Examining the crossover between

the hadronic and partonic phases

in QCD and the structure of sQGPXu Mingmei(许明梅 ), Yu Meiling(喻梅凌 ), Liu Lianshou(刘

连寿 )

CCNU, Wuhan

Introduction Crossover between HG and QGP Structure of sQGP Conclusion and outlook

The workshop for QCD phase transition and HIC USTC, Hefei 2008-07-12

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Introduction

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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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Parton phaseQuarks combine (hadronize) to hadrons

Perturbative vacuum

Hadron phase Hadrons decompose to quarks,

A possible mechanism:

Physical vacuum

Crossover between HG and QGP

Contradicts QCD principle of confinement.

In the intermediate stage there are: quarks moving in physical vacuum or hadrons moving in perturbative vacuum

It is due to the complicated property of QCD vacuum.

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How to solve this problem ?

What is the appropriate mechanism for HG – QGP crossover without contradiction to color confinement?

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Crossover between HG and QGP

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Example: Geometrical percolation modelsite

A bond could be formed between 2 adjacent hadrons 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 hadrons connected by bonds form clusters

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

No contradiction with QCD

Dynamical Model

What is the dynamics for the bond?

How to define the probability for bond formation?

We borrow the concept of quark delocalization from

Quark Delocalization and Color Screening Model

in low energy nuclear physics.

bond

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Bond is formed by quark delocalization

When the distance of two hadrons is large, quarks are confined in each hadron with 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. Quarks in left side have now a probability ε to move in right side.

When ε =1, bond is formed, two hadrons combine to a cluster.

Bond = quark tunneling through barrier

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Our basic assumption: molecule-like aggregation

Usual scheme of hadron aggregation can serve as the picture for 1st order phase transition.

Form ideal gas,• deviates from the picture of sQGP, obtained from experiment and LQCD;• contradicts with color confinement.

Use it for crossover

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

molecule-like aggregation

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Before crossover

All hadrons are connected to an infinite cluster.

gQGP

End of crossover

Tc’

Start of crossover

Begin to form infinite cluster

Tc

Grape-shape QGP (gQGP) is a special form of sQGP.

Grape-shape QGP (gQGP)

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When quarks i,j belong to the same cellWhen quarks i,j belong to two nearby cells

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.

When distance S < S0 , quark fully delocalized.

(i) Dynamics for bond formation --- quark tunnelling

Molecule-like Aggregation Model

Fixed μ

S0

(a) Adiabatic approximation: S is the distance between two hadrons;

(b) μ is a model parameter;

(c) Variational calculation: ε is the variation parameter, characterizing quark delocalization.

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(ii) Use S0 to do bond-percolation

Define: ， the probability for the appearance of event with infinite cluster;

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.

Ns , the number of cells outside of an infinite cluster in an event.

Crossover starts

Crossover ends

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Sharply tends to infinity

sQGP turns to wQGP

Crossover region

Assuming , we get

,

determineμc ,μc’

From Sc Sc’

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Structure of sQGP

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(a)Before crossover; (b) Start of crossover; (c) End of crossover;

gQGP appear. The system turns to gQGP.

The sQGP formed after crossover is of a grape shape — gQGP.

Evolution of structure

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the probability of finding two atoms at a distance r from each other. When there is no correlation, g(r)=1.

The liquid property of gQGP

— Studied by pair distribution function

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In our case, chemical distance D:

Dr

Define new pair distribution function:

: correction factor to eliminate the boundary effect.

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Start of crossover End of crossoverMiddle stage

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

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

Before crossover

The measurement of g(D) indicates liquid behavior of gQGP.

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Conclusion and outlook

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Conclusion:

In order to be consistent with color confinement,

molecule-like hadron aggregation is required in the

crossover.

Based on this assumption, we construct a toy model,

which can describe the crossover from hadronic to

partonic phase and the transition from sQGP to wQGP.

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.

Paper finished:

Xu Mingmei, Yu Meiling and Liu Lianshou, Phys. Rev. Lett. 100, 092301 (2008).

Yu Meiling, Xu Mingmei and Liu Lianshou, submitted.

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We discussed the crossover from low T to high T.

It is worthy to give a unified dynamic model, which includes both 1st order phase transition and the crossover band, and finally characterize the critical point.

T increase

The reverse process from high T to low T, need FTFT.

wQGP

HG

Cluster formation

start of crossover

end of crossover

the process of crossover

sQGP

T decrease

the process of crossover

T

μ

sQGP

wQGP

Outlook:

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Thanks！

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Thanks！

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The toy model needs further improving. But our basic conclusion

is model independent.

Crossover consistent with color confinement requires molecule like hadron aggregation;

Molecule-like aggregation results in grape-shape quark matter;

Grape-shape quark matter has liquid property.

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range of effective interaction potential

mean free path

correlation distance

viscosity