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Xu Mingmei( 许明梅 ), Yu Meiling( 喻梅凌 ), Liu Lianshou( 刘连寿 ) CCNU, Wuhan

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.

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Xu Mingmei( 许明梅 ), Yu Meiling( 喻梅凌 ), Liu Lianshou( 刘连寿 ) CCNU, Wuhan

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  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. Introduction

  3. 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. A possible mechanism: Hadron phase Hadrons decompose to quarks, Parton phase Quarks combine (hadronize) to hadrons Physical vacuum Perturbative vacuum 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.

  5. 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. A bond could be formed between 2 adjacent hadrons with probability p The hadrons connected by bonds form clusters 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. Example: Geometrical percolation model site bond Dynamical Model 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

  8. 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 nowa probability εto move in right side. • When ε=1, bond is formed, two hadrons combine to a cluster. Bond is formed by quark delocalization Bond = quark tunneling through barrier

  9. Usual scheme of hadron aggregation can serve as the picture for 1st order phase transition. Use it for crossover • Form ideal gas, • deviates from the picture of sQGP, • obtained from experiment and LQCD; • contradicts with color confinement. 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.

  10. Tc Tc’ Before crossover Start of crossover End of crossover Begin to form infinite cluster All hadrons are connected to an infinite cluster. gQGP Grape-shape QGP (gQGP) Grape-shape QGP (gQGP) is a special form of sQGP.

  11. Fixed μ When quarks i,j belong to the same cell When quarks i,j belong to two nearby cells S0 Molecule-like Aggregation Model (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: ε is the variation parameter, characterizing quark delocalization. When distance S < S0 , quark fully delocalized.

  12. (ii) Use S0 to do bond-percolation Generate an event sample (ensemble) with many events (or configurations). In each event, for every cell, randomly find three cells within S0around 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

  13. Sharply tends to infinity sQGP turns to wQGP From Sc Sc’ Crossover region determineμc ,μc’ Assuming , we get ,

  14. Structure of sQGP

  15. Evolution of structure (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.

  16. The liquid property of gQGP — Studied by pair distribution function the probability of finding two atoms at a distance r from each other. When there is no correlation, g(r)=1.

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

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

  19. Conclusion and outlook

  20. 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.

  21. wQGP wQGP sQGP T end of crossover sQGP the process of crossover the process of crossover start of crossover T decrease Cluster formation μ HG Outlook: • We discussed the crossover from low T to high T. The reverse process from high T to low T, need FTFT. • 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

  22. Thanks！

  23. Thanks！

  24. 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. correlation distance range of effective interaction potential mean free path viscosity

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