Examining the crossover between hadronic and partonic phases and the liquid property of sQGP

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Examining the crossover between hadronic and
partonic phases and the liquid property of sQGP
Presented by Xu Mingmei
Institute of Particle Physics, Huazhong Normal
University, Wuhan, China

• Introduction
• Crossover between HG and QGP
• Liquid property of sQGP
• Conclusion and outlook

SEWM08 Amsterdam
August 26-29 2008
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Introduction
QCD has complicated phase structure. No
analytical calculation is possible,
due to color-confinement
or infra-red slavery.
Most reliable information comes from lattice QCD.
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Phase diagram from lattice QCD

• 1st order phase transition line ends at the
  critical point, above it is analytic crossover.
• L-QCD is a thermodynamic theory. It does not
  answer Really what happens?!

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1st order phase transition vs. crossover
Example-1 1st order phase transition in QCD
Some nucleons combine to a big bag - QGP droplet
Co-existence of QGP and HG
Example-2 Analytical crossover in QED
Mixture of electrons, positive-ions and neutral
atoms
Ionization of atoms
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Example-3 Analytical crossover in QCD
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2 quarks of opposite spin form a
di-quark, leading to Bose-Einstein condensation.
They might also form loose-knit Cooper
pair, leading to BCS superconducting.
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Mixed state
In the intermediate state of crossover di-quarks
and Cooper pairs mixed in perturbative vacuum.
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Example-4 Analytical crossover in QCD
This case is special.
Crossover between HG and QGP
It is due to the complicated property of QCD
vacuum.
In the intermediate stage there are
quarks
moving in physical vacuum or hadrons moving in
perturbative vacuum
Contradicts QCD principle of confinement.
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Comparison of different cases
Color objects in perturbative vacuum. No
problem
Contradicts confinement,
No vacuum problem
Causing big problem.
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Crossover between HG and QGP
How to solve this problem ?
What is the appropriate mechanism for HG QGP
crossover ?
In order to answer the question, Let us take
still another example.
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Example 5 Geometrical percolation
model
site
Dynamical Model
bond
We borrow the concept of quark delocalization
from Quark Delocalization and Color Screening
Model in low energy nuclear physics.

• What is the dynamics for the bond?
• How to define the probability for bond
  formation?

In this way the crossover from one phase to the
other is realized.
No contradiction with QCD
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Bond is formed by quark delocalization
Since color can transport through bonds, hadrons
in a cluster become colored objects. Only the
cluster as a whole is color-singlet.
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Inspired by the above argument we propose
molecule-like aggregation
Our basic assumption molecule-like aggregation

• Form QGP with liquid property,
• the QGP obtained is strongly
• coupled sQGP
• no contradiction with color
• confinement.

Using this assumption we construct a model
for the crossover between hadronic and partonic
phases.
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Molecule-like Aggregation Model
Tc
Tc
Before crossover
Start of crossover
End of crossover
Clusters of various sizes
All hadrons are connected to an infinite cluster.
Begin to form infinite cluster
This is the base of the MAM. It can be realized
in various ways. For simplicity, we take a toy
model.
Grape-shape QGP (gQGP)
Grape-shape QGP (gQGP) is a special form of sQGP.
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A Toy Model for the realization of MAM
(i) Dynamics for bond formation --- quark
tunnelling
Attention The 6 quark system is a dynamic
system, µ is a dynamic parameter determining the
potential shape. The value of µ depends on the
temperature T of the surrounding hadron gas.

• Adiabatic approximation S
  is the distance between two hadrons
• (b) µ is a model parameter
• (c) Variational calculation
  e is the variation parameter,
  characterizing quark delocalization.

S0 is the largest distance for bond formation.
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(ii) Based on S0 using bond-percolation to form
clusters
Generate an event sample (ensemble) with many
events (or configurations). In each event, for
every cell, randomly find three cells within S0
around it to form bonds. Bonds connect cells to
clusters.
Define ,the
probability for the appearance of event
with infinite cluster
Ns , the number of cells outside of an infinite
cluster in an event.
Crossover starts
Crossover ends
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Assuming , we get
,
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Liquid property of sQGP
We start from the structure of gQGP
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The liquid property of gQGP Studied by pair
distribution function
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In our case, chemical distance D
D
r
Define new pair distribution function
correction factor to eliminate the boundary
effect.
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Before crossover
T0.475Tc
T0.67Tc
T0.80Tc
T0.93Tc
Start of crossover
Middle stage
End of crossover
TTc
T1.21Tc
T1.31Tc
T1.39Tc

• The first high peak is due to intra-cell
  correlations among quarks

• Long before crossover there is no correlation
  peak beside the first high one

• Going nearer to crossover some shoulders appear,
  which develop to peaks, indicating short-range
  order at the start of crossover

• In the process of crossover, correlation peaks
  appear and go farther and farther, which
  indicates the reduction of viscosity in the
  process.

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Conclusion
Conclusion and outlook

• In order to be consistent with color confinement,
  molecule-like hadron aggregation is requied in
  the crossover.
• Basing on this assumption, we propose the MAM
  model for the crossover between hadronic and
  partonic phases and for the structure of QGP.
• Using a toy model to quantify the MAM model the
  two temperature ratios Tc/Tc and Tc/Tc are
  obtained.
• Model provides a live picture for the structure
  of sQGP (grape-shape QGP), and its evolution
  during crossover.
• Pair distribution function of sQGP (gQGP) is
  calculated, which indicates liquid behavior of
  gQGP.

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Outlook
Locate the critical point and study the critical
phenomena This is our next goal.
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Thank you for attention
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Thank you for attention
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correlation distance
As the increasing of T,
range of effective interaction potential
mean free path
viscosity