scaling and Heat Capacity in relativistic heavyion collisions

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?-scaling and Heat Capacity in relativistic
heavy-ion collisions
Yu-Gang Ma Shanghai Institute of Applied
Physics Chinese Academy of Sciences
Collaborated with G.L. Ma, X.Z. Cai,
H.Z. Huang, Z.J. He, J.L. Long, B.H. Sa, W.Q.
Shen
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Outline

• Motivation
• The application of ?-scaling to High Energy HIC
• The possibility to extract heat capacity _at_ RHIC
• Summary and outlook

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Motivation

• Searching for the scaling law is always an
  interesting topic in sciences, some underlying
  physics could be indicated. For instance, there
  are some scaling laws have been observed or
  suggested in RHIC energies. What more can we do?
• There are large hadronic multiplicity in single
  event at RHIC energies, so the temperature
  fluctuation in single event could be measurable
  and heat capacity could be extracted.

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Scaling law _at_ RHIC

• Quark number scaling of v2 and particle-type
  scaling of Rcp
• binary scaling of RAA and its violation
• centrality scaling
• ?-scaling

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Nuclear modification factor and quark number
scaling
baryon
meson
baryon
meson
Quark recombination model works Is there
partonic stage?
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Binary scaling of R-factor and its violation
If R 1 here, nothing new going on
Results show Observed suppression due to nature
of (new) produced matter ! not initial state
effects
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?-scaling of dN/d? at sqrt(s_NN)200GeV/c by
PHOBOS Collaboration
after scaling
Phenix Collaboration arXivnucl-ex/0305036
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(No Transcript)
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Centrality scaling of transverse momentum spectra
R. Hwa et al
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Ncoll 0.44N1.33
K(s,N) is normalized to 1GeV at ?s200GeV, N350.
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Part I ?-scaling in the Luciae Model
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What is ?-scaling?

• ?-scaling law is observed when two or more
  probability distributions Pm of the stochastic
  observable m collapse onto a single scaling curve
  F(z) if a new scaling observable is defined
• z (m-m)/ltmgt?
• This curve is
• ltmgt?Pm F(z) F(m-m)/ltmgt? where ? is a
  scaling parameter, m is the most probable value
  of the variable m, and ltmgt is the mean of m.

Botet et al. 2001 Phys. Rev. Lett. 86 3514
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The delta-scaling in Low-intermediate energy HIC
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(No Transcript)
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Indra data (lt100MeV/u) XeSn
Frankland, NPC18
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Frankland, NPC18
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J. Natowitz, K. Hagel, Y.G. Ma et al.,
Phys Rev Lett. 89, 212701 (2002)
?
The limiting temperature vs A
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Universal fluctuation ?-Scaling Analysis of Zmax
NIMROD DATA
NIMROD
NIMROD DATA, ?- SCALING OF ZMAX SHOWS CHANGE
FROM ?1/2-SCALING BELOW 5.6 MeV/u TO ?1-SCALING
ABOVE 5.6 MeV/u , ? which relates to phase
change
Ref Y.G.Ma, Talk at HIC03 Conf., Canada, June
2003 Y.G.Ma et al., Phys ReV. C, in
preparation
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KNO-scaling as A special case of delta-scaling
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?-Scaling and KNO scaling of multiplicity
distribution
?-Scaling ltmgt? Pm F(z) F(m-m)/ltmgt
? where z (m-m)/ ltmgt ? KNO scaling
?-Scaling with exponent 1
variable rescaling
normalization rescaling
increasing energy
before scaling
after scaling
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KNO scaling of nch in ee- annihilation
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Lepton-proton scattering
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delta-scaling in Relativistic energy HIC
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LUCIAE model

• LUCIAE3.0 is a Monte Carlo model which is an
  extension of the FRITIOF where the
  nucleus-nucleus collision is described as the sum
  of nucleon-nucleon collisions. LUCIAE3.0 made
  improvements in following three aspects
• (1) Re-scattering of final hadrons, spectator and
  participant nucleons are considered in LUCIAE3.0,
  because the role of re-scattering can not be
  neglected in high-energy domain.
• (2) LUCIAE3.0 implements the Firecracker Model
  that includes collective multi-gluon emission
  from the color fields of interacting strings in
  the early stage of relativistic ion collisions.
• (3) LUCIAE3.0 introduces suppression of strange
  quarks and effective string tensor to make some
  parameters related to product of strange quarks
  and string tensor in JETSET depend on incident
  energy, size of system , centrality etc. --Ref.
  SaTai, CPC 116, 355 (1999)

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How to find the BEST ?-scaling?

• If we assume Pm is Gaussian distribution,
• whereµltmgt m and sis the variance,depending
  on the bombarding energy. Assuming these Gaussian
  distribution obey the ?-scaling, we have
• We define L as
• Lltmgt?/RMS
• If L is independent on a certain variable, this
  delta is the best value for the scaling

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Table 1total multiplicity distribution of pp
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Table 2total multiplicity distribution of CC

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Table 3total multiplicity distribution of PbPb
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Which scaling is the BEST ?-scaling?

• We test to use the different values of ? to
  explore the energy dependence of L,it was found
  that the best ?value takes place when L is almost
  constant in the studied energy range.
• The figure shows an example of Energy dependence
  of L in pp collision.

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Results _at_ SPS energy
? 1.35
Gumbel-like function

• We found that scaling values of the best D for
  charged particle multiplicity distributions are
  1.35, 1.00 and 0.80 for pp, CC and PbPb
  collisions from Elab 20 to 200AGeV in SPS
  energy range, respectively.
• G. L. Ma, Y. G. Ma et al., Chin. Phys. Lett.
  20,1013 (2003)

? 1.00
? 0.80
Gaussian-like function
Tend to the Gaussian Delta-scaling in heavier
system. Better thermalization in PbPb?
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Number of strangeness
Scaling for the Number of strangeness
20-200 GeV/c PbPb
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Play a game for uncorrected multiplicity spectra
_at_ RHIC
preliminary

• Peripheral part 70-80,60-70,50-60,40-50
• Central part 30-40,20-30,10-20,0-10

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Delta-scaling _at_ 62GeV/c AuAu
preliminary
?(z)
Centrality Peripheral part ---------------?
Central part The Best ? 0.75
----------------------------? 0.55.
z
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Delta-scaling _at_ 130GeV/c AuAu
preliminary
Centrality Peripheral part ---------------?
Central part The Best ? 0.75
----------------------------? 0.55.
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Delta scaling _at_ 200GeV/c AuAu
preliminary
Centrality Peripheral part ---------------?
Central part The Best ? 0.75
----------------------------? 0.55.
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information entropy

• Information entropy is an observable that was
  proposed to describe fluctuation and disorder of
  system by Shannon. The multiplicity information
  entropy is defined
• H-?P(m)lnP(m)dm
  where?P(m)dm1 .
• Y. G. Ma, Phys. Rev. Lett. 83, 3617 (1999)
• We calculate respective information entropy in
  terms of these distributions of particle
  multiplicity in LUCIAE3.0 model.

G. L. Ma, Y. G. Ma et al., Chin. Phys. Lett.
20,1013 (2003)
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Summary and outlook I

• We have for the first time demonstrated that
  D-scaling and information entropy of particle
  multiplicity for different energies , systems,
  centralities in SPS and RHIC energy in model
  calculation.
• We hope that these two observables are useful to
  search for a possible phase change in
  relativistic nucleus-nucleus collisions
  associated with the onset of a QCD phase
  transition.
• So the further works have to be done, eg.,
• Investigate how the partonic effect on the
  D-scaling and information entropy in models,
  such as AMPT and Parton Cascade Model. The work
  along this line is in progress.
• We try to analyze some physics quantities in RHIC
  data. Such as BRAHMS data for pesudorapidity
  distribution, k/? ratio, ?/? - ratio etc. The
  key point is looking for some order parameters
  which are sensitive to phase change.

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Part II Heat capacity in Luciae Model
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Part II Heat capacity

• Heat Capacity ?? A Basic Thermodynamic Quantity
• Heat Capacity at Constant Volume
• 
  (1)
• Temperature distribution (Heat Capacity and
  Temperature Fluctuation)
• 
  (2)
• ( Laudau L.D. , Lifschitz I.M., Course of
  Theoretical Physics ,Statistical Physics (Third
  Edition). 338-343 )

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Introduction

• Temperature distribution can be described by
  (when the fluctuation of volume can be ignored),
• 
  (3)
• (Stodolsky L . Phys. Rev. Lett., 1995, 75
  1044
• Heiselberg .H. Phys. Rep., 2001, 351
  161 )
• Transverse mass distribution can be described by
  the effective temperature in the following form
• 
  (4)
• A ??Volume (or Multiplicity)
• T?? apparent temperature including collective
  transverse flow

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Temperature distribution

• If we suppose the temperature distribution
  satisfies Eq. (3), we can extract the heat
  capacity. However, this heat capacity is an
  extensive observable since the hadron
  multiplicity depends on the size of reaction
  system , centrality and incident energy , we
  define a normalized heat capacity Cv/N, i.e. the
  heat capacity per hadron multiplicity, where N is
  hadron multiplicity.

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Some results in SPS

• We used LUCIAE to simulate PbPb collisions at
  different incident energy in SPS energy, and
  extract the heat capacity per hadron
  multiplicity.
• Right figure gives the dependence of Cv/N of
  various particles on incident energy in central
  PbPb collision (b0fm).
• GL Ma, YG Ma et al., HIGH ENERG PHYS NUC 28 (4)
  Art. No. 398 APR 2004

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Some results in SPS

• We found that Cv/N of particle increase with mass
  of particle .
• Right figure shows the dependence of Cv/N of
  particle on mass of particle in central PbPb at
  160 AGeV collision (b0 fm).

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Some results in SPS

• We also investigate the dependence of Cv/N for
  on impact parameter (i.e.
  centrality) in PbPb at 160 AGeV collision, and
  this dependence is shown in right figure. We
  found that Cv/N decreases with the increasing of
  impact parameter .

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Some results in SPS

• We also found similar results in CC system , and
  found that heat capacities per hadron
  multiplicity in different reaction systems are
  approximately the same in the same incident
  energy and impact parameter .
• Right figure shows the dependence of Cv/N of
  PbPb and CC on incident energy in central
  collision.

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RHIC results

• We use method (2) to find that Cv/N increases
  with the number of participant nucleons and the
  mass of particle in AuAu 200GeV/c in LUCIAE3.0
  model.
• Right figure shows the dependence of Cv/N of
  pions, kaons and protons on Npart in AuAu 200GeV
  .

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Relationship to other fluctuation observable?
See Rolands talk NA49 k/pi ratio fluctuation
See Westfalls talk _at_ QM04
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Summary and outlook II

• We introduced an operational way to extract
  heat capacity for soft component particles by
  event-by-event fluctuation of apparent
  temperature in relativistic heavy-ion collision.
• We found that heat capacity per particle
  multiplicity decreases with the increasing of
  incident energy and impact parameter, and it is
  insensitive to the reaction system in our LUCIAE
  model. Does it mean that the thermalization has
  been reached better in central collisions.
• We hope that heat capacity can help us to search
  for a possible phase transition in relativistic
  heavy-ions collision. A tentative analysis will
  be done for STAR-data.
• To this end, the further work should be done, for
  instance,
• Investigate the partonic effect on the
  temperature fluctuation and Cv
• Understand the meachanism of Cv as a function of
  Bimp, Ebeam etc.
• Distinguish the dynamics fluctuation from the
  thermal fluctuation in our extraction in heat
  capacity?
• Investigate the Cv as a function of Pt.

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The end --- Thank you for attention!