LAMBDA - NUCLEAR INTERACTION and HYPERON PUZZLE in NEUTRON STARS - - PowerPoint PPT Presentation

LAMBDA-NUCLEAR INTERACTION and HYPERON PUZZLE in NEUTRON STARS

Wolfram Weise

Technische Universität München

Equation of State of dense baryonic matter : constraints from massive neutron stars

1

PHYSIK DEPARTMENT

Hyperon-nucleon interactions from SU(3) chiral effective field theory Hyperon-NN three-body forces

Stefan Petschauer, Johann Haidenbauer, et al. :

• Eur. Phys. J. A (2017) (arXiv: 1612.03758 [nucl-th]); Nucl. Phys. A 957 (2017) 347;
• Phys. Rev. C93 (2016) 014001; Eur. Phys. J. A52 (2016)15; Nucl. Phys. A915 (2013) 24

Emerging repulsions : suppression of hyperons in dense neutron matter

Kyoto, 17 May 2017

2

3

Part I: Prologue

Constsaints on Equatjons of Statf fsom massive Neutson Stars

NEUTRON STARS and the EQUATION OF STATE of DENSE BARYONIC MATTER

Mass-Radius Relation

• J. Lattimer, M. Prakash

STRANGE QUARK MATTER

NUCLEONIC MATTER

Tolman-Oppenheimer-Volkov Equations

• Phys. Reports 442 (2007) 109

dM dr = 4πr2 E c2 dP dr = − G c2 (M + 4πPr3)(E + P) r(r − GM/c2)

• Phys. Reports 621(2016) 127

4

quark matter ??

• J. Antoniadis et al.

Science 340 (2013) 6131

Constraints from massive NEUTRON STARS

M = 2.01 ± 0.04

.8 M⇥ conditions

PSR J0348+0432

P .B. Demorest et al. Nature 467 (2010) 1081

Shapiro delay measurement PSR J1614+2230

.8 M⇥ conditions

M = 1.97 ± 0.04

5

M M

6

0.0 0.5 1.0 1.5 2.0

Population of MILLISECOND PULSARS

mass [M] mass [M]

ms pulsars in binaries e.g. with white dwarfs double neutron stars Note: about 25% of population are massive n-stars (M > 1.5 M)

• J. Antoniadis et al. arXiv:1605.01665

7

CONSTRAINTS from NEUTRON STARS

(contd.)

• F. Özel, D. Psaltis, T. Güver, G. Baym, C. Heinke, S. Guillot
• Astroph. J. 820 (2016) 28

Comprehensive analysis of 12 selected neutron stars Atmosphere model fits of X-ray bursts

SAX J1810.8-2609

R = (11.5 − 13.0) km (M = 1.3 − 1.8 Msolar)

• J. Nättilä et al. : Astron. Astroph. 591 (2016) A25

V.F. Suleimanov et al. : arXiv:1611.09885

6 8 10 12 14 16 18 0.5 1 1.5 2 2.5 20 40 60 80 100 120 140 160 180

3

10 !

R (km) ) M (M >>R

ph

r

• K. Hebeler,
• J. Lattimer,
• Ch. Pethick,
• A. Schwenk:
• Phys. Rev. Lett.

105 (2010) 161102

purely “nuclear” EoS kaon condensate quark matter

“Exotic” equations of state ruled out ?

• A. Akmal,

V.R. Pandharipande, D.G. Ravenhall

• Phys. Rev. C 58 (1998) 1804

A.W. Steiner,

• J. Lattimer, E.F. Brown
• Astroph. J. 722 (2010) 33

Mass- Radius Relation

8

CONSTRAINTS from NEUTRON STARS

• F. Özil, D. Psaltis: Phys. Rev. D80 (2009) 103003
• F. Özil, G. Baym, T. Güver: Phys. Rev. D82 (2010)101301

8 10 12 14 16 0.5 1.0 1.5 2.0 R (km) M/M

NEUTRON STAR MATTER from Chiral EFT and FRG

Symmetry energy range: 30 - 35 MeV

Chiral FRG

• M. Drews, W. W.
• Phys. Rev.

C91 (2015) 035802

• Prog. Part. Nucl. Phys.

93 (2017) 69

Radius window

A.W. Steiner, J.M. Lattimer, E.F. Brown EPJ A52 (2016) 18

ChEFT

• T. Hell, W. W.
• Phys. Rev.

C90 (2014) 045801

Chiral many-body dynamics using “conventional” (pion & nucleon) degrees of freedom is consistent with neutron star constraints

9

Crust: SLy EoS

ρc . 5 ρ0

Central core density

100 1000 10000 1 10 100 1000 10000 pQCD 2-tropes w/o mass constraint 2-tropes with mass constraint Neutron matter HLPS 3-tropes w/o mass constraint

. .

0.1

1

10

ε [GeV/fm3]

[GeV/fm3]

P

10−3 10−2 10−1

10

1

pQCD

Polytropes

(with 2 M mass constraint)

Chiral NM − FRG Neutron matter Chiral EFT − FRG

10

NEUTRON STAR MATTER Equation of State

• K. Hebeler et al.

APJ 773 (2013) 11

• M. Drews, W. W.
• Phys. Rev. C91 (2015) 035802

… and extrapolation to PQCD limit

• A. Kurkela et al.
• Astroph. J. 789 (2014) 127

neutron star core region

ChEFT PNJL, Gv ⇥ 0.5 G PNJL, Gv ⇥ 0

50 100 200 300 500 1000 2000 1 5 10 20 100 200 ⇤ MeV fm3⇥ P MeV fm3⇥

NEUTRON STAR MATTER Equation of State

quark-nuclear coexistence can occur at baryon densities realistic “conventional” EoS (nucleons & pions)

quark - nuclear coexistence

see also:

• K. Masuda, T. Hatsuda, T. Takatsuka

PTEP (2013) 7, 073D01

pressure energy density

• Th. Hell, W. W.
• Phys. Rev. C90 (2014) 045801

neutron star constraints

conventional (hadronic) equation of state seems to work

11

ρ > 5 ρ0

(ρ0 = 0.16 fm−3)

In-medium Chiral Effective Field Theory up to 3 loops

(reproducing thermodynamics of normal nuclear matter) 3-flavor PNJL (chiral quark) model at high densities (incl. strange quarks)

12

NEUTRON STAR MATTER including HYPERONS

• T. Hell, W. W.
• Phys. Rev. C90 (2014) 045801

plus hyperons (incl. potential consistent with hypernuclei) 3-flavor PNJL model at high densities (incl. strange quarks)

Λ

In-medium Chiral Effective Field Theory (3-loops) Particle composition: Fraction of particle species as function of baryon density Equation of state too soft : maximum neutron star mass too low

d quarks u quarks s quarks protons L hyperons neutrons

2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 rêr0 ri ê r tot

n p

d u s

quarks

Λ ρi ρ ρ/ρ0

Mmax . 1.5 M

• ccurrence of

hyperons

Λ

µn = µΛ

0.0001 0.001 0.01 0.1 1 1 2 3 4 5 6 !B[!0] "EFT600 p n # e µ K0=200 MeV at=32 MeV

0.5 1 1.5 2 2.5 3 10 12 14 16 M [M0] R [km] K0=300 MeV at=32 MeV NN NSC97a NSC97c NSC97f NSC89 J04 !EFT600

Adding hyperons: equation of state far too soft “Hyperon Puzzle”

NEUTRON STAR MATTER including HYPERONS

• H. Djapo,

B.-J. Schaefer,

• J. Wambach
• Phys. Rev. C81

(2010) 035803

Λ

n p N

N + Λ

13

NEUTRON STAR MATTER including HYPERONS

Inclusion of hyperons: EoS too soft to support 2-solar-mass n-stars unless: strong repulsion in YN and YNN … interactions

M [M0] R [km] PNM N N + NN (I) N + NN (II) 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 11 12 13 14 15

PSR J1614-2230 PSR J0348+0432 n − matter

ΛN

ΛN

ΛN

ΛNN(1) ΛNN(2)

+ +

ChEFT QMC

R [km] M MO

.

• T. Hell, W.W.

PRC90 (2014) 045801

Quantum Monte Carlo calculations using phenomenological hyperon-nucleon and hyperon-NN three-body interactions constrained by hypernuclei

• D. Lonardoni,
• A. Lovato,
• S. Gandolfi,
• F. Pederiva
• Phys. Rev. Lett.

114 (2015) 092301

QMC computations (hyper-neutron matter): ChEFT calculations “conventional” n-star matter

14

Part II

Hyperon - Nucle0n Intfractjons fsom Chiral SU(3) Effectjve Field Tieory

15

u, d

s

MeV 100

c b t

1 10 100 GeV

Hierarchy of QUARK MASSES in QCD

“light” quarks “heavy” quarks

• Separation of Scales -

PDG 2016

Basic principles of

LOW-ENERGY QCD :

Confinement of quarks & gluons in hadrons

Chiral Symmetry

Spontaneously broken (QCD dynamics) Explicitly broken by non-zero quark masses

16

SU(3)L × SU(3)R

NAMBU - GOLDSTONE BOSONS:

Spontaneously Broken CHIRAL SYMMETRY

SU(3)L × SU(3)R

Pseudoscalar SU(3) meson octet

{φa} = {π, K, ¯

K, η8}

DECAY CONSTANTS:

µ

ν

axial current

π

K

Chiral limit: f = 86.2 MeV

⟨0|Aµ

a(0)|φb(p)⟩ = iδab pµ fb

m2

π f 2 π = −mu + md

2 ⟨¯ uu + ¯ dd⟩

Gell-Mann, Oakes, Renner relations

m2

K f 2 K = −mu + ms

2 ⟨¯ uu + ¯ ss⟩

+ higher order

corrections

Order parameter :

17

fπ = 92.21 ± 0.16 MeV

fK = 110.5 ± 0.5 MeV

4π f ∼ 1 GeV

Chiral Effective Field Theory

SU(3)L × SU(3)R

Pseudoscalar meson octet of Realization of Low-Energy QCD for energies / momenta

SU(3)L × SU(3)R

coupled to baryon octet Nambu-Goldstone bosons

× P =    

π0 √ 2 + η √ 6

π+ K+ π− − π0

√ 2 + η √ 6

K0 K− ¯ K0 − 2η

√ 6

   

, B =   

Σ0 √ 2 + Λ √ 6

Σ+ p Σ− − Σ0

√ 2 + Λ √ 6

n −Ξ− Ξ0 − 2Λ

√ 6

   (15)

+ . . .

short distance dynamics: contact terms

+ +

[8] [8] [8] [8] [8] [8]

meson-baryon interaction vertices

based on SU(3) Non-Linear Sigma Model plus (heavy) baryons

Q < 4π f ∼ 1 GeV

18

Chiral Effective Field Theory

SU(3)L × SU(3)R

Starting point: Meson-Baryon Lagrangian (chiral limit)

× P =    

π0 √ 2 + η √ 6

π+ K+ π− − π0

√ 2 + η √ 6

K0 K− ¯ K0 − 2η

√ 6

    , B =   

Σ0 √ 2 + Λ √ 6

Σ+ p Σ− − Σ0

√ 2 + Λ √ 6

n −Ξ− Ξ0 − 2Λ

√ 6

   (15)

LMB = tr ¯ B

• iγµDµ − M0
• B
• − D

2 tr ¯ Bγµγ5{uµ, B}

• − F

2 tr ¯ Bγµγ5[uµ, B]

• with DµB = ∂µB + [Γµ, B],
• space. The constant M0 de

B], Γµ = 1

2(u†∂µu + u∂µu†) a

denotes the baryon mass i ) and uµ = i(u†∂µu − u∂µu†), n the three-flavor chiral lim

Chiral covariant derivative: Chiral (pseudoscalar Nambu-Goldstone boson) field :

U(x) = u2(x) = exp i √ 2P(x) f !

U → R U L†

L ∈ SU(3)L

R ∈ SU(3)R

transforms as

19

Chiral Effective Field Theory

SU(3)L × SU(3)R

Interaction Lagrangian: expand in powers of meson fields P(x)

L1 = − √ 2 2f0 tr

• D ¯

Bγ µγ5{∂µP,B} + F ¯ Bγ µγ5[∂µP,B]

• L2 =

1 4f 2 tr

• i ¯

Bγ µ [P,∂µP],B

• mass terms

+

Input :

Lint = L1 + L2 + . . .

F = 0.46

D = 0.81

(gA = F + D = 1.27)

f = 0.09 GeV

[8] [8]

+ +

[8] [8]

Physical meson and baryon masses (SU(3) breaking)

20

L1 = −fNNπ ¯ Nγµγ5τN · ∂µπ + ifΣΣπ ¯ Σγµγ5 × Σ · ∂µπ −fΛΣπ ¯ Λγµγ5Σ + ¯ Σγµγ5Λ

• · ∂µπ − fΞΞπ ¯

Ξγµγ5τΞ · ∂µπ −fΛNK ¯ Nγµγ5Λ∂µK + h.c.

• − fΞΛK

¯ Ξγµγ5Λ∂µK + h.c.

• −fΣNK

¯ Nγµγ5τ∂µK · Σ + h.c.

• − fΣΞK

¯ Ξγµγ5τ∂µK · Σ + h.c.

• −fNNη8 ¯

Nγµγ5N∂µη − fΛΛη8 ¯ Λγµγ5Λ∂µη −fΣΣη8 ¯ Σ · γµγ5Σ∂µη − fΞΞη8 ¯ Ξγµγ5Ξ∂µη .

• duced the isospin doublets

by [46] fNNπ = f, fNNη8 =

1 √ 3(4α − 1)f,

fΛNK = − 1

√ 3(1 + 2α)f,

fΞΞπ = −(1 − 2α)f, fΞΞη8 = − 1

√ 3(1 + 2α)f,

fΞΛK =

1 √ 3(4α − 1)f,

fΛΣπ =

2 √ 3(1 − α)f,

fΣΣη8 =

2 √ 3(1 − α)f,

fΣNK = (1 − 2α)f, fΣΣπ = 2αf, fΛΛη8 = − 2

√ 3(1 − α)f,

fΞΣK = −f.

+ +

[8] [8]

Chiral Effective Field Theory : meson-baryon vertices SU(3)L × SU(3)R

G G

G

G

G

G G

G G

G

G G

G = gA 2f ' 7 GeV −1 ' 1.4 fm α = F F + D = 0.36

21

Λ Λ Λ N N N π

π

Σ N

22

Chiral SU(3) Effective Field Theory and Hyperon-Nucleon Interactions

Leading

• rder

(LO) Next-to-leading order (NLO)

• J. Haidenbauer, S. Petschauer, N. Kaiser, U.-G. Meißner, A. Nogga, W. W. : Nucl. Phys. A 915 (2013) 24

Example:

Λ N

interaction

Λ Λ Λ N N N

K

K

Λ Λ η N N

2nd order tensor force

V (0)

BB→BB = CS + CT σ 1 · σ 2

V (2)

BB→BB = C1q2 + C2k2 +

• C3q2 + C4k2

σ 1 · σ 2 + i 2C5(σ 1 + σ 2) · (q × k) + C6(q · σ 1)(q · σ 2) + C7(k · σ 1)(k · σ 2) + i 2C8(σ 1 − σ 2) · (q × k),

Hyperon - Nucleon Interaction Contact Terms

• S. Petschauer,
• N. Kaiser
• Nucl. Phys.

A 916 (2013) 1-29

⊗ ⊕ ⊕ ⊕ ⊕ ⊕

S Channel I V 1S0, 3P0, 3P1, 3P2 V 3S1, 3S1-3D1, 1P1 NN → NN – C10∗ NN → NN 1 C27 – −1 ΛN → ΛN

1 2 1 10

!

9C27 + C8s"

1 2

!

C8a + C10∗" ΛN → ΣN

1 2 3 10

!

−C27 + C8s"

1 2

!

−C8a + C10∗" ΣN → ΣN

1 2 1 10

!

C27 + 9C8s"

1 2

!

C8a + C10∗" ΣN → ΣN

3 2

C27 C10

[Polinder, Haidenbauer, Meißner, NPA779, 2006] [Petschauer, Kaiser, NPA91

8 ⊗ 8 = 27 ⊕ 8s ⊕ 1 ⊕ 10 ⊕ 10∗ ⊕ 8a

SU(3) symmetry reduces number of independent constants

23

500 1000 1500 2000 2500 3000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 V!r" [MeV] r [fm]

V

!#$"

• 100
• 50

50 100 0.0 0.5 1.0 1.5 2.0 2.5 u,d,s=0.13840

VC

500 1000 1500 2000 2500 3000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 V!r" [MeV] r [fm]

V

!#s"

1000 2000 3000 4000 5000 6000 0.0 0.5 1.0 1.5 2.0 2.5 u,d,s=0.13840

VC

• 8s: strong repulsive core. repulsion only.

年 月 日水曜日

ΛN(1S0) = 9 10[27] + 1 10[8s]

ΛN(3S1) = 1 2[10∗] + 1 2[8a]

Hyperon - Nucleon Interactions from Lattice QCD

• T. Inoue et al.

(HAL QCD) PTP 124 (2010) 591

• Nucl. Phys.

A881 (2012) 28

mps = 0.47 GeV

note: strong short-distance repulsive interaction towards physical quark masses

24

• 500

1000 1500 2000 2500 3000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 V!r" [MeV] r [fm]

V

!#$*"

• 100
• 50

50 100 0.0 0.5 1.0 1.5 2.0 2.5 u,d,s=0.13840

VC VT

• 年 月

日水曜日

• 500

1000 1500 2000 2500 3000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 r [fm]

V

!#a"

• 100
• 50

50 100 0.0 0.5 1.0 1.5 2.0 2.5 u,d,s=0.13840

VC VT

年 月 日水曜日

25

Two−nucleon force Three− LO NLO N2LO N3LO

NN force 3N for

LO NLO N2LO N3LO NN interaction

N2LO N3LO N3LO 4N force 3N force

BARYON-BARYON INTERACTIONS from CHIRAL EFFECTIVE FIELD THEORY Systematically organized hierarchy in powers of

Q Λ (Q: momentum, energy, pion mass)

NN interaction state-of-the-art: N4LO plus convergence tests at N5LO

BB interactions

3 − body forces

4 − body forces

YN interaction (limited data base): NLO plus three-body forces

TJ

βα(pf, pi; √s) = VJ βα(pf, pi) +

X

γ

Z ∞ dp p2 (2π)3 VJ

βγ(pf, p)

2µγ p2

γ − p2 + iεTJ γα(p, pi; √s)

Coupled-Channels Lippmann-Schwinger Equation

T

=

V

+

T V

α α α

J J J J

β

β β

γ

On-shell momentum of intermediate channel Partial waves (LS)J , baryon-baryon channels α, β

γ determined by :

√s = q M 2

γ,1 + p2 γ +

q M 2

γ,2 + p2 γ

Relativistic kinematics relating lab. and c.m. momenta

26

LO NLO LO NLO

repulsion

phase shift

Hyperon - Nucleon Interaction from Chiral SU(3) EFT

• J. Haidenbauer, S. Petschauer, N. Kaiser,

U.-G. Meißner, A. Nogga, W. W.

• Nucl. Phys. A 915 (2013) 24

27

moderate attraction at low momenta relevant for hypernuclei strong repulsion at higher momenta relevant for dense baryonic matter

LO NLO

δ Λ δ Λ 200 400 600 800 plab (MeV/c)

• 80
• 70
• 60
• 50
• 40
• 30
• 20
• 10

10 20 δ (degrees) Λp

3S1

δ Λ 200 400 600 800 plab (MeV/c)

• 30

30 60 90 120 150 180 δ (degrees) Λp

3S1

δ Λ

Hyperon - Nucleon Interaction (contd.)

Λ Λ N N π

π

Σ N

Triplet-S channel and Λ N ↔ Σ N coupling (2nd order tensor force) In-medium (Pauli) suppression of Λ N ↔ Σ N coupling : increasing repulsion with rising density

ChEFT

ChEFT

Jülich NSC97f

28

included turned off

100 200 300 400 500 600 700

plab (MeV/c)

50 100 150 200

σ (mb)

Eisele et al. Kondo et al.

Σ

−p -> Σ −p

100 200 300 400 500 600

plab (MeV/c)

50 100 150

σ (mb)

Engelmann et al. Stephen

Σ

−p -> Σ 0n

100 120 140 160 180

plab (MeV/c)

50 100 150 200 250

σ (mb)

Eisele et al.

Σ

+p -> Σ +p

Hyperon - Nucleon Interaction (contd.)

elastic and charge exchange scattering

ΣN

LO LO LO NLO NLO NLO

Quest for much improved hyperon-nucleon scattering data base !

• J. Haidenbauer, S. Petschauer, N. Kaiser,

U.-G. Meißner, A. Nogga, W. W.

• Nucl. Phys. A 915 (2013) 24

29

100 200 300 400 500 600

plab (MeV/c)

50 100 150

σ (mb)

Engelmann et al. Stephen

Σ

−p -> Λn

100 120 140 160 180

plab (MeV/c)

50 100 150 200 250 300

σ (mb)

Engelmann et al.

Σ

−p -> Λn

Hyperon - Nucleon Interaction (contd.)

reaction

• J. Haidenbauer, S. Petschauer, N. Kaiser,

U.-G. Meißner, A. Nogga, W. W.

• Nucl. Phys. A 915 (2013) 24

ΣN → ΛN

Quest for much improved hyperon-nucleon scattering data base !

LO LO NLO NLO

30

Part III

Hyperon Intfractjons in Nuclear and Neutson Matuer

31

Density dependence of

• nuclear single particle potential

YNN three-body forces from Chiral SU(3) EFT Towards a solution of the “hyperon puzzle” in neutron stars ?

Λ

32

HYPERON - NUCLEON - NUCLEON THREE-BODY FORCES from CHIRAL SU(3) EFT

NNLO:

[8] [8] [8] [8] [8]

Chiral SU(3) Effective Field Theory: interacting pseudoscalar meson & baryon octets + contact terms 3-baryon sector: Chiral SU(3) Effective Field Theory with explicit decuplet baryons:

explicit baryon decuplet : promotion to NLO

[10] [10] [10] [10]

• S. Petschauer et al. Phys. Rev. C93 (2016) 014001

6

• S

−1 −2 −3 I3 − 3

2−1 − 1 2 0 1 2

1

3 2

T T T T T T       q q q q q q q q q q

∆− ∆0 ∆+ ∆++ Ξ∗− Ξ∗0 Σ∗+ Σ∗− Σ∗0 Ω−

Decuplet Dominance in YNN three-body forces

Estimates of YNN 3-body interactions assuming dominant decuplet (Σ∗, ∆)intermediate states

[10]

[10] [10] [10] [10]

… much reduced set of parameters basic vertices :

• vertices
• n
• ne constant

nt (C = 3

4gA ≈ 1 from ∆ → Nπ)

two

two constants (Pauli-forbidden in NN sector) [8] [10] [10] [8] [8] [8] [8]

33

transition type B∗ NNN → NNN ππ ∆ ΛNN → ΛNN ππ Σ∗ ΛNN → ΛNN πK Σ∗ ΛNN → ΛNN KK Σ∗ ΛNN → ΛNN π Σ∗ ΛNN → ΛNN K Σ∗ ΛNN → ΛNN ct Σ∗ ΛNN ↔ ΣNN ππ ∆, Σ∗ ΛNN ↔ ΣNN πK ∆, Σ∗ ΛNN ↔ ΣNN πη Σ∗ ΛNN ↔ ΣNN KK Σ∗ ΛNN ↔ ΣNN Kη Σ∗ ΛNN ↔ ΣNN π ∆, Σ∗ ΛNN ↔ ΣNN K Σ∗ ΛNN ↔ ΣNN η Σ∗ ΛNN ↔ ΣNN ct Σ∗ → ΛNN → ΛNN NN NN

Example : three-body interactions

ΛNN

Λ

Σ∗

N N

π π

Λ

Σ∗

N N

π

Λ N N Λ N N

K

Λ

Σ∗

N N

Λ N N

K K

T q q q q

q q q

—

—

—

π

Σ∗

Λ N N

Λ N N

—

Σ∗

Λ N N Λ

N N

K

LO

6q q

— —

—

Λ N N Λ N N

Σ∗ 34

Density-dependent EFFECTIVE HYPERON - NUCLEON INTERACTION from CHIRAL THREE-BARYON FORCES

• S. Petschauer, J. Haidenbauer, N. Kaiser, U.-G. Meißner, W. W. Nucl. Phys. A957 (2017) 347

V12 = X

B

tr3 Z

|~ k|kB

f

d3k (2⇡)3 V123 ,

LO N LO N

LO

density-dependent effective interaction

Λn

V eff,ππ

Λn

= C2g2

A

2f 4 ∆ [ρn + 2ρp] + F(kp

F , kn F ; p, q)

V eff,π

Λn

= CH gA 9f 2 ∆ [ρn + 2ρp] + G(kp

F , kn F ; p, q)

V eff,ct

Λn

= H2 18∆ [ρn + 2ρp]

Decuplet-octet mass difference ∆ = M[10] − M[8] = 270 MeV

repulsive repulsive

+/-

Coupling parameters : C = 3

4gA ' 1 − 1 f 2 . H . + 1 f 2

(dim. arguments natural size)

35

36

ΛNN three-body force transformed into

density-dependent effective two-body interaction Momentum-space potentials increasing repulsion ~ proportional to density

0.0 0.5 1.0 1.5 2.0 0.2 0.4 V(p,p) [fm]

VΛn VΛn+V

med(ρ0)

VΛn+V

med(2ρ0)

VΛn+V

med(3ρ0)

0.0 0.5 1.0 1.5 2.0 p [fm

• 1]
• 0.1

0.1 0.2 3P0 3P1

effective interaction in neutron matter

• S. Petschauer, J. Haidenbauer, N. Kaiser, U.-G. Meißner, W. W.

NP A957 (2017) 347

Density-dependent EFFECTIVE HYPERON - NUCLEON INTERACTION from CHIRAL THREE-BARYON FORCES

Λn

0.0 0.5 1.0 1.5 2.0

• 2
• 1.5
• 1
• 0.5

0.5 1 V(p,p) [fm]

VΛn VΛn+V

med(ρ0)

VΛn+V

med(2ρ0)

VΛn+V

med(3ρ0)

0.0 0.5 1.0 1.5 2.0 p [fm

• 1]

0.5 1 1.5 2 2.5 3 3.5 4 V(p,p) [fm] 1S0 3S1

˜ V(p, p) [fm]

(H = + 1 f 2 )

0.8 1.0 1.2 1.4 1.6 1.8 2.0 kF [fm−1] −80 −70 −60 −50 −40 −30 −20 −10 UΛ(kΛ = 0) [MeV]

χEFT LO 650 χEFT NLO 650 Nijmegen ’97

Density dependence of single particle potential

Λ

0.6 0.8 1.0 1.2 1.4 1.6 kF (1/fm)

• 60
• 45
• 30
• 15

UΛ (MeV)

LO NLO LO NLO

hypernuclei Brueckner calculations

using chiral SU(3) interaction=

+

G G

Λ

Λ

dense matter

• J. Haidenbauer,

U.-G. Meißner,

• Nucl. Phys. A 936 (2015) 29
• S. Petschauer et al.,
• Eur. Phys. J. A52 (2016) 15

37

G(!) = V + V Q e(!) + i✏G(!)

(“continuous choice”)

in symmetric nuclear matter - YN two-body interactions only

Λ

0.5 1.0 1.5 2.0 ρ / ρ0

• 40
• 20

20 UΛ (MeV)

(a) 38

Density dependence of single particle potential

Λ

Brueckner calculations

using chiral SU(3) interactions

= +

G G

… towards a possible solution of the “hyperon puzzle”

• J. Haidenbauer,

U.-G. Meißner,

• N. Kaiser,
• W. W.

arXiv:1612.03758 EPJA (2017) to appear

symmetric nuclear matter

hypernuclei

NLO NLO+3BF NSC97f Jülich‘04

Chiral SU(3) 2- and 3-body forces

0.5 1.0 1.5 2.0 ρ / ρ0

• 40
• 20

20 UΛ (MeV)

(b)

NLO NLO+3BF

Nijmegen NSC97f

neutron matter

G(!) = V + V Q e(!) + i✏G(!)

(H = − 1 f 2 )

39

ρ ρ

• 40
• 20

20 UΛ (MeV)

(b)

NLO NLO+3BF

neutron matter

0.5 1.0 1.5 2.0 ρ / ρ0

• 40

Λ

Nijmegen NSC97f

• 10
• 30

ρ ρ

• 20

UΛ (MeV) ρ ρ

Λ

• 10

10

towards a possible solution of the “hyperon puzzle” in neutron stars

E = (En + EΛ)ρ

µn = ∂E ∂ρn

EΛ ' 3 (kΛ

F )2

10 M ∗

Λ

+ UΛ(ρ)

grows as fast as

EΛ

with increasing density: no hyperons in n-star matter

Chiral SU(3) 2- and 3-body forces

If

Hyperons in the core of neutron stars ?

Quick estimate

SUMMARY

Constraints on dense baryon matter equation-of-state from neutron stars : Single particle potential of a in nuclear and neutron matter

40

Progress in constructing hyperon-nuclear interactions from Chiral SU(3) Effective Field Theory very stiff EoS required ! “non-exotic” EoS (nuclear chiral dynamics) seems to work hyperon puzzle: naively adding hyperons implies far too soft EoS YN two-body interactions at NLO YNN three-body forces

Λ N ↔ Σ N

importance of (2nd order pion exchange tensor force)

Λ

moderately attractive at low density (hypernuclei) strongly repulsive at high density . . . towards solution of “hyperon problem” in neutron stars