中性子星における
Σハイペロン混合の効果について
Kohsuke Tsubakihara
Department of Cosmophysics,
Hokkaido University
Akira Ohnishi
YITP, Kyoto University

Introduction• Our interest: dense matter EOS including YNS matter, SN

Finite system andnuclear matter

Dense matter EOSΛSdu

HyperonpotentialΛ, Σ and Ξ hypernuclei(bound state spectroscopy)[1] Lattimer and Swesty, NPA 535 (1991) 331. [2] Shen et al., PTP 100 1013. [3] Yamamoto, Nishizaki and Takatsuka, NPA 691 (2001) 432c.
[4] Schaffner and Mishustin PRC 53 (1996) 1416. [5] Schaffner-Bielich, NPA 804 (2008) 309..

Chiral symmetry
in hadron phase• Chiral symmetry in hadron:
π as Nambu-Goldstone bosonand its chiral partner, σ• Chiral potential in RMF model:suggested from QCD (c.f. NJL model) andcorresponding to chiral restoration in nuclearmedium• ω and ρ mass modification[12]▫ Evidences of partial chiral symmetry
restoration in nuclear medium?
▫ Theoretical model overestimates
mass modification compared to [13]where all of vector meson mass is generated from chiralcondensate.

[6] Naruki et al., PRL 96 (2006) 092301. [7] Brown and Rho, PR 363 (2002) 85; Hatsuda and Lee, PRC 46 (1992) R34.

Motivation• Our interest: dense matter EOS with Y
NS matter
Finite system andnuclear matter

Hyperonpotential

Dense matter EOS
RMF model withchiral potential
explaining
hypernuclear dataΛ, Σ and Ξ hypernuclei(Hard to directly observe)

Field theoreticalmodel

PhysicalSymmetry
Flavor symmetry,
Chiral symmetry[1] Lattimer and Swesty, NPA 535 (1991) 331. [2] Shen et al., PTP 100 1013. [3] Yamamoto, Nishizaki and Takatsuka, NPA 691 (2001)
432c.

Model description• RMF LagrangianScalar mesons: Attractive
part of baryon interaction

Kinetic part of mesons


Vector mesons: Repulsive
part of baryon interaction

Effective potential ofmesons

Long standing problems: Too early chiral restoration,very stiff EOS, instability on chiral potential
What form should the meson potential have?
⇒ Constrained by chiral symmetry, derived from SCL-LQCD

Chiral potential
derived from SCL• Start point: Action of gluon and fermion on strong
coupling limit of Lattice QCD ( g→∞) at T = 0S= SG + SF +m0 χχ• After bosonizing fermion pair and integratingfermion U= − a log  σ  +bσ 2  − a log  det MM†  +btr  MM† 22SUf(2) caseaU= − log  det MM †  +b tr MM† −cσ σ2[ ]

1 ϕ−a log  f π +ϕ − ϕ+2 fπ
11 mσ ϕ 2 m π π 222222aSUf(3) case
U= − log  det MM †  +b tr MM† −cσ σ −c ζ ζ2+d det M+ det M† [[−a log  f π +ϕ π −   ] ]ϕ πfπ1 ϕ π
2 fπa1 ϕ ζ− log  f ζ +ϕ ζ −ϕ ζ 22 fζ2211 mσ ϕ σ  m π π 22222211 mζ ϕ ζ  m K K 222222+ξ σζ ϕ σ ϕ ζ[8] Kawamoto and Smit, NPB 190 (1981) 100. [9] Kawamoto, Miura, Ohnishi and Ohnuma PRD 75 (2007) 014502.

SCL3 RMF model• Logarithmic SCL Chiral PotentialProperty of chiral potential: Neither
instability nor abnormal vacuumConsistent with reproducing BE ofnormal nuclei, SΛ of single Λ nuclei,ΔBΛΛ of 6ΛΛHe and FP EOS(K～210MeV softened by hidden
strange condensate ζ= SS
 Calculated NS mass underlies the mostreliable observation, 1.44 M☉ when weinclude hyperon degrees of freedom
What are key ingredients which are efficient to refine ?
[10] KT, Maekawa, Matsumiya and Ohnishi, arXiv:0909.5058

Scalar and vector
potential in matter• Repulsive potential from ω:Good agreement withDBHF result by 3ρ0 but
seems to be insufficientfrom higher ρB• Cω: Strength of ω meson
potential and known as thesuppresser of vector meson
fieldC ω ＝0C ω ～70C ω ＝200 and300

To reduce this strength, we would like to suggest“Density dependent type coupling (σωN)”Density dependent typecoupling• May be derived from
NLO calculation on SCL-LQCD• Scalar potential(∝σ)⇒saturateVector potential (∝ω)
⇒increase linearly• σωN coupling: effective aroundρ0 and not important in high ρBHere, we introduce σωN couplingg ω =gω0 +gσωN ϕ σand we examine its effect to the propertyof sym. nuclear matter and NS matter

Interesting feature• Is the ratio of hyperon fraction in NS changed by Σhyperon potential?


Determined by SUf(3) symmety and the atomicshifts(AS) of Σ－
Repulsive but weak vector-isovector meson
coupling: Σ hyperon may appear on NS

Aim of this study• Is SCL3 RMF model be able to support
maximum mass of neutron star?
–Can density dependent type coupling resolve
this problem?

• On another RMF model, is the ratio of hyperon
fraction in NS also changed by Σ hyperonpotential determined by the atomic shifts(AS) ofΣ－?

Result(1)• Σ hyperon potential:
determined by the atomicshifts(AS) of Σ－• Σ－ appear at lower ρB than
Λ → contradict to other calc.
where AS are not reproduced.

Result(2)• To confirm this situation, we also use thephenomenological RMF model with non-linear
potential(TM1)• We can find the same situation occurred in thiscalculation and Σ can appear in NS matter even
if it has a repulsive potentialResults(3)Maximum mass of Neutron Star
Neutron Star EOS with Hyperon effect:→Inclusion of Hyperon make NS EOS softened athigh density phase
Recent observation
may confirm heavier
maximum mass ofneutron star, 1.7M☉
New SCL3 DDC RMF
model seems not tobe enough to explain
this observation.

Summary• RMF model with chiral SU(3) potential (SCL3)▫ Saturation property, incompressibility, BE, S Λ, and ΔBΛΛare well reproduced in appropriate parameter range.
▫ Calculated NS matter EOS underestimates observed NS mass.

• Key for the property in high ρB phase: Cω▫ Density dependent type coupling (σωN type coupling)⇒This needs not too large Cω to reproduce nuclear property.
Calculated results seems not to support 1.7 M ☉ if hyperon effects aretaken into account properly.
• Ordering of hyperon appearance▫ Atomic shifts of Σ－: one of key ingredients of this topic▫ Ordering may be changed but that does not affect the final result somuch so far.

• In future……
▫ Finite temperature EOS for supernovae simulation

Thank you for listening!!