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A new approach for locating the
Dynamics of QCD phase diagram
critical point in RHIC low energy
and the locating of critical point
scan experiments
in RHIC low energy scan
• Introduction
Xu Mingmei, Yu Meiling, Liu Lianshou
• New approach for locating critical point
Presented by Liu Lianshou
• Application to RHIC energy-scan
SQM08, October 2008, Beijing
Introduction
The difficulty in understanding the
mechanism of crossover
Part I
The Molecule-like Aggregation Model- MAM
Application to the study of liquid property
of sQGP
Part II
A new approach for locating the critical
point in RHIC low energy scan experiment
Introduction
The difficulty in understanding the
mechanism of crossover
Commonly accepted phase diagram
• 1st order phase transition line ends at the
critical point, above it is analytic crossover.
• How is the mechanism of crossover? How is
it different from 1st order phase transition?
1st order phase transition vs. crossover
order
phase
transition
Example-1 1st 1st
order
phase
transition
in QCD
Boundary
Some nucleons
combine to a big
bag - QGP droplet
Co-existenceofofQGP
two phases
Nucleon gas
Co-existence
and HG
Analytical
crossover
Example-2 Analytical
crossover
in QED
+
+
+ +
++
+
+ +
+
+
+ +
+
E-M plasma
Ionization
atoms
Mixture
of
two
Mixture
ofofelectrons,
components
positive-ions
and
neutral
atomsand phase separation.
Without phase
boundary
Neutral atom gas
Example-3 Analytical crossover in QCD - 1
wQGP
BEC-BCS is a phase change
within deconfined phase.
2 quarks of opposite
spin form a di-quark,
They might also form
loose-knit Cooper pair,
leading to BoseEinstein condensation.
leading to BCS
superconducting.
Mixed state
In the intermediate stage of
crossover di-quarks and Cooper
pairs mixed in perturbative vacuum.
Example-4 Analytical
crossover
This case is
special. in QCD - 2
Crossover
between
HG andcases.
QGP
Let us compare
the different
A possible mechanism:
Hadrons in
Physical vacuum
Hadrons
decompose to
quarks,
Used in AMPTand qMD
Quarks combine
(hadronize) to
hadrons
Partons in
Perturbative
vacuum
In the intermediate stage there are:
quarks moving in physical vacuum or
hadrons moving in perturbative vacuum
Contradicts color confinement.
Atomic gas ~
EM plasma
BEC ~ BCS
HG ~ QGP
+
+
+
Mixture of
electrons,
positive ions and
neutral atoms
No vacuum
problem
Mixture of diquarks and
Cooper pairs
The mixture of
quarks (colored objects)
and hadrons (color-singlets)
Color objects
in perturbative
vacuum.
No problem
Contradicts
confinement,
Causing big
problem.
Part I
The Molecule-like Aggregation Model
.
Let us take still another example
.
Example 5: Geometrical bond
model
site percolation
Dynamical Model
A bond could be formed between
two adjacent hadrons
We borrow the concept of quark
from
Thedelocalization
hadrons connected
by Screening
bonds formModel
clusters
Quark Delocalization and Color
in low energy nuclear physics.
When an infinite cluster,
i.e. a cluster extending
from one boundary to
the other, is formed, we
say that the system
turns to a new phase.
In this way the crossover from one phase to the other is realized.
No contradiction with QCD
 When
the distance of two hadrons
is large, quarks are confined in each
hadron by a confinement potential.
 When two hadrons close enough,
the infinite potential in between drops
down, forming a potential barrier.
Quarks can tunnel the barrier and
move in a delocalized orbit.
Bond is formed by quark delocalization
Since color can flow through bonds,
hadrons in a cluster become colored objects.
Only the cluster as a whole is color-singlet
Inspired by the above observation we propose:
Our basic assumption: molecule-like aggregation
Usual scheme of hadron aggregation
can serve as the picture for 1st order
phase transition.
Use it for crossover
Form ideal gas,
• contradicts color confinement.
Form QGP with liquid property,
• no contradiction with color
confinement.
Using this assumption we propose a model for
the crossover between hadronic and partonic phases
Molecule-like Aggregation Model
Tc
Before crossover
Start of crossover
Tc’
End of crossover
Clusters of
Begin
to formof crossover,
All hadrons are connected
At
the
intermediate
stage
various sizes
infinite cluster
to an infinite cluster.
there is a mixture of gQGP (infinite cluster)
Grape-shape
QGP clusters).
(gQGP)
and hadronic states
(small
Grape-shape
(gQGP)
a special form of sQGP.
Both QGP
of them
areiscolor-singlets.
No contradiction with color-confinement.
A simple application of MAM
----- the liquid property of sQGP
The liquid property of gQGP
— Studied by pair distribution function
Pair distribution function：
the probability of finding two atoms at a distance r from each other.
When there is no correlation, g(r)=1.
In our case,
chemical distance D:
D
r
Define new pair distribution function:
: correction factor to eliminate
the boundary effect.
Before crossover
T=0.475Tc
Start of crossover
T=Tc
T=0.67Tc
T=0.80Tc
Middle stage
T=1.21Tc
T=0.93Tc
End of crossover
T=1.31Tc
T=1.39Tc
• 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 more and more and
extend farther and farther, indicating the reduction of viscosity .
Part II
A new approach for locating the
critical point in RHIC low energy
scan experiments
In order to experimentally test the predicted phase
diagram, RHIC has started Low-Energy Scan program
LQCD predictions for critical points
Chemical freeze-out
Experimental freeze-out
What to measure?
The region covered by Low-E Scan
WhatThe
variable
iscovered
effective
for locating critical point?
total region
by RHIC
Many variables have been proposed. Most of them
are based on the assumption that these variables
have large fluctuations at the critical point.
These fluctuations are Event-by-Event, and so are
contaminated by the statistical ones coming from
the limited number of particles in a single event.
Various attempts have been made to eliminate the
statistical fluctuations, but none are decisive.
It is unclear whether such a kind of fluctuationsignal for critical point could survive after the
elimination of statistical fluctuations.
Since
the
systems
have
arrived
equilibrium,
there is no
This
Collide
is
a
2nd
A+A
order
at
various
phase
energies
transition
How whether
to avoid
troublesome
SF?
difference
theythe
are different
systems produced
Duringcollisions
the 2ndor
order
phase
transition,
the
in different
they
are
the
evolution
of
a
single
Let us examine the energy scan process.
system
willtohave
noticeable
change
system
A instructure
T,μplane due
the exchange
of heat
and
particle withwhile
an external
heat-critical
and particlebath.
passing
point.
second order
phase transition
second order
phase transition
Let us find a variable to chracterize
first order
first order
phase transition change while
the structure
phasepassing
transition
critical point.
When system goes along ph-trans-line, passing critical
The
change
inapassing
CP
point
the structure
pT distribution
will present
noticeable change
Crossover
Molecule-like aggregation
Basic elements are clusters.
First order phase transition
Gas-like aggregation
Basic elements are single
particles --- partons at ABC,
This effect should be observable
and could
serve as
and hadrons
at A’B’C’abc.
a signal for locating the critical point
Thermal motion +
Zero-point vibration
Besides thermal + radial
flow pT, the hadrons get
extra pT from zero-point
vibration
Thermal motion
While freezeout the hadrons
get thermal + radial flow pT
In order to get an idea about how large is the effect of
we use the experimentally fitted parameters β and Tfz of
Au+Au collisions at sNN  4.88 GeV and 62.3 GeV to
make an interpolation. Assuming that the critical point is
located in this energy region, e.g. at sNN  20 GeV,
T fz
A jump at the critical point can clearly be seen.
For ω= 0.15 and 0.40 GeV the relative rise of the
first, second, third order moments are
5.8, 8.7, 9.9 %
and 14, 23,
27 %, respectively.
Such an effect should be observable in a high quality data.
The sensitivity of the amount of moment-rising on the
value of ω can be used to get the value of ω and
wherefrom obtain the bond strength, which is a piece of
useful information in the study of QCD phase structure.
Advantage of the new approach
• pT moments are averaged over whole sample
instead of single event. No statistical fluctuation.
• For the fluctuation signal, If it is not by occasion
that some energy used in the first round just
locates at the vicinity of the fluctuation peak, we
will see nothing in the first round and the
subsequent scan has to be carried out in finer
steps over the whole energy range.
• On the contrary, if the higher order scaled pT
moments have a sudden rise while passing
through the critical point, then already in the first
round of energy scan we will observe a rise of
these moments, and most probably the critical
point is located in the region of the moment-rising.
Summary
• Applying the usual gas-like aggregation to
crossover contradicts color confinement.
• Molecule-like aggregation is the appropriate
scheme for crossover.
• Using Molecule-like Aggregation Model - MAM
to study the pair distribution function the liquid
property of sQGP is obtained.
• Basing on MAM a new approach for locating
critical point is proposed which is free from the
contamination of statistical fluctuations and is
easier to be used.
Thank you for attention !
As the increasing of T, correlation distance
range of effective interaction potential
mean free path
viscosity
Thank you for attention !
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.