TOPICS in LOW - ENERGY QCD with STRANGE QUARKS Wolfram Weise T - - PowerPoint PPT Presentation

TOPICS in LOW-ENERGY QCD with STRANGE QUARKS

31st Reimei Workshop 18 January 2016

Wolfram Weise Symmetry breaking patterns in low-energy QCD: Chiral SU(3) effective field theory Strangeness in dense baryonic matter Constraints from two-solar-mass neutron stars Hyperon-nucleon interactions: Chiral EFT and Lattice QCD

Technische Universität München

Antikaon-nucleon interactions and status of systems:

Λ(1405)

¯ KNN

reactions

K− d

ASRC Tokai, Japan

1

PHYSIK DEPARTMENT

Kaonic deuterium and In-medium meson spectral function and implications

φ

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 2014

• wn

Basic principles of

LOW-ENERGY QCD :

special role of STRANGE QUARKS

Confinement of quarks & gluons in hadrons

Chiral Symmetry

spontaneously broken (QCD dynamics) explicitly broken by non-zero quark masses

2

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 :

3

fπ = 92.21 ± 0.16 MeV

fK = 110.5 ± 0.5 MeV

4π f ∼ 1 GeV

4

Spontaneously Broken CHIRAL SYMMETRY

GOLDSTONE’s Theorem: Massless Nambu-Goldstone bosons do not interact in the limit of zero momentum (long-wavelength limit) S-wave interactions of NG bosons

T ∼ E f 2

scattering amplitude

explicit chiral symmetry breaking meson decay constant

• rder parameter of

spontaneous chiral symmetry breaking E = p m2 + k2

Tomozawa - Weinberg low-energy theorem

(d)

CHIRAL SU(3) EFFECTIVE FIELD THEORY

• rdered hierarchy of driving interactions

next-to-leading order (NLO) input: several low-energy constants

O(p2) [8] [8]

pseudoscalar meson octet baryon

• ctet

Leading order terms (Weinberg & Tomozawa) Examples: (S = -1) and (S = +1) threshold (s wave) amplitudes :

¯ KN

KN

T(K+p)thr = 2 T(K+n)thr = −mK f 2

T(K−p)thr = 2 T(K−n)thr = mK f 2

attractive repulsive

+ +

5

6

PART I

Antikaon - Nucleon Interactions and the K(1405)

• brief status report -

th

L

**(1520)

L

*(1405)

S

*(1385)

`KN

Sp Lp

1500

• rld of antikaon-nucleon scattering

KN

_

√s [MeV]

Low-Energy Interactions

Chiral Perturbation Theory NOT applicable:

Λ(1405)resonance 27 MeV below threshold

• N. Kaiser, P

. Siegel, W. W. (1995)

• E. Oset, A. Ramos (1998)

Leading s-wave I = 0 meson-baryon interactions (Weinberg-Tomozawa)

¯ K

N

π

Σ ¯ K N

π

Σ ¯ K N Σ

π

¯ KN

πΣ

channel coupling Framework: Chiral SU(3) Effective Field Theory . . . but :

Non-perturbative Coupled Channels approach based on Chiral SU(3) Dynamics

Recent Review:

• T. Hyodo, D. Jido
• Prog. Part. Nucl. Phys. 67 (2012) 55

K−p

7

KN

SIDDHARTA

CONSTRAINTS from SIDDHARTA

Kaonic hydrogen precision data

• M. Bazzi et al. (SIDDHARTA collaboration)
• Phys. Lett. B 704 (2011) 113

Strong interaction 1s energy shift and width

∆E = 283 ± 36 (stat)± 6 (syst) eV

Γ = 541 ± 89 (stat)± 22 (syst) eV

Hydrogen spectrum

Kaonic hydrogen

K K higher

KO76 KN65 Cu Ti K Ti K KC65 KC75 KO65 KC54 KAl87

EM value K-p K

8

− ε1s =

0.5 1 1.5 2 2.5 1340 1360 1380 1400 1420 1440 E (MeV)

[fm] Im f(K−p → K−p)

• 1
• 0.5

0.5 1 1.5 1340 1360 1380 1400 1420 1440 E (MeV)

Re f(K−p → K−p) [fm] √s [MeV]

√s [MeV]

Re a(K−p) Im a(K−p)

K−p

SCATTERING AMPLITUDE from CHIRAL SU(3) COUPLED CHANNELS DYNAMICS Complex scattering length (including Coulomb corrections)

f(K−p) = 1 2

• f ¯

KN(I = 0) + f ¯ KN(I = 1)

• Im a(K−p) = 0.81 ± 0.15 fm

Re a(K−p) = −0.65 ± 0.10 fm

Λ(1405)

Λ(1405)

: ¯ KN (I = 0) quasibound state embedded in the πΣ continuum

• Y. Ikeda, T. Hyodo, W. W.

PLB 706 (2011) 63 NPA881 (2012) 98

Prototype example for emergence of resonant structure close to a threshold

9

• incl. SIDDHARTA

constraints

plus potentially important information about K-NN absorption

CHIRAL SU(3) COUPLED CHANNELS DYNAMICS

Predicted antikaon-neutron amplitudes at and below threshold

• Y. Ikeda, T. Hyodo, W. Weise : Phys. Lett. B 706 (2011) 63 , Nucl. Phys. A 881 (2012) 98

Needed: accurate constraints from antikaon-deuteron threshold measurements

complete information for both isospin I = 0 and channels

I = 1 ¯ KN

0.8 0.6 0.4 0.2 0.0

• 0.2
• 0.4

1440 1420 1400 1380 1360

real part WT WTB NLO

0.8 0.6 0.4 0.2 0.0 1440 1420 1400 1380 1360

imaginary part WT WTB NLO

Re f(K−n → K−n) Im f(K−n → K−n) [fm] [fm] √s [MeV] √s [MeV]

TW TW TW + Born TW + Born NLO NLO

a(K−n) = 0.57+0.04

−0.21 + i 0.72+0.26 −0.41 fm

10

Re a(K−d) [fm] Im a(K−d) [fm]

excluded excluded (a) (b) (c)

ANTIKAON - DEUTERON SCATTERING LENGTH Calculations using SIDDHARTA - constrained input

Three-body multiple scattering using IkedaHyodoW scattering lengths

• S. Ohnishi, T. Hyodo,
• Y. Ikeda, W. W. (2014)

Faddeev calculation separable “chiral” amplitudes

N.V. Shevchenko NPA 890-891 (2012) 50

• M. Döring, U.-G. Meißner
• Phys. Lett. B 704 (2011) 663

Non-relativistic effective field theory

11

Looking forward to: KAONIC DEUTERIUM measurements SIDDHARTA2 and J-PARC E57

Λ(1405) : RECENT NEWS

@ CLAS / JLab

)

2

) (GeV/c

• π

+

Σ M(

1.35 1.4 1.45 1.5 1.55

)

2

counts /(5 MeV/c

500 1000 data (1405) Λ (1520) Λ

+

Σ

*

K (1385) Σ (1670)

*

Y

(a)

• )

2

) (GeV/c

• +

M(K

1 1.5

)

2

) (GeV/c

• +
• M(

1.3 1.4 1.5 1.6 1.7 1.8 10 20 30 40

(b)

Detailed analysis of

γ p → K+ π− Σ+

• K. Moriya et al. (CLAS collaboration)
• Phys. Rev. Lett. 112 (2014) 068103

Σ+π− Σ+

JP = 1 2

−

distribution and polarization confirms

• f Λ(1405)

12

• K. Moriya et al.

(CLAS collaboration)

• Phys. Rev.

D88 (2013) 045201

0.2 0.4 0.6 0.8 296 ¯ KN πΣ qqq |Λ∗|n|2

m [MeV]

570 ¯ KN Σ

] m

570 ¯ KN πΣ qqq 0.2 0.4 0.6 0.8 |

Λ(1405)

Structure of from Lattice QCD

|Λ∗⟩ = a|uds⟩ + b|(udu)(¯ us)⟩ + . . .

• quasi

molecular

constituent quark dominated

8 |Λ∗|n|2

“light” quarks

structure

¯ KN

“heavier” quarks

mπ ≃ 0.3 GeV

mπ ≃ 0.6 GeV

J.M.M. Hall et al. ; Phys. Rev. Lett. 114 (2015) 132002

Note: qualitative structural change depending on quark mass

(interplay of spontaneous & explicit chiral symmetry breaking)

Recent developments:

13

light sector strange sector 0.0 0.1 0.2 0.3 0.4 0.0 0.2 0.4 0.6 0.8 1.0 mΠ

2 @GeVêc2D

GM @ΜND

14

• Λ(1405)

Structure of from Lattice QCD (contd.)

Strangeness magnetic form factor of Λ(1405)

0−

1 2

+

Quasi-molecular state: s-quark localised in Kbar subcluster

J.M.M. Hall et al.

• Phys. Rev. Lett.

114 (2015) 132002

strange quark does not contribute to magnetic structure

!"## !"$# !""# !"%# &$# &"# &%# &'# #($ #(" #(% #(' #($ #(" #(% #('

!"#$%&

!"#$%&#'"(% )*#$%&#'"(% +,+&#-.'"(%

• T. Hyodo, D. Jido, arXiv:1104.4474

¯ KN

πΣ

The TWO POLES scenario

• D. Jido et al.
• Nucl. Phys. A723 (2003) 205

d

• m

i n a n t l y

π Σ

dominantly

¯ KN

• T. Hyodo, W. W.
• Phys. Rev. C 77 (2008) 03524
• T. Hyodo, D. Jido
• Prog. Part. Nucl. Phys. 67 (2012) 55

Pole positions from chiral SU(3) coupled-channels calculation with SIDDHARTA threshold constraints:

E1 = 1424 ± 15 MeV Γ1 = 52 ± 10 MeV

Γ2 = 162 ± 15 MeV

E2 = 1381 ± 15 MeV

• Y. Ikeda, T. Hyodo, W. W. :
• Nucl. Phys. A 881 (2012) 98

Characteristic feature of Chiral SU(3) Dynamics : Energy dependent driving interactions

Note: phenomenological potential approach is qualitatively different: energy-independent interaction, single pole Λ(1405)

15

• Y. Akaishi, T.

Yamazaki

0.1 0.2 0.3 1350 1400 1450 1500

(a) E-dep.

dσ/dMπΣ(µb/MeV) MπΣ(MeV) π+Σ- π-Σ+ π0Σ0

• Scenarios:

TWO-POLES ENERGY-DEPENDENT vs. SINGLE-POLE ENERGY-INDEPENDENT

Three-body coupled channels (Faddeev) calculations

• S. Ohnishi,
• Y. Ikeda, T. Hyodo, W. W. : arXiv:1512.00123, Phys. Rev. C (2016)

E-dependent - two poles E-independent - one pole

Neutron energy spectrum mass distributions

(J-PARC E31)

→ πΣ

K−d → nπ+Σ− K−d → nπ−Σ+

16

0.1 0.2 0.3 1350 1400 1450 1500

(b) E-indep.

MπΣ(MeV)

K−d → nπ0Σ0

plab

K

= 1 GeV

17

𝜌+Σ−/𝜌−Σ+ 𝑒 𝐿−, 𝑜 𝑌𝜌±Σ∓

𝑒 𝐿−, 𝑜 𝑌𝜌±Σ∓ S 𝐿−𝑞

• sresol. ~ 10 MeV

possible structure around missing mass 1.42 GeV ?

Present status of K−d → n πΣ experiment E 31 @ J-PARC

separation of and modes Focus on: spectra above threshold

π−Σ+

π+Σ−

KN

Neutron detected in forward direction

18

PART II

• NEW -

In-medium z Meson Spectral Functions

and

Strange-Quark Content of the Nucleon

19

IN-MEDIUM MESON SPECTRAL FUNCTIONS

φ

New QCD sum rules analysis Implications for strangeness sigma term of the nucleon Starting point: strange quark vector current jµ(x) = 1

3 ¯ s(x) γµ s(x)

and its correlator Π(q)µν = i Z d4x eiqxhT[jµ(x)jν(0)]i Spectral function

R(q) = − 3 πq2 Im Πµ

µ(q)

Operator product expansion of QCD Finite energy sum rules for moments of the spectral function

ρ

K

K N N

φ

10-2 10-1 100 101 102 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 ω [GeV]

• nly φ contribution (K+ K-)
• incl. continuum (K+ K-)

full spectral function perturbative QCD limit

full spectrum

• pert. QCD

K+K− + nπ K+K−continuum

φ resonance

20

10-2 10-1 100 101 102 0.7 0.8 0.9 1.0 1.1 1.2 1.3 ω [GeV] ρ = 0 ρ = ρ0 (S) ρ = ρ0 (S+P)

2

φ

vacuum nuclear matter

R(!, ~ q = 0) R(!, ~ q = 0; ⇢ = ⇢0)

from chiral SU(3) EFT

MESON SPECTRAL FUNCTIONS in vacuum and in nuclear matter

• F. Klingl, T. Waas, W. W.
• Phys. Lett. B431 (1998) 254
• Ph. Gubler, W. W.
• Phys. Lett. B751 (2015) 396

data

J.P . Lees et al. (BABAR collaboration)

• Phys. Rev. D88 (2013) 032013

plus earlier

e+e− → K+K−

e+e− → K+K− + nπ data

21

Sum rule for 0th moment :

FINITE ENERGY QCD SUM RULES for moments of the spectral function

φ

Sum rule for 1st moment :

s0 ' 2.4 GeV2

Delineation scale between hadronic and perturbative QCD :

5 5.5 6 6.5 7 7.5 8 1.4 1.45 1.5 1.55 1.6 1.65 1.7 0th moment ×102 [GeV2] (s0)1/2 [GeV] s0 c0 + c2 ∫ ds R(s) 5 6 7 8 9 10 11 12 13 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1st moment ×102 [GeV4] (s0)1/2 [GeV] s0

2 c0/2 - c4

∫ ds s R(s) √

• Ph. Gubler, W. W.
• Phys. Lett.

B751 (2015) 396

c4 = 1 12hαs π G2i 8ms h¯ ssi

. . . in vacuum gluon condensate strange quark condensate

Z s0 ds R(s) = s0 4π2 ⇣ 1 + αs π ⌘ − 3m2

s

2π2 Z s0 ds s R(s) = s2 8π2 ⇣ 1 + αs π ⌘ − c4

22

FINITE ENERGY QCD SUM RULES for moments of the spectral function

in the nuclear medium

φ

1st spectral moment involves in-medium gluon and strange quark condensates:

⟨ss⟩ρ ≃ ⟨ss⟩+⟨N|ss|N⟩ρ = ⟨ss⟩+ σsN ms ρ, αs

2

αs

2

αs

2

⟨ ⟩ ≃ ⟨ ⟩ ⟨ | | ⟩ ⟨ ⟩ m αs π G2

ρ ≃

αs π G2 +

• N
• αs

π G2

• N
• ρ
• 8
• =

αs π G2 − 8 9

• MN −σπN −σsN
• ρ

Sigma terms of the nucleon:

… plus correction from twist-2 operator prop. to As

2 = 2

1

0 dx x

• s(x)+s(x)
• coefficient c of Eq. (12) then read

−δc4(ρ) = ✓ 2 27 − As

2

◆ MN − 2 27 (28 σsN + σπN)

• ρ
• mass, σπN = 2mq⟨N|qq|N⟩
• nucleon. There is furthermore

and

and σsN = ms⟨N|ss|N⟩ a twist-2 operator:

In-medium sum rule for 1st spectral moment : strong sensitivity to strangeness sigma term

Z s0 ds s R(s; ρ) − s2 8π2 ⇣ 1 + αs π ⌘ = −c4 − δc4(ρ)

0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 25 50 75 100 125 150 175 200 mφ(ρ0)/mφ(0) σsN [MeV]

23

Correlation between in-medium “mass”

and

strangeness sigma term of the nucleon

φ

Default case - if NO in-medium shift of 1st spectral moment, this implies:

σsN = MN − σπN 28 (1 − 13.5 As

2) ' (13 ± 5) MeV

• Ph. Gubler, K. Ohtani
• Phys. Rev. D90 (2014) 094002

FESR estimate (preliminary)

Scalar strange-quark density

• f the nucleon

ys = hN|¯ ss|Ni hN|¯ qq|Ni

= 2mq ms σsN σπN

24

STRANGENESS SIGMA TERM

• f the NUCLEON from LATTICE QCD

This work JLQCD 21f overlap 18 Junnarkar and WalkerLoud 21f DWF on staggered 19 Engelhardt 21f DWF on staggered 15 MILC 21f HISQ 16 MILC 21f Asqtad 13 ETMC 211f twisted mass 17 Dürr etc. 21f Wilson 9 QCDSFUKQCD 21f clover 10 Young and Thomas 21f 22 QCDSF 2f Wilson 21 JLQCD 2f overlap 12

50 100 150

• M. Gong et al., Phys. Rev. D88(2013) 014503

Y.B. Yang et al., arXiv:1511.09089

• S. Dürr et al., arXiv:1510.08013

NEW:

σsN [MeV]

• A. Abdel-Rehim et al., arXiv:1601.01624

25

50 100 150

counts/[6.7MeV/c ] counts/[6.7MeV/c ]

χ2/ndf=83/50

Cu Cu

1.25< <1.75 βγ<1.25

Hints about in-medium effects

• n the spectral function

φ

• K. Muto et al.
• Phys. Rev. Lett.

98 (2007) 042501

KEK E325

Looking forward to J-PARC E16

√s [GeV]

counts / dE

0.9 1.0 1.1 1.2

26

PART III

• NEW -

Hyperon - Nucleon Interactions

from

SU(3) Chiral Effective Field Theory

and the issue of

Strangeness in Neutron Star Matter

27

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

× 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)

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

• . . . generate Nambu-Goldstone boson exchange processes

Interaction terms involving baryon and pseudoscalar meson octets . . .

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

• J. Haidenbauer et al.: Nucl. Phys. A 915 (2013) 24

Recent developments:

Λ Λ Λ Λ Λ Λ N N N N N N

K

π

π

Σ N

LO NLO LO NLO

repulsion

phase shift

Hyperon - Nucleon Interaction (contd.)

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

U.-G. Meißner, A. Nogga, W. W.

• Nucl. Phys. A 915 (2013) 24

28

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

= +

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(Ê) = V + V Q e(Ê) + i‘G(Ê)

G G

Λ Λ

dense matter

• J. Haidenbauer,

U.-G. Meißner,

• Nucl. Phys.

A 936 (2015) 29

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

EPJA (2015) ; arXiv:1507.08808 [nucl-th] 29

No condensation

• f (anti)KAONS

but

¯ KNN → ΛN

Note: STIFF equation of state requires STRONG hyperon-nuclear REPULSION at high density

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

• 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

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

30

STRANGE QUARK MATTER NUCLEONIC MATTER

New constraints from 2-solar-mass NEUTRON STARS

sufficiently stiff equation of state required: exotic scenarios (quark matter, kaon condensation etc.) unlikely

31

Mass vs. Radius relation

• f

Neutron Stars

• J. Antoniadis et al.

Science 340 (2013) 6131

New constraints from 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

Text

PSR J1614+2230

.8 M⇥ conditions

M = 1.97 ± 0.04

32

33

1 10 100 1000 Quark Chemical Potential µ − µiron/3 (MeV) 1e-06 0.001 1 1000 Pressure (MeV fm

• 3)

inner

• uter

matter neutron crust crust pQCD matter

?

SB limit

Central µ in maximally massive stars

NEUTRON STARS EQUATION of STATE

• A. Kurkela et al.
• Astroph. J.

789 (2014) 127

0.93 0.95 1.0 1.5 2.0 4.0

Baryon Chemical Potential

µB [GeV]

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

News from NEUTRON STARS

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

105 (2010) 161102

purely “nuclear” EoS kaon condensate quark matter Constraints from neutron star observables “Exotic” equations of state ruled out ?

• A. Akmal,

V.R. Pandharipande, D.G. Ravenhall

• Phys. Rev. C 58 (1998) 1804
• F. Özil, D. Psaltis: Phys. Rev. D80 (2009) 103003
• F. Özil, G. Baym, T. Güver: Phys. Rev. D82 (2010)101301

A.W. Steiner,

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

Mass-Radius Relation

34

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 occurs (if at all) only 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

35

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)

B [MeV] A-2/3 exp N N + NN (I) N + NN (II) 0.0 10.0 20.0 30.0 40.0 50.0 60.0 0.0 0.1 0.2 0.3 0.4 0.5

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

NEUTRON STAR MATTER including HYPERONS

with inclusion of hyperons: EoS too soft to support 2-solar-mass star unless strong short-range repulsion in YN and / or YNN interactions

QMC calculations using phenomenological hyperon-nucleon & hyperon-NN three-body interactions

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

114 (2015) 092301

Mass - radius relation of neutron stars

36

constrained by hypernuclei

New developments: towards hyperon-NN three-body forces from Chiral SU(3) Effective Field Theory

R [km]

A−2/3

• S. Petschauer, N. Kaiser, J. Haidenbauer, U.-G. Meißner, W. W. : Phys. Rev. C93 (2016) 014001

: quasibound state

SUMMARY

Chiral SU(3) Effective Field Theory

well controlled coupled-channels framework for both antikaon- and hyperon-nuclear systems

Systems with strangeness S = -1 and baryon no. B = 1,2

progress in understanding the Λ(1405) threshold and subthreshold physics: focused experimental programs at J-PARC and elsewhere

¯ KNN

Role of strangeness in dense matter

quest for strong short-distance repulsion in hyperon-nuclear two- and three-body interactions:

37

¯ KN

πΣ z meson spectral functions in vacuum and in-medium

QCD sum rules and strangeness content of the nucleon two-solar-mass neutron stars imply stiff equation-of-state embedded in continuum