1. Examining the crossover between the hadronic and partonic phases in QCD and the structure of sQGP Xu 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

2. 2/21 Introduction

3. 3/21 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?

4. 4/21 Parton phase Quarks 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.

5. 5/21 How to solve this problem ? What is the appropriate mechanism for HG – QGP crossover without contradiction to color confinement?

6. Crossover between HG and QGP

7. 7/21 Example: Geometrical percolation model site 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

8. 8/21 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

9. 9/21 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

10. 10/21 Before crossover All hadrons are connected to an infinite cluster. gQGP End of crossover T c’ Start of crossover Begin to form infinite cluster TcTc Grape-shape QGP (gQGP) is a special form of sQGP. Grape-shape QGP (gQGP)

11. 11/21 When quarks i,j belong to the same cell When 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 < S 0, quark fully delocalized. (i) Dynamics for bond formation --- quark tunnelling Molecule-like Aggregation Model Fixed μ S0S0 (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.

12. 12/21 (ii) Use S 0 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 S 0 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

13. 13/21 Sharply tends to infinity sQGP turns to wQGP Crossover region Assuming, we get, determineμ c,μ c’ From S c S c’

14. 14/21 Structure of sQGP

15. 15/21 (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

16. 16/21 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

17. 17/21 In our case, chemical distance D: D r Define new pair distribution function: : correction factor to eliminate the boundary effect.

18. 18/21 Start of crossover End of crossover Middle stage T=0.475T c T=0.67T c T=0.80T c T=0.93T c T=T c T=1.21T c T=1.31T c T=1.39T c Before crossover The measurement of g(D) indicates liquid behavior of gQGP.

19. 19/21 Conclusion and outlook

20. 20/21 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 T c’ /T c and T c’’ /T c 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.

21. 21/21  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:

22. 22/21 Thanks ！

23. 23/21 Thanks ！

24. 24/21 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.

25. 25/21 range of effective interaction potential mean free path correlation distance viscosity