Effects of Σ and Ξ
isovector potentials toneutron star EOS
KOHSUKE TSUBAKIHARA, TORU HARADAOSAKA ELECTRO-COMMUNICATION UNIVERSITYAKIRA OHNISHIYITP, KYOTO UNIVERSITY

Introduction

Ambiguity in dense inner region of NS• New DOF such as Exotic
particle soften NS EOS• Emergence of hyperon:needs to treat “finite”
hypernuclear systems inorder to determine
hyperon potential• Framework which enable
to treat finite/infinite system→RMF modelIntroduction
Observation of massive neutron star

“Most EOS curves involving exotic
matter, such as kaon condensatesor hyperons tend to predict
maximum masses well below 2.0 M☉
and are therefore ruled out.”

Personal motivationPrevious works on SCL3 RMF model• Logarithmic meson potential
derived from Strong Coupling
Limit of lattice QCD• Emergence of Σ－: suggested fromreduced IV potential of Σ
• Smaller NS mass: requirement ofmany-body interaction in RMF?

Hypernulcer Symmetry EnergyAtomic shift of Σ－: Attractive potential around surface

Difference between Σ＋ and Σ－ potentials→ proportional to“Hypernulcear” symmetry energy: 15MeV(SU(3))→5MeV(fit)Σ－ fraction in NS EOSBaryon fraction and Efi － qBiμC (Efi =2𝑝𝑓𝑖+ 𝑀∗ 2 + 𝑉vec )Physical motivationMore massive NS than 2M☉:
How can be explained in RMF model?
→ n=3 meson-baryon couplingsCan Σ－ survive in NS EOS in case we consider aboven= 3 couplings and how large effects does Σ－ takefrom those couplings

Heavier negative-charged hyperon Ξ－:Which will appear on NS EOS at high ρB, Σ－ or Ξ－?

①n=3 RMF model

FOR UNDERSTANDING
MAXIMUM MASS OF NSRMF model

n=B/2+M+D=2 RMF Lagrangian + meson potentials

Non-linear meson potentials
Interactions among mesons in finite/infinite system

Higher order terms than n=3 meson-baryon couplings

n=3 coupling in RMF



n=B/2+m+D=3 couplings

Number n corresponds to the number of baryons
participating in each interactionIsoscalar type couplings

Isovector type couplings
それぞれscalar、vector型結合

Parameter setting

n=2 couplings→Saturation point ofSym. matter, Binding/Separationenergy of normal/hyper nuclei,
and charge rms radii of finite nuclei

n=3 couplings①Scalar potential in nuclear matteraround ρ0②Symmetry energy of pure neutron
matter around ρ0

Results: SΛ from single Λ hypernuclei• Role of incompressibility toSΛ⇒Almost free if we decide
n=3 couplings where Λparticipate⇔ We can determine thestrengths of n=3 couplings of Λ
enough to each parameterset characterized by theincompressibility.

Results: Σ－ optical potential

Smaller hypernuclear
symmetry energy: 5～0MeV
suggested from factorized
n=3 coupling of Σ－Baryon Fraction plot with 𝜇• Emergence of hyperons is pushed tohigher ρB region.
• Calculated NS mass can excess 2M☉
although hyperons are taken intoaccount.(K=325MeV)

②Isovector pot.
of hyperons

FOR UNDERSTANDINGCOMPOSITION OF NS

Σ－ fraction in NS EOSFor simplicity, we start from TM1 RMF model (n=2 coupl. and Ueff)

Ξ－ Atomic Shifts(Preliminary results)Difference from isovector(IV) pot.

R: ratio to SU(3)constraind IV coupl.

 Difference on Ξ－ AS: seen in heavier core
 Almost free from hyperon-hyperon int.
⇒constrained by SU(6)/SU(3) symmetry

Baryon Fraction of Σ and Ξ(Preliminary results)

Dotted line: Ξ－Σ－ may survive in NS matter even if Ξ－ is taken into account (UΞ(12C-Ξ－)=-14MeV).

SummaryΣ－ may allow to emerge in NS matter EOS if we respect theexperimental results of Σ－ atomic shifts.

Ξ－ may be dominant negative-charged hyperon but Σ－
may also survive and that depends on Ξ－ IV interaction
which may be examined by Ξ－ atomic shifts.

n=3 couplings in RMF model:well characterized by incompressibility and constrained byreproducing experimental/empirical values ofnuclear/hypernuclear systems.

Calculated NS mass excess 2M☉(K=325MeV).

Even if we introduced n=3 coupling to Σ－, Σ－ may appear in
NS EOS as substitute of negative particles.

Thank you
for your listening.
THAT’S ALL.