in collaboration with C. Nonaka, B. M

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New Ways to Look for the Critical Point and
Phase Transition
Masayuki Asakawa
Department of Physics, Osaka University
in collaboration with C. Nonaka, B. Müller, and
S.A. Bass
S. Ejiri and M. Kitazawa
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QCD Phase Diagram
T
CEP(critical end point)
160-190 MeV
crossover
1st order
order ?

• chiral symmetry breaking
• confinement

mB
5-10r0
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Punchlines Quantities to Look at
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CEP 2nd order phase transition, but...
If expansion is adiabatic AND no final
state int.
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Critical Slowing Down and Final State Int.
Furthermore, critical slowing down limits the
size of fluctuation, correlation length !
Time Evolution along given isentropic
trajectories (nB/s fixed)
Model H (Hohenberg and Halperin RMP49(77)435)
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Locally Conserved Charges

• Net Electric Charge

1. Net Baryon Number
2. Net Electric Charge
3. Net Strangeness
4. Energy ...

Hadron Gas Phase
QGP Phase
Heinz, Müller, and M.A., PRL (2000) Also, Jeon
and Koch, PRL (2000)
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Charge Fluctuation at RHIC

• D-measure

Predictions
QGP phase
Hadron phase
( hadron resonance gas)
Experimental Value
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Odd Power Fluctuation Moments
We are in need of observables that are not
subject to final state interactions

• Fluctuation of Conserved Charges not subject to
  final state interactions

One of exceptions Stephanov (2008) in
conjunction with CEP
Absolute values carry information of states
Asakawa, Heinz, Müller, Jeon, Koch
On the other hand,

• Odd power fluctuations

NOT positive definite

• Sign also carry information of states

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Physical Meaning of 3rd Fluc. Moment
cB
Baryon number susceptibility
in general, has a peak along phase transition
changes the sign at QCD phase boundary !

• In the Language of fluctuation moments

more information than usual fluctuation
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(Hopefully) More Easily Measured Moments

• Third Moment of Electric Charge Fluctuation

singular _at_CEP
iso-vector susceptibility nonsingular when
Isospin-symm.
Hatta and Stephanov 2002
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Mixed Moments

• Energy is also a conserved charge
• and mesurable !

E total energy in a subvolume
Regions with Negative fluctuation moments

• Result with the standard
• NJL parameters (Nf2)

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More and More 3rd Moments

• diverges at critical end point
• peaks on phase transition line

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Comparison of Various Moments
2-flavor NJL with standard parameters
Far Side
G5.5GeV-2 mq5.5MeV L631MeV
Near Side

• Different moments have different regions with
  negative moments

By comparing the signs of various moments,
possible to pin down the origin of moments

• Negative m3(EEE) region extends to T-axis (in
  this particular model)
• Sign of m3(EEE) may be used to estimate heat
  conductivity

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Principles to Look for Other Observables
We are in need of observables that are not
subject to final state interactions
Chemical Freezeout

• usually assumed
• momentum independent

• but this is not right

chemical freezeout time pT (or bT) dependent

• Larger pT (or bT),
• earlier ch. freezeout

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Emission Time Distribution
Emission Time

• Larger bT, earlier emission

• No CEP effect (UrQMD)

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Principle II

• Further Assumptions

• Size of Critical Region

• No general universality
• Lattice calculation not yet V?? limit
• Effective Model Results ?

need to be treated as an input, at the moment
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Singular Part Non-singular Part

• Matching between Hadronic and QGP EOS

• Entropy Density consists of Singular and
  Non-Singular Parts

• Only Singular Part shows universal behavior

• Requirement
• reproduce both the singular behavior and
  known asymptotic limits

• Matched Entropy Density

• Dimensionless Quantity Sc

D related to extent of critical region
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Isentropic Trajectories

• In each volume element, Entropy (S) and Baryon
  Number (NB) are conserved,
• as long as entropy production can be ignored (
  when viscosities are small)

Isentropic Trajectories (nB/s const.)
Near CEP s and nB change rapidly
isentropic trajectories show non-trivial behavior
Bag Model EOS case
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Consequence
For a given chemical freezeout point, prepare
three isentropic trajectories w/ and w/o CEP
Along isentropic trajectory
Principle I
As a function of pT(bT)
Bag Model EOS (w/o CEP, usual hydro input)
near CEP steeper
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Evolution along Isentropic Trajectory
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Summary

• Final State Interaction and Critical Slowing Down

• Conserved Charges and Higher Moments

• i) Third Fluctuation Moments of Conserved
  Charges
• take negative values in regions on the
  FAR SIDE of Phase Transition
• (more information!)
• ii) Different Moments have different regions
  with negative moments
• By comparing different moments, possible
  to pin down the origin
• of hot matter, get an idea about heat
  conductivity...etc.

• i) Chemical Freezeout is pT(bT) dependent
• ii) Isentropic Trajectory behaves
  non-trivially near CEP (focusing)

Information on the QCD critical point such as
location, size of critical region, existence...