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Chiral Symmetry and Isospin Symmetry aChiral Symmetry and Isospin Symmetry at CSR Energyt CSR Energy

ZHUANG Pengfei (Tsinghua University)ZHUANG Pengfei (Tsinghua University)

● ● Friedel Oscillation at High Baryon DensityFriedel Oscillation at High Baryon Density

/ ● ● MMass-splitting Induced Ratio at CSR Energyass-splitting Induced Ratio at CSR Energy

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HENP known difference between T andknown difference between T and

both T and can induce QCD phase transitionsboth T and can induce QCD phase transitions

● ● T effect (in early universe and at RHIC and LHC):T effect (in early universe and at RHIC and LHC):

continuous change, continuous change, second order phase second order phase transition,transition,

reliable lattice simulation reliable lattice simulation

170 MeVcT

● ● effect (in compact stars and at CSR and FAIR):effect (in compact stars and at CSR and FAIR):

sudden jump, sudden jump, first order phase transition,first order phase transition,

model calculation model calculation

900 MeVc

0 1 !

0 3

qq

qq

partial chiral restoration in normal nuclear matter:partial chiral restoration in normal nuclear matter:

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HENP bound states at high densitybound states at high density

● ● ultracold atom gas: ultracold atom gas: from recent experiment for highly imbalanced Fermi gas, the dfrom recent experiment for highly imbalanced Fermi gas, the di-fermion bound states can survive in the symmetry restoration pi-fermion bound states can survive in the symmetry restoration phase.hase.

● ● relativistic heavy ion collisions: relativistic heavy ion collisions: sQGP above the phase transitionsQGP above the phase transition

C.H.Schunck et al., Science 316, 867(2007)C.H.Schunck et al., Science 316, 867(2007)

Shuryak, Zahed,2004Shuryak, Zahed,2004

NJL calculation, Jin, He, Zhuang, 2005NJL calculation, Jin, He, Zhuang, 2005

★?

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HENP Friedel oscillation by sharp Fermi surface Friedel oscillation by sharp Fermi surface

Yukawa potential (1934-1935): Yukawa potential (1934-1935):

Friedel oscillations in nuclear matterFriedel oscillations in nuclear matter (Alonso, et al., 1989,1994)(Alonso, et al., 1989,1994), , hadronic matter hadronic matter (Mornas et al., 2001), (Mornas et al., 2001), and quark matter and quark matter (Flambaum, Shuryak, 2007).(Flambaum, Shuryak, 2007).

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3( ) (0, )

(2 )ik rd k

V r e U k

integration over boson momentumintegration over boson momentum

fermion distribution:fermion distribution:

0.1 0.2 0.3 0.4 0.5k

0.2

0.4

0.6

0.8

1

f

2 2 /( ) 1/( 1)

m p Tf p e

fp

3

1( ) cos(2 )fV r p r

r

Friedel oscillationFriedel oscillation

0T 0T

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HENP quark potential in a quark-meson plasma quark potential in a quark-meson plasma

SU(2) NJL model:SU(2) NJL model:

quark-quark scattering diagram in RPA :quark-quark scattering diagram in RPA :

mesonsmesons

meson polarization function :meson polarization function :

S: mean field quark propagatorS: mean field quark propagator

order parameter of chiral phase transition:order parameter of chiral phase transition:

Mu, Zhuang, EPJC, 2008Mu, Zhuang, EPJC, 2008

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HENP Friedel OscillationFriedel Oscillation

the Friedel oscillation is important at high matter density the Friedel oscillation is important at high matter density and low temperature.and low temperature.

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the potential becomes saturatethe potential becomes saturated and approaches zero at T/T_c d and approaches zero at T/T_c = 3, namely the quark system is = 3, namely the quark system is weakly coupled at high enough weakly coupled at high enough temperature.temperature.

remarkable potential at extremely high densityremarkable potential at extremely high density

the potential does not approach the potential does not approach zero even at extremely high zero even at extremely high matter density ! There will be a matter density ! There will be a wide bound state region at high wide bound state region at high density. density.

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HENP strongest coupling at critical densitystrongest coupling at critical density

Shuryak, Zahed, 2004Shuryak, Zahed, 2004

large ratio means strong coupling, large ratio means strong coupling, and small ratio indicates and small ratio indicates weak couplingweak coupling

maximum coupling at the chiral phase transition !maximum coupling at the chiral phase transition !

potential energy

kinetic energy

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density effect is quite different from temperature effect in QCD density effect is quite different from temperature effect in QCD phase structure, and there is a wide quark-bound-state region at phase structure, and there is a wide quark-bound-state region at high density. high density.

ConclusionConclusion

QuestionsQuestions

are quark stars located in this strongly coupled quark-hadron are quark stars located in this strongly coupled quark-hadron region?region?

if there exists such a quark-hadron region at FAIR and CSR, if there exists such a quark-hadron region at FAIR and CSR, what are the signatures?what are the signatures?

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● ● isospin asymmetric nuclear collisions:isospin asymmetric nuclear collisions: Au-Au at 1 A GeV (SIS/GSI) N / Z = 118 / Au-Au at 1 A GeV (SIS/GSI) N / Z = 118 / 79 U-U at 0.6 A GeV (CSR/La79 U-U at 0.6 A GeV (CSR/Lanzhou) N / Z = 146 / 92nzhou) N / Z = 146 / 92

●● isospin symmetry at finite T and : isospin symmetry at finite T and : explicit and spontaneous isospin symmetexplicit and spontaneous isospin symmetry breaking, pion superfluidityry breaking, pion superfluidity

何联毅何联毅 ,, 郝学文郝学文 ,, 金猛金猛 ,, 庄鹏飞庄鹏飞 :: PRD75: PRD75:096004,2007096004,2007 ；； PLB652:275,2007 ； PRD74:036005,2006 PRD71:116001,2005 ； PLB615:93,2005

isospin symmetry breakingisospin symmetry breaking

(negative !)(negative !)

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isospin induced mass splitting,isospin induced mass splitting, Goldstone modeGoldstone mode

●● which final state distribution is sensitive to the isospin which final state distribution is sensitive to the isospin symmetry breaking?symmetry breaking?

2

5 // 1.95

5( / ) /

Z N

Z N Z N

/ 1.94

/ ratio !ratio !experiment data for Au-Au at 1 A GeV: experiment data for Au-Au at 1 A GeV:

isobar model which is valid around 1 A GeV:isobar model which is valid around 1 A GeV:R.Stock, Phys. Rep. 135(1986)259.R.Stock, Phys. Rep. 135(1986)259.

A.Wagner et al., PLB 420(1998)20.A.Wagner et al., PLB 420(1998)20.

pion mass splittingpion mass splitting

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the energy dependence is explained by (the energy dependence is explained by (variablevariable) Coulomb potential ) Coulomb potential between charged pions and the nuclear matterbetween charged pions and the nuclear matter

A.Wagner et al., PLB 420(1998)20A.Wagner et al., PLB 420(1998)20

M.Gyulassy, S.K.Kauffmann, NPA 362(1981)503; M.Gyulassy, S.K.Kauffmann, NPA 362(1981)503; Bao-an Li, PLB 346(1995)5, PRC 67(2 Bao-an Li, PLB 346(1995)5, PRC 67(2003)017601; A.Wagner et al., PLB 420(199003)017601; A.Wagner et al., PLB 420(1998)20; …...8)20; …...●● our idea: our idea:

we self-consistently explain the energy dependence of we self-consistently explain the energy dependence of in the frame of isospi in the frame of isospin symmetry breaking. n symmetry breaking. isospin-induced maisospin-induced mass splitting ss splitting

light particles are easily created at low momentum and heavy particles light particles are easily created at low momentum and heavy particles are hard to be produced.are hard to be produced.

/

much larger than 1much larger than 1

close to 1close to 1

the energy dependence the energy dependence disappears at high energy disappears at high energy and in peripheral collisions.and in peripheral collisions.

●●kinetic energy dependence ofkinetic energy dependence of /

momentum dependencemomentum dependence

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2 2 , , , ( )B t l l tT u u u u u

2 2 2

3

3 ( ) /( 1 )

1

1t tM p p u T u

d NV

d p e

1.95N

N

0 , ,

I

● ● particles ( ) are statistically emitted at freeze-out,particles ( ) are statistically emitted at freeze-out,

for particles emitted from central rapidity region,for particles emitted from central rapidity region,

5 parameters:5 parameters:

are determined by particle spectra and they are well-known, are determined by particle spectra and they are well-known,

is determined by the ratio for Au-Au at 1 A GeVis determined by the ratio for Au-Au at 1 A GeV

●●particle masses cab be calculated via effective models, particle masses cab be calculated via effective models, such as NJL, linear sigma model, and chiral perturbation theory, thsuch as NJL, linear sigma model, and chiral perturbation theory, the results are almost the same.e results are almost the same.

( , , )B IM T

thermal productionthermal production

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our predicition for our predicition for U-U at 0.6 A GeVU-U at 0.6 A GeV

● ● preliminary numerical resultspreliminary numerical results

KAOS data KAOS data for Au-Au at 1 A GeV for Au-Au at 1 A GeV

our theoretical calculationour theoretical calculation

● ● summarysummary the isospin symmetry breaking, especially the mass splitting, cthe isospin symmetry breaking, especially the mass splitting, c

an self-consistently explain the ration and its energy depan self-consistently explain the ration and its energy dependence.endence.

we also calculated the ratio . we also calculated the ratio .

/

/n p

numerical resultnumerical resultHao, Xiao, Zhuang, 2008Hao, Xiao, Zhuang, 2008

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● ● a support to our ideaa support to our idea

isospin symmetric collisions Ca-Ca: isospin symmetric collisions Ca-Ca: N/Z = 20/20N/Z = 20/20

/ 1 data:data:

Coulomb explanation fails: Coulomb explanation fails: there is still Coulomb there is still Coulomb potential, but the ratio is about 1 potential, but the ratio is about 1 !!

mass-splitting calculation works: fmass-splitting calculation works: for isospin symmetric systems, tor isospin symmetric systems, there is no mass splitting, here is no mass splitting, and therefore we have always and therefore we have always

/ 1

an experimental supportan experimental support

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肖志刚肖志刚