent
of vsNN 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 vsNN.
At low vsNN, baryon dominance at
mid-rapidity ? Nch /Ndecays Np /(NpNn)
0.45 for Au Au.
The vsNN independence of the ratios is a direct
consequence of saturation of Tch at high
energies and ?B becoming very small at high vsNN.
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 ltETgt 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 vsNN using statistical HG
  model .
• A constant ET/Nch (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 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