从强子物质到夸克物质的平滑过渡和 sqgp 的结构许明梅喻梅凌刘连寿...

从强子物质到夸克物质的平滑过渡

和 sQGP 的结构许明梅喻梅凌刘连寿

• Introduction• Crossover in QCD• Structure of sQGP• Summary and discussion

Phys.Rev.Lett.100,092301

Research in progress

衷心感谢王凡、平加伦教授的支持与帮助

1st order Phase

Transition

Crossover

Introduction

are still open Questions

• What happens in crossover ?

• What is different between crossover and phase transition?

The answer to these questions is essential for a thorough understanding of vacuum structure in QCD .

Crossover at high T has been firmly settled by lattic QCD

Crossover in QCD

Nucleon gas Co-existence of QGP droplet and nucleon gas

Physical picture for 1st order phase transitionSome nucleons combine to a bigger bag - QGP droplet

Perturbative vacuum

Boundary

Physical vacuum Physical vacuum

• Example from Electro-Magnetic plasma

Neutral atom

gas

However, this picture could not be extended to QCD, because of vacuum problem

Physical picture for crossover ?

A rule in QCD: Isolated colour objects in physical vacuum has infinite energy

Atoms ionized one by one

Physical vacuum

If this is hadron matter

hadrons

Cross over to E-M plasma

Physical vacuum

Hadrons decompsed to quarks one by one

+

The process goes on gradually,

The two phases are mixed instead of co-exist .

No boundary.

Most of the Models on the market

for “crossover in QCD”

have not taken this severe rule of QCD into account.

Let us take 2 models as example.

• Multi-phase transport model AMPT

Components of A MultiPhase Transport Model (AMPT v2.11)

Partons hadronize when interaction ceases.

Initial conditions: (x,p) distributions of minijet partons from hard process and strings from soft process ,strings are melted to be partons

Partonic transport:

only two-body elastic scatterings

two partons collide if

Hadronization:

Hadron transport:

/l

Z.W.Lin et al. PRC 72(2005)064901

Example 1

Partons hadronize one by one

Variation of the percentage of parton and hadron with time:

When t<5fm/c, partons dominate, system in deconfined phase

When t>30fm/c, hadrons dominate, system in confined phase

A few partons move in physical vacuum

Contradicts QCD

Quark Molecular Dynamics - qMD M.Hofmann et al., Phys.Lett.B478(2000)161

Model Hamiltonian

Hadronization through requirement: Total color interaction from a pair or 3 quarks with the remaining system vanishes:

A smooth crossover of thermodynamic quantities is successfully obtained.

The hadrons are formed one by one in the environment of quark-gluon.

Example 2

When most of the partons have been hadronized a few partons will remain moving in physical vacuum

—— the same problem as in AMPT model.

All this kind of models neglect

color confinement,

and the different vacua in QCD.

Unacceptable

Difficulty in describing crossover in QCD

QCD has different vacua

—— Perturbative vacuum & Physical vacuum.

The difficulty of crossover in QCD lies in:

How to crossover from one vacuum to the other ?

In this respect it is worthwhile noticing another kind of model,

which is a geometrical model instead of a dynamical one.

Geometrical percolation model

H. Satz, Nucl. Phys. A642 (1998) 130

A bond could be formed between 2 adjacent nucleons with probability p

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.

The nucleons connected by bonds form clusters

In this way the crossover from one phase to the other is realized.

No contradiction with QCD

Dynamical ModelG.Baym, Physica 96A (1979) 131

sitebond

Turn bond percolation to dynamical ?• What is the nature of bonds ?

• How to calculate the probability p ?

The idea comes from modern nuclear force theory

Quark Delocalization & Color Screening Model F. Wang et al., Phys.Rev.Lett. 69 (1992) 2901

2006 年度学术交流会

• A quadratic confinement potential inside nucleon

• Potential barrier between

2 adjacent nucleons

Quark can tunnel through the barrierS

11

Delocalization

10

Confinement

• When ε=1 a bond is formed, and the two nucleons are combined to a cluster

• Bond is the tunnel of potential barrier

Basic assumption

Before crossover

Crossover started when infinite cluster is formed

Tc

Begin of crossover

Crossover ended when all the cells are combined in a unique cluster

Tc’

End of crossover

Use dynamical model to realize the idea

Variation method

S0

S

ε

Delocalization occures only when S < S0

For fixed μ

Use S0 to develop percolationNEW

In N events, M events have infinite cluster(s), then

There are NS cells outside of the infinite cluster

Crossover starts

Crossover ends

Dynamical calculation

S0

S

ε For fixed μ

Maximum distance for bond formation

Sharply tends to infinity

Assuming , we get,

From Sc Sc’ determine μc ,μc’

sQGP turns to wQGP

Crossover region

Structure of sQGP

The evolution of matter structure

Start of crossover

End of crossover —— sQGP

Before crossover

We can study the structure of matter from the starting to the end of crossover

Characteristic quantity of liquid structure

Pair distribution function

The normalization is that g(r)=1 when there is no correlation.

Pair distribution function

Unpenetrablecore

H2O

There are picks

with diminishing

height up to 9 A,

showing short-

range correlation

in liquid.

Example – H2O

For percolation the correlation distance D is not the geometrical one but the distance along bonds, which is

referred to as chemical distance

Dr

The pair correlation is

normalized by total number N of cells in an event

In our case the boundary effect should be considered

D

For a fixed D the summation over r should be in the 2π ring, but our cells only lie in an arc of angle θ. So we give a weight w=2π/θ and define

The result is

Start of crossover

End of crossoverMiddle stage

It can be seen that in the process of crossover the correlation goes farther and farther.

T=Tc T=1.21Tc T=1.31Tc

T=1.39Tc

In order to compare with the pair distribution of liquid we define

Note that it is impossible to impose the requirement —— g(D)=1 when there is no correlation, because when correlation is absent there is no D.We use 2πρr dr as denominator is to compare with usual lioquid.

Before crossover

Start of crossover End of crossoverMiddle stage

• The first high peak is due to several quarks in each cell.

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

• Going nearer to crossover shoulder appears and develops to a peak.

• During the process of crossover more and more peaks appear and go farther and farther-

T=0.475Tc T=0.67Tc T=0.80Tc T=0.93Tc

T=Tc T=1.21Tc T=1.31Tc T=1.39Tc

Summary and discussion

• We found that, in order for the crossover between hadronic and partonic matter to be consistent with color confinement, hadrons have to be able to aggregate in molecuar form.

• Basing on this assumption we have constructed a simple model for the crossover to sQGP and the transition to wQGP.

• Using this model the ratios of the temperature of the end of crossover and transition to wQGP to that of the beginning of crossover are obtained.

• Our model provides a clear picture for the structure of sQGP and the evolution of the structure in the process of crossover.

Before crossover Begin of crossover End of crossover

• Using this model the pair-dis-function of sQGP and the evolution of this distribution in the whole process of crossover are obtained.

Qualitative picture

Quantitative picture

• Calculate the viscosity and thermodynamic quantities of sQGP using the proposed model.

• Construct a unified model for QCD phase diagram, including :

crossover - 1st order phase transition - critical point

What’s next ?

Crossover

1st order phase transition

with a clear picture for the internal structure of both the matter and the vacuum.

The key is in the QCD vacuum• What is the essence of the two topologically diff

erent forms of vacuum —— bag shape and grape shape?

• How to perform analytic calculation on these vacua?

There is still long way to go!

Bright future is in front of us!

努力在崎岖的道路上攀登

以求登上光辉的山峰

希望得到大家

的监督和帮助Thanks

Vacuum crossover

r

E


Neutral atom

gas





Physical vacuum


hadrons


Physical vacuum


+

The process goes on 1) gradually, 2) no boundary.



Neutral atom

gas





Physical vacuum


hadrons


Physical vacuum


+

The process goes on gradually,


No boundary.


Neutral atom

gas





Physical vacuum


hadrons


Physical vacuum


+

The process goes on 1) gradually, 2) no boundary.


Use S0 to develop percolationNEW

Use a maximum distance S0

to substitute probability p .

S0 has dimension and can be related

to T.

p has no dimention, unrelated to T

从强子物质到夸克物质 的平滑过渡 和 sqgp 的结构 许明梅 喻梅凌 刘连寿...

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从强子物质到夸克物质的平滑过渡和 sqgp 的结构许明梅喻梅凌刘连寿...