Isospin Matter

CPOD2011CPOD2011，　　，　　Wuhan, ChinaWuhan, China 11

Isospin Matter Isospin Matter Pengfei ZhuangPengfei Zhuang 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　

　　 Tsinghua University, BeijingTsinghua University, Beijing

● ● Phase Diagram at finite Phase Diagram at finite μμII

● ● BCS-BEC Crossover in pion superfluid BCS-BEC Crossover in pion superfluid

QCD Phase DiagramQCD Phase Diagram

Questions: 1) What is the phase of quark matter at finite Questions: 1) What is the phase of quark matter at finite μμII ? ?

2) Is 2) Is μμII effect similar to effect similar to μμBB effect? effect?


D. T. Son and M. A. Stephanov, Phys. Rev. Lett. 86, 592(2001)D. T. Son and M. A. Stephanov, Phys. Rev. Lett. 86, 592(2001)J. B. Kogut, D. K. Sinclair, Phys. Rev. D 66, 034505(2002)J. B. Kogut, D. K. Sinclair, Phys. Rev. D 66, 034505(2002)K. Splittorff, D. T. Son, and M. A. Stephanov, Phys. Rev. D64, 016003 (2001)K. Splittorff, D. T. Son, and M. A. Stephanov, Phys. Rev. D64, 016003 (2001)M. Loewe and C. Villavicencio, Phys. Rev. D 67, 074034(2003)M. Loewe and C. Villavicencio, Phys. Rev. D 67, 074034(2003)Michael C. Birse, Thomas D. Cohen, and Judith A.McGovern, Phys. Lett. B 516, 27 (2001)Michael C. Birse, Thomas D. Cohen, and Judith A.McGovern, Phys. Lett. B 516, 27 (2001)D. Toublan and J. B. Kogut, Phys. Lett. B 564, 212 (2003)D. Toublan and J. B. Kogut, Phys. Lett. B 564, 212 (2003)A.A.Barducci, R. Casalbuoni, G. Pettini, and L. Ravagli, Barducci, R. Casalbuoni, G. Pettini, and L. Ravagli, Phys. Rev. D 69, 096004 (2004)Phys. Rev. D 69, 096004 (2004)M. Frank, M. Buballa and M. Oertel, Phys. Lett. B 562, 221 (2003)M. Frank, M. Buballa and M. Oertel, Phys. Lett. B 562, 221 (2003)L. He and P. Zhuang, Phys. Lett. B 615, 93 (2005)L. He and P. Zhuang, Phys. Lett. B 615, 93 (2005)

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BCS and BEC PairingBCS and BEC Pairing

in BCS, Tin BCS, Tcc is determined by thermal excitation of fermions, is determined by thermal excitation of fermions,

in BEC, T in BEC, Tcc is controlled by thermal excitation of is controlled by thermal excitation of

collective modes.collective modes.

Is there a similar BCS-BEC structure for QCD condensed matter ?Is there a similar BCS-BEC structure for QCD condensed matter ?

CPOD2011CPOD2011，　　，　　Wuhan, ChinaWuhan, China

44

●●there is reliable lattice QCD result at finite T, there is reliable lattice QCD result at finite T, but not yet precise but not yet precise

lattice simulation at finite lattice simulation at finite μμ, we have to consider effective models. , we have to consider effective models.

● ● the physics is the physics is vacuum excitationvacuum excitation at finite T at finite T but but vacuum condensatevacuum condensate

at finite at finite μμ..

●●the BCS inspired Nambu-Jona-Lasinio (NJL) model successfully the BCS inspired Nambu-Jona-Lasinio (NJL) model successfully

describes the chiral condensate and color condensate. describes the chiral condensate and color condensate.

NJL ModelNJL Model

chiral thermodynamicschiral thermodynamics

chiral and color condensatechiral and color condensate


55

NJL with isospin symmetry breakingNJL with isospin symmetry breaking

2 2 1

2 2 2 2

2 2 2 2

( ) Tr Ln

0, 0, 0, 0, 0, 0, 0, 0u u d d

TG S

V

q q

2 2

0 0 5NJL iL i m G i

, , u d u duu dd chiral and pion condensates with finite pair momentumchiral and pion condensates with finite pair momentum

quark propagator in MFquark propagator in MF 0 51

5 0

2( , )

2u

d

p q m iGS p q

iG p q m

0 2m m G

2 25 52 ( 0), 2 ( 0)

2 2iq x iq x

I Iui d e for di u e for

quark chemical potentialsquark chemical potentials

0 / 3 / 2 0

0 0 / 3 / 2u B I

d B I

gap equations:gap equations:

NJL at Finite NJL at Finite μμII


He, Jin and PZ, PRD71, (2005)116001He, Jin and PZ, PRD71, (2005)116001

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Phase Structure of Pion SuperfluidPhase Structure of Pion Superfluid

μμBB

μμII


He and PZ, PRD74, (2006)036005He and PZ, PRD74, (2006)036005

Jiang and PZ, arXiv:1104.0094Jiang and PZ, arXiv:1104.0094

77

5

5

3 5 0

1,

,

,

,

m

m

i m

i m

i m

4

*4

( ) Tr ( ) ( )(2 )mn m n

d pk i S p k S p

meson polarization functionsmeson polarization functions

meson propagator at RPAmeson propagator at RPA

pole of the propagator determines meson masses pole of the propagator determines meson masses

the new eigen modes are linear combinations of the new eigen modes are linear combinations of

considering all possible channels in the bubble summationconsidering all possible channels in the bubble summation

0

0

0

0 0 0 0 00 , 0

1 2 ( ) 2 ( ) 2 ( ) 2 ( )

2 ( ) 1 2 ( ) 2 ( ) 2 ( )det

2 ( ) 2 ( ) 1 2 ( ) 2 ( )

2 ( ) 2 ( ) 2 ( ) 1 2 ( )mk M k

G k G k G k G k

G k G k G k G k

G k G k G k G k

G k G k G k G k

0

, ,

mM

, ,

D

Quantum Fluctuations (Mesons) in RPAQuantum Fluctuations (Mesons) in RPA

, ,

mixing among normal in pion superfluid phasemixing among normal in pion superfluid phase


He, Jin, and PZ, PRD71, (2005)116001He, Jin, and PZ, PRD71, (2005)116001

88

Meson Mixing and Goldstone ModeMeson Mixing and Goldstone Mode

mixing angles mixing angles αα between between σσ and and ππ++ , ,

ββ between between σσ and and ππ__ , ,

and and γγ between between ππ++ and and ππ__


Hao and PZ, PLB652, (2007)275Hao and PZ, PLB652, (2007)275

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Meson Spectral FunctionsMeson Spectral Functions

( , ) 2 Im ( , )Rk D k

BEC BCS

meson spectra function between the temperatures Tmeson spectra function between the temperatures Tcc and T* and T*


Sun, He and PZ, PRD75, (2007)096004Sun, He and PZ, PRD75, (2007)096004

ππ – – ππ scattering and BCS-BEC Crossover scattering and BCS-BEC Crossover

BCS: overlapped molecules, largeBCS: overlapped molecules, large π π – – ππ cross section cross sectionBEC: identified molecules, ideal Boson gas limitBEC: identified molecules, ideal Boson gas limit

BECBEC BCSBCS

Normal PhaseNormal PhasePion SuperfluidPion Superfluid


talk by Shijun Mao, November 10talk by Shijun Mao, November 10

1010

BECBEC BCSBCS

Yukawa Potential in Quark MatterYukawa Potential in Quark Matter

meson exchange in nucleon scattering (1934-1935)meson exchange in nucleon scattering (1934-1935)

UU

pp

nn nn

pp

32

3( ) (0, )

(2 )ik rd k

V r e TrD k

stable quark potentialstable quark potential

( )Mre

V rr

meson exchange in NJL at quark levelmeson exchange in NJL at quark level

screen massscreen mass


Mu and PZ, Eur. Phys. J C58, (2008)271Mu and PZ, Eur. Phys. J C58, (2008)271

Meson Screening Mass Meson Screening Mass

corresponding to the global isospin symmetry breaking, there is a corresponding to the global isospin symmetry breaking, there is a Goldstone mode in the pion superfluid, which leads to a long Goldstone mode in the pion superfluid, which leads to a long range force between two quarks ! range force between two quarks !


Jiang and PZ, arXiv:1104.0094Jiang and PZ, arXiv:1104.0094

Quark Potential in Pion SuperfluidQuark Potential in Pion Superfluid

1) the maximum potential is located at the phase boundary . 1) the maximum potential is located at the phase boundary . 2) the potential in pion superfluid is non-zero at extremely high isospin 2) the potential in pion superfluid is non-zero at extremely high isospin density, totally different from the temperature and baryon density effects !density, totally different from the temperature and baryon density effects !

talk by Yin Jiang, talk by Yin Jiang, November 11November 11


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Conclusion and OutlookConclusion and Outlook

1)There exists a pion superfluid at high isospin density, and the 1)There exists a pion superfluid at high isospin density, and the Goldstone mode controls the thermodynamics of the system. Goldstone mode controls the thermodynamics of the system.

2) There exists a BCS-BEC crossover in the pion superfluid.2) There exists a BCS-BEC crossover in the pion superfluid.

3) The maximum coupling is located at the phase transition 3) The maximum coupling is located at the phase transition boundary, similar to the temperature and baryon density effects. boundary, similar to the temperature and baryon density effects.

4) The coupling is non-zero even at extremely high isospin density, 4) The coupling is non-zero even at extremely high isospin density, totally different from the temperature and baryon density effects.totally different from the temperature and baryon density effects.

Applications in neutron stars and intermediate energy nuclear Applications in neutron stars and intermediate energy nuclear collisions, like mass-radius relation, pion superfluid in curved collisions, like mass-radius relation, pion superfluid in curved space, and pion_-/pion_+ ratio. space, and pion_-/pion_+ ratio.


Isospin Matter

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