# Presentation: 014920

## Relation between color deconfinement and chiral restoration

- Kenji Fukushima   (MIT / U.Tokyo)

- References:   K. Fukushima          Phys. Lett. B553,  38  (2003)
-                          K. Fukushima          Phys. Rev. D68, 045004 (2003)
-                          K. Fukushima          hep-ph/0310121
-                          Y. Hatta and K. F.   hep-ph/0307068,   hep-ph/0311267

- Quark Matter 2004

## Question and Conclusion

- Question
- What is the QCD phase transition like?    Deconfinement  or  Chiral restoration
- What happens for                    ?
- Conclusion
- There is only one phenomenon for any *m*q.

- Well-defined at

- Well-defined at

- Simultaneous transitions are really simultaneous.

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## Some Basics

- “Confinement” cannot be recognized.
- Chiral restoration is approximately realized.

- One might think...
-     There is only one phenomenon, *i.e*., chiral restoration.
*    **l* reflects the singularity of          due to mixing effects.

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## That means...

- The deconfinement phase transition is so smeared that we cannot see its remnant.
- Then...the QCD phase transition is nothing more than a chiral phase transition?
- Even though we have no rigorous definition, the notion of “deconfinement” is indispensable to understand the QCD phase transition.
- Thermodynamic quantities (e.g. entropy)

- However...

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## Linking deconfinement and chiral phase transitions

- Two true phase transitions are connected.
- (This is the fact observed in the lattice QCD simulation.)

- Not disconnected like

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## Evidence

- Fukugita, Ukawa
-     PRL57, 503 (1986)

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**Notes:**
After that, Fukugita and Ukawa investigated in full QCD simulation for various quark masses. The upper figures show the Polyakov loop and the lower figures show the chiral condensate.

## Evidence

- Fukugita, Ukawa
-     PRL57, 503 (1986)

- “The deconfining and chiral transitions occur at the same temperature. The strength of transition weakens initially as the quark mass decreases from infinity, but at small quark masses it strengthens again ...”

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**Notes:**
This is the quotation from the abstract of their paper. They concluded “The deconfining and chiral transitions occur at the same temperature.” And moreover, they added an important observation. “The strength of transition weakens initially as the quark mass decreases from infinity, but at small quark masses it strengthens again.” What they say is, in the temperature-quark mass plane, there is one simultaneous transition and, on this transition line, the transition is strong at small and large quark masses. This is quite natural because at small quark mass we can expect a chiral phase transition and at large quark mass the deconfinement phase transition is manifested.

## Effective  Potential

- Around C, *l* sees the singularity of **  in *V*chiral through *V*int

- Around D, ** sees the singularity of *l* in *V*glue through *V*int

- To link C and D, *V*int must have special properties.

- Polyakov loop, *l*, couples with **  through quasi-quark excitations.

- then the mixing

- A simple mixing argument is challenged.

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## Model

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## Soft  Mode

*l* does not correspond to physical excitations.
- Electric glueballs, *G*E, couple to *l* to be a soft-mode.
- Alternatively we can define

- where

- It is proven that *G*E becomes massless at D.

- should be distinguished from *G*M

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## Level  Repulsion

- Schematic picture of soft ** mode

- If level repulsion between
** and ***’***is strong enough,
- only ** becomes a soft-mode
- and ***’* remains heavy.

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## Conclusion again

-  Chiral and Deconfinement phase transitions are extreme manifestations of one phenomenon characterized by one soft-mode.

- Chiral phase transition

- Deconfinement transition

- 2nd

- 2nd

- Simultaneous transitions indicate not only mixing effects but also true simultaneous realization of remnants of two transitions.

- Quark Matter 2004