Hot and dense QCD matter

APCTP-WCU Focus Program “From dense matter to campact stars in QCD and hQCD”, Pohang, May 24-June 4, 2010

Mei Huang IHEP, CAS

TPCSF, CAS

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Content

I. QCD Phase structure chiral restoration & deconfinement phase transition

II. Locate CEP from viscosities shear viscosity/entropy density ratio

bulk viscosity/entropy density ratio

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I. QCD Phase Structure

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1974 ---- 1999 1999 ---- 2002

HM

QGP

CSCHM

QGP

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Compact Star

sQGP E. Shuryak, I. Zahed

Pseudogap phase Hatsuda,Kunihiro

After 2003 High T part

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After 2003 High density part

Abuki-Baym-Hatsuda-Yamamoto, arXiv:1003.0408

Darmstadt and Frankfurt CSC group, Phys.Rev.D72:034004,2005

Many people contributed on the rich structure of CSC

APCTP focus program 2006

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After 2007: Chiral symmetric but confined phase

Quarkyonic and half-Skymion phase

L. McLerran, R. Pisarski

Phase diagram at large Nc Skymion crystal

See M. Rho’s talk

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HM

QGP

CSC

Can Quarkyonic phase be realized in real QCD phase diagram?

Fukushima, Hatsuda,arXiv:1005.4814

HM

QGP

CSC

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Quarkyonic phase in PNJL model

Different choices of Polyakov potential: fixed by lattice QCD at finite T

10Kenji Fukushima, arXiv:0803.3318

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Quarkyonic phase in PLSM model

H. Mao, J. Jin, MH, arXiv:0906.1324

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In PNJL or PLSM model, at zero baryon density, whether chiral phase transition and deconfinement phase transition coincide or not depends much on parameters used.

In these models, there are no interplay between chiral phase transition and deconfinement phase transition.

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Lattice results on Tc at zero mu

Chiral limit: coincide

Physical quark mass (2+1):

RBC-Bielefeld: coincide

Wuppertal-Budapest: (crossover feature)

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An equivalent order parameter for deconfinement phase transition:

Gattringer,PRL97(2006)032003Bilgici et.al. PRD77(2008)094007Braun, Hass,Marhauser,Pawlowski, arXiv:0908.0008

Order parameter of center symmetry

Confinement: center symmetry

Deconfinement:

center symmetry breaking

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The periodicity property of the quark fields change under the the gauge transformation Uz:

Dual observables:

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n=1: dressed Polyakov loop

Dual quark condensate:

order parameter of center symmetry

Dressed Polyakov loop in NJL model

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Chiral limit: coincide

T.Mukherjee, H.Chen,M.Huang, arXiv:1005.2482

18T.Mukherjee, H.Chen,M.Huang, arXiv:1005.2482

Physical quark mass:

crossover region

1st order:

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Why for 1st and 2nd phase transition?

T.Mukherjee, H.Chen,M.Huang, arXiv:1005.2482

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Why for crossover?

T.Mukherjee, H.Chen,M.Huang, arXiv:1005.2482

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Mass effect

Nf=2+1 in NJL model is in progress

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II. Locate CEP by viscosities

shear viscosity/bulk viscosity

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Relativistic Heavy Ion Collision

Discovery of “Perfect fluid” at RHIC

Hydrodynamics

???

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A little bit Hydrodynamics

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Increase shear viscosity reduces elliptic flow!

P. Romatschke, U. Romatschke, nucl-th/0706.1522

Before 2003, people believed that de-confined QCD matter would be weakly coupled gas. Therefore, bulk viscosity is neglected, only consider shear viscosity corrections to the ideal hydro.

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Discovery of sQGP at RHIC

Low shear viscosity

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Handling strongly coupled system by using AdS/CFT

Minimum bound?

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sQGP: Most “perfect fluid” known

• Lattice: C0.13 0.03, at T=1.65 Ts

Nakamura-Sakai(2004)

Meyer (2007)

~ 10s

• Water

10.08

4s

Policastro, Son, and Starinets;Kovton, Son and Starinets; Buchel, J. Liu; Nakamura, Sin; Maeda, Natsuume, Okamura; ……

• N=4 SYM:

0.1 0.2s

• RHIC: Teaney (2003)

Romatschke-Romatschke (2007)

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Interesting global feature of /s

Does /s make some sense?

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Phys.Rev.Lett.97:152303,2006

Proposal:

Sufficient precise Experimental measurement of /s to pinpoint the location of phase transitions or crossover.

Empirical observation:

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Lacey et al., PRL 98:092301,2007

Probe CEP by /s

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Results from real scalar model

Yagi, Hatsuda, Miake, “Quark-Gluon Plasma”

Can /s characterize phase transitions?

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1, Minimum at Tc, most difficult condition for momentum transportation.

2. The value of /s at phase transition decreases with increases of coupling strength

J.W Chen, MH, Y.H. Li, E. Nakano, D.L.Yang, Phys.Lett.B670:18-21,2008, arXiv: 0709.3434

/s characterizes phase transitions CJT+Boltzmann Eq

Dmitri Kharzeev, Kirill Tuchin arXiv:0705.4280 [hep-ph],F.Karsch, Dmitri Kharzeev, Kirill Tuchin arXiv:0711.0914 [hep-ph],Harvey Meyer arXiv:0710.3717 [hep-ph],

However: large bulk viscosity of QCD matter near phase transition

Pure gluodynamics 2-flavor case

Bulk viscosity is related to nonconformality

Several quantities measure conformality

LQCD results:

trace anomaly shows a sharp peak near phase transition

BNL-Columbia-RBRC-Bielefeld, arXiv:0710.0354 Bielefeld, hep-lat/9602007

BNL-Columbia-RBRC-Bielefeld arXiv:0710.0354

LQCD results:

soft EOS & small sound velocity near phase transition

Gubser et al, 0804.1950

AdS/CFT

Gravity duals, nonconformal

Bulk viscosity in gravity dual models

Results from scalar model: 2nd order phase transition

Trace anomaly: height is DOF dependent

Baochun Li, Mei Huang, Phys.Rev.D78:117503,2008 arXiv: 0807.0292

EOS & sound velocity

Baochun Li, Mei Huang, Phys.Rev.D78:117503,2008 arXiv: 0807.0292

Bulk viscosity/entropy density

Baochun Li, Mei Huang, Phys.Rev.D78:117503,2008 arXiv: 0807.0292

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Results from a more realistic model: PLSM model

H. Mao, J. Jin, M. Huang, arXiv: 0906.1324[hep-ph]

Comparing with LQCD

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Sound velocity square at Tc: 0.05 in PLSM, 0.07 in LQCD

H. Mao, J. Jin, M. Huang, arXiv: 0906.1324[hep-ph]

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Comparing with LQCD: Bulk viscosity/entropy density

H. Mao, J. Jin, M. Huang, arXiv: 0906.1324[hep-ph]

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Dependence of bulk viscosity/entropy density on the order of phase transition: large for 1st order phase transition, small for crossover. Thus, bulk viscosity/entropy density is better than shear viscosity/entropy density to probe CEP.

H. Mao, J. Jin, M. Huang, arXiv: 0906.1324[hep-ph]

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Shear viscosity: how much entropy is produced bytransformation of shape at constant volume

Bulk viscosity: how much entropy is produced bytransformation of volume at constant shape

Physical quantities related bulk viscosity

Generated bytranslations

Generated bydilatations

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Conclusion and discussion

1, Interplay between chiral phase transition and

deconfinement phase transition.

2, Locate CEP by bulk viscosity/entropy density

Observables related to bulk viscosity?

Radial flow?

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What’s the effect of large bulk viscosity near Tc?

Breakdown of hydrodynamic picture

Slow down the expansion of the system

Clustering at hadroniztion

……

G.Torrieri, B.Tomasik, I.Mishustin, arXiv:0707.4405[hep-ph]

G.Torrieri, I.Mishustin, arXiv:0805.0422[hep-ph]

R.J.Fries, B.Muller,A.Schafer, arXiv:0807.4333[hep-ph]