Aug. 19-22, 2013 @ TAMU

Symmetry energy with non-nucleonic degrees of freedom

Wei-Zhou JiangDepartment of Physics,

Southeast University, China

Collaborators: Bao-An Li, et al.

Aug. 19-22, 2013 @ TAMU

Introduction Hyperons, quarks, dark matter? Symmetry energy and quarks &

hyperons Interaction of quarks and its effects In neutron stars, effect of dark

matter? Summaries

Outline

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— E=

Liquid-drop model for nuclei

SYMMETRY ENERGY

W. D. Myers, W.J. Swiatecki, P. Danielewicz,……

s2 4

ym ( )( , ) ( ), ( ),0) /( n pE OE E

In isospin asymmetric matter:

Aug. 19-22, 2013 @ TAMU

Where it is the matter, there is the symmetry energy.

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L.W.Chen,et.al., PRC72, 064309 (05)Fuchs, et.al., arXiv:nucl-th/0511070

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Diverse trends from data

1. Xiao, Li, et.al PRL102, 062502 (2009) 2. Feng&Jin, PLB683 (2010) 140

3. P. Russotto,W. Trauntmann, Q.F. Li et al., PLB697, 471(2011)

31.6(ρ/ρ)γ,with γ=0.9+/-0.4 ： almost linear

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Factor to soften greatly the Symmetry Energy:• Tensor force

C. Xu and B. A. Li, PRC81, 064612:

I. Vidana, A. Polls, and C. Providencia, PRC 84, 062801(R)

.

The dense the matter, the uncertain the symmetry energy

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Significant points:

• To go ahead to deal with Tensor force with pion & rho: the most important ingredients of the chiral perturbative theory in Density dependent RHF approach: the simple, self-consistent and covariant framework.

• Here, we just go beyond this point to discuss contributions of non-nucleonic components to the symmetry energy.

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Non-nucleonic degrees of freedom

• Threshold for hyperons reaches at high densities; 2ρ0-4ρ0

• Hadron-Quark transition may occur for nucleon overlaps >2ρ0

• In astrophysical extraction of the symmetry energy, there may be the effect of unknown dark matter.

• What is the effect of these components in dense matter? Matter changes, so does the interaction, so does the symmetry energy?

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Model Lagrangian (RMF) :

with

Hyperons:

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).-)/(-(

,)()(// 20

pn

symEeAE

N

F

FNsym E

kCE *

222

0

2

2

6

1

2

1)/(

)1)((4

1)(

pnsymE

EoS with inclusion of hyperons

Definition of symmetry energy:

at given hyperon fraction.

for charge neutral and chemical equilibrated matter

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RMF models: SLC and SCLd

Jiang， Li， and Chen, PLB653， 184 （ 07）；PRC76, 054314 (07); ApJ756， 56（ 12）

Demorest, et al., Nature 467, 1081(2010)： PSR J1614-2230

RMF model NL3: Lalazissis, et. al. PRC 55, 540(97).

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symE

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Symmetry energy with quarks

QH

QH

YY

YY

)1(

)1(

).)/(-(

,),(),(),(),(// 220

pnpnH

QQsymH

Hsym YEYEYeY

3/3/ ,3/23/ , ensdenuQH pp

Y is the quark phase proportion, determined by Gibbs conditions.We just consider the symmetric matterα=0

a function of α

0

2

2 )/(

2

1

symE

Step 1: no interaction between Qs & Ns

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Critical density

Calculation detail: Charge chemical potential neglected here!

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HsymE

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Symmetry energy of quark flavor

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With Λ hyperons

Jiang et al,PRC87, 064314(2013)

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Questions:

• Clear model dependence of the transition density and the symmetry energy

• Why the transition density is so small as the strange quarks are included?

• Chemical potential and mechanical equilibriums should be corrected by interactions between quarks

Aug. 19-22, 2013 @ TAMU

Grand thermodynamical potential of quarks

,3

1)1(

34

1

?,)()()(

,

23/44

3/23/20

3/2

3/12

,,QQQQQ

sduiiQM

QM

aa

ppp

p

Qii

ii U

p

;

)/(2

Weissenborn, et al, arXiv:1102.2869Alford, et al, APJ629:969(2005)

Mechanical and chemicalequilibriums

Step 2: interactions for quarks

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Preliminary results:

3-flavor

2-flavor

No QCD correction

QCD corr., a4=0.6

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No QCD corrections No correction to asymmetric part

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23/4

3

1QQa

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• Symmetry energy: calculation is yet to make

• Step 3: interaction between Q’s & N’s

),(),(),(),(

),(

),(),(),(),(//

0000

220

YeYeYeYe

YE

YEYEYeY

MQH

QHM

QQsymH

Hsym

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Dark matter in neutron stars

Only gravitational attraction between normal matter and dark matter

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Symmetry energy extraction with Dark matter

Steiner:PRL 108, 081102 (2012)

Effect of Dark Matter?

Guillot et al. 2013, ApJ 772

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DM with interactions

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Summary

• Non-nucleonic degrees of freedom do affect the symmetry energy.

• Experimental extraction of symmetry energy at high densities should be of caution about the effects of new phases

• The astrophysical extraction of symmetry energy could undergo the influence of celestial dark matter that belongs to an unknown universe.

Aug. 19-22, 2013 @ TAMU

Thank you for your attention!Thank you for your attention!