CPOD2011 , Wuhan, China 1 Isospin Matter Pengfei Zhuang Tsinghua University, Beijing ● Phase...
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Transcript of CPOD2011 , Wuhan, China 1 Isospin Matter Pengfei Zhuang Tsinghua University, Beijing ● Phase...
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?
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China 22
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
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●●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
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China
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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
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China
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
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China
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
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China
He, Jin, and PZ, PRD71, (2005)116001He, Jin, and PZ, PRD71, (2005)116001
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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__
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China
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*
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China
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
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China
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
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China 1111
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 !
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China 1212
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
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China 1313
1414
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.
CPOD2011CPOD2011, , Wuhan, ChinaWuhan, China