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Some aspects of pSome aspects of phase transition hase transition in dense quark matterin dense quark matter

Qun WangUniversity of Science and Technology of China

Phases in QCD Lattice results at finite temperature Dense baryonic matter Diquarks in cold baryonic matter

QCD phase transition and RHIC physics Weihai, August 9-14, 2009

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Research groups in China Research groups in China (QCD phase transition theory)(QCD phase transition theory)

北大，清华高能所

南大

中科大

华中师大在职研究人员（ 2009.8 ）教授、研究员： 5±1 人副教授： 2±1 人讲师、博士后： 3±2 人

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Phase diagram ofPhase diagram of SStrongly interacting trongly interacting QQuark uark GGluon luon PPlasmalasma

See e.g.

• Braun-Munzinger, Wambach, 2008 (review)

• Ruester,Werth,Buballa, Shovkovy,Rischke,2005

•Fukushima, Kouvaris, Rajagopal, 2005

•Blaschke, Fredriksson, Grigorian, Oztas, Sandin, 2005

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Freezeout temperature and chemical Freezeout temperature and chemical potential in potential in HHeavy eavy IIon on CCollisionsollisions

Andronic, Braun-Munzinger, Stachel, 2006Braun-Munzinger,Magestro,Redlich,Stachel, 2001 Cold baryonic matter

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Lattice QCD Lattice QCD at finite temperatureat finite temperature

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Lattice QCD at finite temperatureLattice QCD at finite temperature

Early papers:

0. Wilson, PRD1974

1. McLerran and Svetitsky, PLB1981,PRD1981

2. Kuti, Polonyi and Szlachanyi, PLB1981

3. Engels, Karsch, Montvay and Satz, PLB1981

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Lattice QCD at finite temperatureLattice QCD at finite temperature

Partition function of QCD

lattice size

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Lattice QCD: gluon sectorLattice QCD: gluon sector

Gauge link

Wilson action

n n+μ

n+μ+νn+ν

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Lattice QCD: fermion sectorLattice QCD: fermion sector

The problem of fermion sector: 1. Fermion number doubling2. Essential symmetries (chiral symmetry) of the continuum action are violated

Solution: 1. Wilson fermion, add a higher derivative term2. Staggered fermion, distribute components of the fermion Dirac spinors over several lattice sites, [Kogut and Susskind, PRD1975].

The Kogut-Susskind staggered fermion action:

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Lattice QCD partition functionLattice QCD partition function

C

Wilson loop C

reflect confinement property

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ConfinementConfinement

C

confining potential

T: virtual time

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Polyakov LoopPolyakov Loop

Polyakov loop

Free energy for qq-bar

Polyakov loop as order parameter for phase transtion

q at x q-bar at y

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Deconfinement phase transitionDeconfinement phase transition

Center of SU(3)_c group

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Two phase phase transitionsTwo phase phase transitions

1. chiral phase transition order parameter: chiral condensate well-define for

2. deconfinement phase transition order parameter: polyakov loop well-defined for

3. What happen to real world:

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Lattice QCD: Phase diagramLattice QCD: Phase diagram

Laerman,Philipsen, Ann.Rev.Nucl.Sci. 2003

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Lattice QCD: recent resultsLattice QCD: recent results

arXiv:0903.4379

Bernard et al, (MILC) PRD 75 (07) 094505, Cheng et al, (RBC-Bielefeld) PRD 77 (08) 014511 Bazavov et al, (HotQCD), arXiv:0903.4379

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Lattice QCD: recent resultsLattice QCD: recent results

Speed of sound

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Lattice QCD: recent resultsLattice QCD: recent results

Polyakov loopChiral condensate

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Y.G.Ma, Workshop on RHIC Physics and CSR physics, Weihai, 2009/8/9-14

What viscosities will do?

Shear viscosity:

-The velocity gradient are directly related to viscous behavior of the fluid

-Viscosities reflect resistance to flow

Bulk viscosity:

Lacey et al, PRL(2007)

Lattice:Meyer, PRD(2007), PRL(2008)

η/s around phase transitionη/s around phase transition

ζ/s around phase transitionζ/s around phase transition

Karsch, Kharzeev, TuchinPLB 2008Noronha ^2, Greiner, 2008Chen, Wang, PRC 2009......

η/sη/s of gluon gas -- variation method of gluon gas -- variation method

Variation method:Chen, Dong, Ohnishi, Wang, arXiv:0907.2486

Cascade model:Xu, Greiner, PRL(2008)

Ratio of 22+23/22Ratio of 22+23/22 of gluon gas of gluon gas--variation method--variation method

Variation method:Chen, Dong, Ohnishi, Wang, arXiv:0907.2486

Cascade model:Xu, Greiner, PRL(2008)

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Dense baryonic matterDense baryonic matter

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Dense baryonic matterDense baryonic matter

1. non-perturbative method lattice QCD, Dyson-Schwinger eq., AdS/QCD [Y.X. Liu, H.S. Zong, ......]

2. effective models chiral perturbation theory chiral models (NJL, linear-σ, etc) [P.F. Zhuang, Y.X.Liu, M. Huang, Q.Wang, ......]

3. Perturbative method [D.F.Hou, Q.Wang, ......]

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NJL + Polyakov = PNJLNJL + Polyakov = PNJL

constant field, Polyakov gauge

Fukushima, PLB 2004;Ratti, Thaler, Weise,PRD 2006;Zhang, Liu, PRC 2007......

NJL-part gluonic part

NJL + Polyakov = PNJLNJL + Polyakov = PNJL

Thermodynamical potential

inspired by lattice result

PNJL: Gap equationPNJL: Gap equation

parameters

PNJL: resultsPNJL: results

K. Fukushima, PRD 2008

PNJL: resultsPNJL: results

K. Fukushima, PRD 2008

critical point (NJL): (T,μ)=(48,324) MeV (PNJL): (T,μ)=(102,313) MeV

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Diquark in baryonic matterDiquark in baryonic matter--from weak to strong couplings--from weak to strong couplings

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WhyWhy c coolloorr superconductivity superconductivity

Anti-symmetric channel: attractive interaction

Energy gap in quasi-particle excitation

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CCoolloorr superconductivity - weak coupling superconductivity - weak coupling

Weak coupling gap equation (DS equation) in asymptotically high density

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[Son 1999; Schafer,Wilczek 2000; Hong et al. 2000; Pisarski,Rischke 2000; Brown et al 2000; Wang,Rischke 2002; Schmitt,Wang,Rischke 2003]

Weak coupling solution to gap equation Weak coupling solution to gap equation

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Pairings within the same flavorPairings within the same flavor

Schmitt, QW, Rischke, Phys.Rev.Lett.91, 242301(2003)Schmitt, Phys.Rev.D71, 054016(2005)

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Meissner effects in weak couplingMeissner effects in weak coupling

Son, Stephanov, Phys.Rev.D61,074012(2000);Schmitt, QW, Rischke, Phys. Rev. D69, 094017(2004); Phys. Rev. Lett.91, 242301(2003)

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Meissner effects in weak coupling: resultsMeissner effects in weak coupling: results

■ Rotated photon in CSL phase has a non-vanishing mass: ElectromagneticMeissner effect.■ Although rotated photon in polar phase has a zero mass but a system with 2 or 3 favors still exhibits Electromagnetic Meissner effect because of different chemical potential or no single mixing angle for all favors.

Schmitt, QW, Rischke, PRL(2003)

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Effective Theory of dense matterEffective Theory of dense matter

Hong, 2000Schaefer, 2002, 2003Reuter, QW, Rischke, 2004

Controlled calculation in QCD

physics dominated by strip close to Fermi surface

separation of scales and need for EFT

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It (QCD) provides the answer to a child-like question: What happens to matter, as you squeeze it harder and

harder?

-- Wilczek

Answer: Perturbation in QCD in weak coupling

An opposite question: What happens to matter, as you increase interactions stronger and stronger?

What happens to quark-quark pairings: do they survive stronger and stronger interactions?

Answer: unclear

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BCSBCS--BECBEC Crossover Crossover

Science

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RRelativistic BCS-BEC crossoverelativistic BCS-BEC crossover

Recent works by other group:

• Nishida & Abuki, PRD 2007 -- NJL approach – Abuki’s Talk• Abuki, NPA 2007 – Static and Dynamic properties • Sun, He & Zhuang, PRD 2007 – NJL approach • He & Zhuang, PRD 2007 – Beyond mean field• Kitazawa, Rischke & Shovkovy, arXiv:0709.2235v1 –

NJL+phase diagram – Kitazawa’s Talk• Brauner, arXiv:0803.2422 – Collective excitations – Brauner’s Talk• Chatterjee, Mishra, Mishra, arXiv:0804.1051 -- Variational

approach

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Relativistic boson-fermion Relativistic boson-fermion model (model (MFAMFA))

With With bosonicbosonic and and fermionicfermionic degrees of freedom and their degrees of freedom and their coupling, but neglect the coupling of thermal bosons coupling, but neglect the coupling of thermal bosons

and fermions as and fermions as MMean ean FField ield AApproximationpproximation Friedberg-Lee model, 1989

zero mode of boson

J. Deng, A. Schmitt, QW, Phys.Rev.D76:034013,2007

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Thermodynamic potetialThermodynamic potetial

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Density and gap Density and gap equationsequations

Crossover parameterCrossover parameter

x<0, BCS regimex>0, BEC regime

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At zero T or critical TAt zero T or critical T

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Dispersion Dispersion relationrelation

In In BCSBCS regime, fermions are slightly gapped, anti- regime, fermions are slightly gapped, anti-fermions are strongly gapped. fermions are strongly gapped.

In In BECBEC regime, both are strongly gapped, indicating the regime, both are strongly gapped, indicating the formation of bound states with large binding energyformation of bound states with large binding energy

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Unitary RegimeUnitary Regime

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Pairing with imbalance populationPairing with imbalance population----Fermi surface topologiesFermi surface topologies

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Homogeneous Homogeneous solutionsolution

The fermion-boson mixture in BCS-BEC regime has been found The fermion-boson mixture in BCS-BEC regime has been found in cold atomic system. Stable gapless phase in strong in cold atomic system. Stable gapless phase in strong coupling (see also Kitazawa,Rischke, Shovkovy, 2006) coupling (see also Kitazawa,Rischke, Shovkovy, 2006)

[ Realization of a strongly interacting Bose-Fermi mixture [ Realization of a strongly interacting Bose-Fermi mixture from a two-component Fermi gas, MIT group, arXiv:0805.0623 from a two-component Fermi gas, MIT group, arXiv:0805.0623 ]]

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Phase diagramPhase diagram

Shaded area: unstable, with negative susceptibility

Non-relativistic relativistic

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Beyond mean-field aproximationBeyond mean-field aproximation----At small TAt small T

The results are similar to the The results are similar to the MFAMFA results results

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At T=TcAt T=Tc

Fluctuations become important in Fluctuations become important in BECBEC regime.regime.In In BECBEC regime T*>Tc. regime T*>Tc.

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T-dependenceT-dependence

The fluctuation effects become larger.The fluctuation effects become larger.BEC criterion is related to the minimization BEC criterion is related to the minimization of the thermodynamic potential.of the thermodynamic potential.

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Introduction of term in : Introduction of term in :

B.I.Halperin, T.C.Lubensky and S. Ma 1974B.I.Halperin, T.C.Lubensky and S. Ma 1974 (magnetic field fluctuations)(magnetic field fluctuations)I. Giannakis, D. f. Hou, H. c. Ren and D. H. Rischke, 2004I. Giannakis, D. f. Hou, H. c. Ren and D. H. Rischke, 2004 ((Gauge Field Fluctuations)Gauge Field Fluctuations)Sasaki, Friman, Redlich, 2007Sasaki, Friman, Redlich, 2007 (baryon number fluctuation in 1st chiral phase transition)(baryon number fluctuation in 1st chiral phase transition)

1st order phase transition from 1st order phase transition from fluctuations: fixed fluctuations: fixed μμ

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Diquarks in baryonsDiquarks in baryons

Quarks, diquarks and pentaquarks, Jaffe, Wilczek, 2004[Diquarks as building blocks of exotic hadrons]

Diquark models:Anselmino, et al., 1993Abu-Raddad,Hosaka,Ebert,Toki, 2002Many other papers……

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Diquarks in baryonsDiquarks in baryons

Diquark-cluster Meson Cloud

Diquark configuration in proton: positive magnetic moments from strange quarks Zou, Riska, 2005

u

du

SS

Su

uS

d

Diquark configuration: inverse mass order in resonances Zou, 2007

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Quark-baryonic matter crossover Quark-baryonic matter crossover in N_f=3 dense matter in N_f=3 dense matter

BCS-BEC crossoverwith boson-fermion model

crossover of quark-baryonic matter

■ Continuity of quark and hadron matter, Schafer, Wilczek, 2000[ CFL-hadronic matter: a weak coupling realization of confinement and chiral symmetry breaking in idealization of QCD ]

■ New critical point induced by the axial anomaly in dense QCD, Hatsuda, Tachibana, Yamamoto, Baym, 2006

■ N_f=3, there is a new critical point near chemical potential axis due to coupling of chiral and diquark condensate: quark-nuclear matter crossover

■ N_f=2, no critical point: quark-nuclear matter transition

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SummarySummary

There are many efforts in exploring the QCD phase diagram boThere are many efforts in exploring the QCD phase diagram both experimentally and theoretically. th experimentally and theoretically.

On the theory side, there are lattice and effective model approOn the theory side, there are lattice and effective model approach to QCD phase diagram. ach to QCD phase diagram.

A lot of progress has been made in dense regime of phase diagrA lot of progress has been made in dense regime of phase diagram where diquark correlation plays an important role. am where diquark correlation plays an important role.

The community of QCD phase transition is in small scale and stThe community of QCD phase transition is in small scale and still has room to expand. ill has room to expand.