Hyperon-nucleon interaction from chiral EFT

Johann Haidenbauer

IAS & JCHP, Forschungszentrum Jülich, Germany

Hypernuclear Workshop, Newport News, May 28, 2014

Johann Haidenbauer Hyperon-nucleon interaction Outline

1 Introduction

2 YN in chiral effective field theory

3 YN Results

4 Three- and four-body systems

Johann Haidenbauer Hyperon-nucleon interaction NN in chiral effective field theory

0 1 10 3 60 1 P P S -10 1 0 0 0 -20

40 -10

Phase Shift [deg] -30 Phase Shift [deg]

-20 -40 20 0 50 100 150 200 250 0 50 100 150 200 250 Lab. Energy [MeV] Lab. Energy [MeV] 0

Phase Shift [deg] 50 -5 3 3 0 P P -10 1 40 2 -15 30 -20 -20 -25 20 Phase Shift [deg] Phase Shift [deg] -30 10 -35 150 0 3 0 50 100 150 200 250 0 50 100 150 200 250 S1 Lab. Energy [MeV] Lab. Energy [MeV] 5 4 ε 100 1 3 2 1 0 Phase Shift [deg] 50 -1 Phase Shift [deg] -2 0 50 100 150 200 250 Lab. Energy [MeV] 0 0 50 100 150 200 250 Lab. Energy [MeV]

NLO, N2LO, N3LO

(E. Epelbaum, W. Glöckle, Ulf-G. Meißner, NPA747 (2005) 362)

Johann Haidenbauer Hyperon-nucleon interaction YN in chiral effective field theory

Advantages: Power counting systematic improvement by going to higher order Possibility to derive two- and three baryon forces and external current operators in a consistent way Obstacle: YN data base is rather poor

about 35 data points, all from the 1960s 10 data points from the KEK-PS E251 collaboration (1999-2005) constraints from hypernuclei no polarization data ⇒ no phase shift analysis

→ impose SU(3)f constraints

We∗ follow the scheme of S. Weinberg (1990) in complete analogy to the study of NN in χEFT by E. Epelbaum et al.

∗J.H., N. Kaiser, S. Petschauer, U.-G. Meißner, A. Nogga, W. Weise

Johann Haidenbauer Hyperon-nucleon interaction Power counting

X ν Veff ≡ Veff(Q, g, µ) = (Q/Λ) Vν (Q/µ, g) ν

Q ... soft scale (baryon three-momentum, Goldstone boson four-momentum, Goldstone boson mass) Λ ... hard scale g ... pertinent low–energy constants µ ... regularization scale

Vν ... function of order one ν ≥ 0 ... chiral power

Leading order (LO): ν = 0 a) non-derivative four-baryon contact terms b) one-meson (Goldstone boson) exchange diagrams

Next-to-leading order (NLO): ν = 2 a) four-baryon contact terms with two derivatives b) two-meson (Goldstone boson) exchange diagrams

Johann Haidenbauer Hyperon-nucleon interaction Contact terms for BB

e.g.,LO contact terms for BB:

¯ ¯ 1 ˜ 1 ¯ ¯ = Ci NΓi N NΓi N = C BaBb (Γi B) (Γi B) , L ⇒ L i b a 2 ˜ 2 ¯ ¯

= Ci Ba (Γi B) Bb (Γi B) , L a b 3 ˜ 3 ¯ ¯ = Ci Ba (Γi B) Bb (Γi B ) L a b

0 √Σ + √Λ Σ+ p 2 6 0 B = Σ− −√Σ + √Λ n  2 6  Ξ− Ξ0 √2Λ  − − 6    a, b ... Dirac indices of the particles

µ µν µ Γ1 = 1 , Γ2 = γ , Γ3 = σ , Γ4 = γ γ5 , Γ5 = γ5 ˜ Ci , Ci ... low-energy constants

Johann Haidenbauer Hyperon-nucleon interaction Contact terms for BB

spin-momentum structure of the contact term potential: BB contact terms without derivatives(LO):

(0) V = C , → + CT ,BB→BB ~σ1 ~σ2 BB→BB S BB BB · BB contact terms with two derivatives(NLO):

(2) 2 2 2 2 V = C1~q + C2~k + (C3~q + C4~k )(~σ1 ~σ2) BB→BB · i + C5(~σ1 + ~σ2) (~q ~k) + C6(~q ~σ1)(~q ~σ2) 2 · × · · i + C7(~k ~σ1)(~k ~σ2) + C8(~σ1 ~σ2) (~q ~k) · · 2 − · ×

note: Ci → Ci,BB→BB

~q = ~p0 − ~p; ~k = (~p0 + ~p)/2

Johann Haidenbauer Hyperon-nucleon interaction SU(3) symmetry

10 independent spin-isospin channels in NN and YN (for L=0) (NN (I=0), NN (I=1), ΛN, ΣN (I=1/2), ΣN (I=3/2), ΛN ΣN) ↔ in principle (atLO), 10 low-energy constants ⇒ SU(3) symmetry only5 independent low-energy constants ⇒ SU(3) structure for scattering of two octet baryons: direct product: ∗ 8 8 = 1 8a 8s 10 10 27 ⊗ ⊕ ⊕ ⊕ ⊕ ⊕

CS,i , CT ,i , C1,i , etc., can be expressed by the constants corresponding to the SU(3)f irreducible representations: ∗ C1, C8a , C8s , C10 , C10, C27

Johann Haidenbauer Hyperon-nucleon interaction SU(3) structure of contact terms for BB

Channel I V1S0, V3P0,3P1,3P2 V3S1, V3S1−3D1, V1P1 V1P1−3P1 ∗ S = 0 NN → NN 0 – C10 – NN → NN 1 C27 – – “ ∗ ” S = −1 ΛN → ΛN 1 1 `9C27 + C8s ´ 1 C8a + C10 √−1 C8s8a 2 10 2 20 “ ∗ ” ΛN → ΣN 1 3 `−C27 + C8s ´ 1 −C8a + C10 √3 C8s8a 2 10 2 20 √−1 C8s8a 20 “ ∗ ” ΣN → ΣN 1 1 `C27 + 9C8s ´ 1 C8a + C10 √3 C8s8a 2 10 2 20 3 27 10 ΣN → ΣN 2 C C –

Number of contact terms: NN: 2 (LO) 7 (NLO) YN : +3 (LO) +11 (NLO) YY : +1 (LO) + 4 (NLO) C1 contributes only to I = 0, S = 2 channels!! ⇒ −

Johann Haidenbauer Hyperon-nucleon interaction Pseudoscalar-meson exchange

SU(3)f -invariant pseudoscalar-meson-baryon interaction Lagrangian:

fi fl gA(1 − α) ¯ µ gAα ¯ µ L = − √ Bγ γ5 {∂µP, B} + √ Bγ γ5 [∂µP, B] 2Fπ 2Fπ

f = gA/(2Fπ); gA ' 1.26, Fπ ≈ 93 MeV

α = F/(F + D) with gA = F + D

0 0 η 1 √π + √ π+ K + 2 6 B 0 C P = B π− −√π + √η K 0 C 2 6 @ 0 A K − K¯ − √2η 6

f = f f = √1 (4α − 1)f f = − √1 (1 + 2α)f NNπ NNη8 3 ΛNK 3 f = −(1 − 2α)f f = − √1 (1 + 2α)f f = √1 (4α − 1)f ΞΞπ ΞΞη8 3 ΞΛK 3 f = √2 (1 − α)f f = √2 (1 − α)f f = (1 − 2α)f ΛΣπ 3 ΣΣη8 3 ΣNK f = 2αf f = − √2 (1 − α)f f = −f ΣΣπ ΛΛη8 3 ΞΣK

Johann Haidenbauer Hyperon-nucleon interaction Pseudoscalar-meson (boson) exchange

One-pseudoscalar-meson exchange (V OBE )[LO]

OBE ~σ1 ~q ~σ2 ~q 0 0 = 0 0 VB B →B B fB1B P fB2B P · · 1 2 1 2 − 1 2 ~ 2 + 2 q
mP

f 0 ... coupling constants B1B1P mP ... mass of the exchanged pseudoscalar meson

dynamical breaking of SU(3) symmetry due to the mass splitting of the ps mesons (mπ = 138.0 MeV, mK = 495.7 MeV, mη = 547.3 MeV) taken into account already atLO!

Details: (H. Polinder, J.H., U.-G. Meißner, NPA 779 (2006) 244; PLB 653 (2007) 29)

Johann Haidenbauer Hyperon-nucleon interaction Two-pseudoscalar-meson exchange diagrams

Two-pseudoscalar-meson exchange diagrams (V TBE )[NLO]

Σ N Σ N Σ N Σ N π π π π

u u u u u u u u π π u u π uπ u Σ N Σ N Σ N Σ N

Σ N Σ N Σ N η π K u u Λ u u Ξ u uΣ ···

uη u u π u uK u Σ N Σ N Σ N

⇒ J.H., S. Petschauer, N. Kaiser, U.-G. Meißner, A. Nogga, W. Weise, NPA 915 (2013) 24

Johann Haidenbauer Hyperon-nucleon interaction Coupled channels Lippmann-Schwinger Equation

ν0ν,J 0 ν0ν,J 0 Tρ0ρ (p , p) = Vρ0ρ (p , p) Z ∞ 00 002 X dp p ν0ν00,J 0 00 2µν00 ν00ν,J 00 + V 0 00 (p , p ) T 00 (p , p) (2π)3 ρ ρ p2 − p002 + iη ρ ρ ρ00,ν00 0

ρ0,ρ = ΛN, ΣN

LS equation is solved for particle channels (in momentum space) Coulomb interaction is included via the Vincent-Phatak method The potential in theLS equation is cut off with the regulator function:

ν0ν,J 0 Λ 0 ν0ν,J 0 Λ Λ −(p/Λ)4 Vρ0ρ (p , p) f (p )Vρ0ρ (p , p)f (p); f (p) = e → consider values Λ = 450 - 700 MeV [500 - 650 MeV]

Johann Haidenbauer Hyperon-nucleon interaction NLO Results

Pseudoscalar-meson exchange All one- and two-pseudoscalar-meson exchange diagrams are included SU(3) symmetry is broken by using the physical masses of the pion, kaon, and eta SU(3) breaking in the coupling constants is ignored Fπ = FK = Fη = F0 = 93 MeV; gA = 1.26 o assume that η η8 (i.e. θP = 0 and fBBη 0) ≡ 1 ≡ assume that α = F/(F + D) = 2/5 (semi-leptonic decays ⇒ α ≈ 0.364) Correction to V OBE due to baryon mass differences are ignored

(A fit with two-pion-meson exchange diagrams is possible!)

(A fit with physical values for Fπ, FK , Fη is possible!)

Johann Haidenbauer Hyperon-nucleon interaction Contact terms

SU(3) symmetry is assumed (at NLO SU(3) breaking corrections to theLO contact terms arise!) 10 contact terms in S-waves no SU(3) constraints from the NN sector are imposed! 3 3 12 contact terms in P-waves and in S1– D1 SU(3) constraints from the NN sector are imposed! 1 3 1 contact term in P1– P1 (singlet-triplet mixing) is set to zero

contact terms in S-waves: can be fairly well fixed from data some correlations between NLO andLO LECs

Johann Haidenbauer Hyperon-nucleon interaction Contact terms inP-waves

contact terms in P-waves are much less constrained use SU(3) and fix some (5) LECs from NN the others (7) are fixed from “bulk” properties:

(1) σΛp 10 mb at plab 700 900 MeV/c ≈ ≈ − (2) dσ/dΩ − at plab 135 160 MeV/c Σ p→Λn ≈ −

Other (future) options: consider matter properties: use spin-orbit splitting of the Λ single particle levels in nuclei

Consider the Scheerbaum factor SΛ calculated in nuclear matter to relate the strength of the Λ-nucleus spin-orbit potential to the two body ΛN interaction (R.R. Scheerbaum, NPA 257 (1976) 77)

Johann Haidenbauer Hyperon-nucleon interaction YN integrated cross sections

− Λp -> Λp Λp -> Λp Σ p -> Λn

300 70 300 + 0 Σ n -> <- Σ p EFT LO EFT LO NLO EFT NLO 60 EFT LO 250 Jülich ’04 Sechi-Zorn et al. Kadyk et al. Engelmann et al. Kadyk et al. Jülich ’04 Alexander et al. Hauptman Juelich '04 50 200 200

40

150 (mb) (mb) (mb)

σ σ 30 σ

100 100 20

50 10

0 0 0 100 200 300 400 500 600 700 800 900 500 600 700 800 100 120 140 160 180 plab (MeV/c) plab (MeV/c) plab (MeV/c)

Johann Haidenbauer Hyperon-nucleon interaction YN integrated cross sections

− 0 − − + + Σ p -> Σ n Σ p -> Σ p Σ p -> Σ p

500 300 250

EFT LO EFT LO NLO NLO 250 Jülich ’04 EFT LO Jülich ’04 400 Eisele et al. 200 NLO Eisele et al. Jülich ’04 Engelmann et al.

200

300 150

150 (mb) (mb) (mb) σ σ σ 200 100

100

100 50 50

0 0 0 100 120 140 160 180 100 120 140 160 180 100 120 140 160 180 plab (MeV/c) plab (MeV/c) plab (MeV/c)

Johann Haidenbauer Hyperon-nucleon interaction YN integrated cross sections - higher energies

− 0 − − + + Σ p -> Σ n Σ p -> Σ p Σ p -> Σ p

150 200 200

EFT LO EFT LO NLO NLO Jülich ’04 EFT LO Jülich ’04 Engelmann et al. NLO Eisele et al. Stephen Jülich ’04 Ahn (2005) 150 Eisele et al. 150 Kondo (2000)

100

100 100 (mb) (mb) (mb) σ σ σ

50

50 50

0 0 0 100 200 300 400 500 600 100 200 300 400 500 600 700 100 200 300 400 500 600 700 plab (MeV/c) plab (MeV/c) plab (MeV/c)

Johann Haidenbauer Hyperon-nucleon interaction YN differential cross sections

− − − − Σ p -> Λn Σ p -> Λn Σ p -> Σ p

150 140 140 p = 160 MeV/c p = 160 MeV/c plab = 135 MeV/c lab lab

120 120

100 100 100 (mb) (mb) (mb) 80 80 θ θ θ /dcos /dcos /dcos

σ 60 σ 60 σ d d d 50

40 40

20 20

0 0 0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 cos θ cos θ cos θ

Johann Haidenbauer Hyperon-nucleon interaction YN differential cross sections

− − + + + + Σ p -> Σ p Σ p -> Σ p Σ p -> Σ p

60 100 70

plab = 550 MeV/c p = 450 MeV/c plab = 170 MeV/c lab 60 50 80

50 40

60 40 (mb) (mb) (mb) θ θ θ 30

/dcos /dcos /dcos 30

σ σ 40 σ d d d 20 20

20 10 10

0 0 0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 cos θ cos θ cos θ

Johann Haidenbauer Hyperon-nucleon interaction YN scattering lengths [fm]

EFT LO EFT NLO Jülich ’04 NSC97f experiment∗ Λ [MeV] 550 ··· 700 500 ··· 650 Λp +2.3 as −1.90 ···− 1.91 −2.90 ···− 2.91 −2.56 −2.51 −1.8−4.2 Λp +1.1 at −1.22 ···− 1.23 −1.51 ···− 1.61 −1.66 −1.75 −1.6−0.8 Σ+p as −2.24 ···− 2.36 −3.46 ···− 3.60 −4.71 −4.35 Σ+p at 0.60 ··· 0.70 0.48 ··· 0.49 0.29 −0.25 χ2 ≈ 30 15.7 ··· 16.8 ≈ 25 16.7

3 (ΛH) EB −2.34 ···− 2.36 −2.30 ···− 2.33 −2.27 −2.30 -2.354(50)

∗A. Gasparyan et al., PRC 69 (2004) 034006 ⇒ extract ΛN scattering lengths from final-state interaction: pp → K +Λp (COSY - Jülich) γd → K +Λn (SPring-8, CLAS)

Johann Haidenbauer Hyperon-nucleon interaction + ~pp K Λp at plab = 2.95 GeV/c →

Λp invariant mass spectrum M 2 1 dσ | | ∝ pΛp dmΛp

) 10 2 3500 9 all data 3000 8 upper region +1.5 units 2500 lower region +1.5 units 7 [arbitrary units] N/A/(2MeV/c 2000 2 |M| 6 1500 5 1000 4 500 3

0 2060 2080 2100 2120 2140 2160 2180 2200 2220 2240 2260 A m [MeV/c^2] 2 0.2 pΛ 0.1 1 0 0 2060 2080 2100 2120 2140 2160 2180 2200 2220 2240 2260 2050 2060 2070 2080 2090 2100 2110 2 m [MeV/c2] mpΛ [MeV/c ] pΛ

M. Röder et al., EPJA 49 (2013) 157

Johann Haidenbauer Hyperon-nucleon interaction + ~pp K Λp at plab = 2.95 GeV/c → need to separate singlet and triplet amplitude consider spin observables ⇒

0.25 coefficients 0.2

0.15

0.1

0.05

0

0 20 40 60 80 100 120 140 160 180 200 220 2 mpΛ - mΛ - mp [MeV/c ]

spin triplet contributions only: ◦ A0y σ0(θ = 90 ) ◦ ◦ (1 − Axx )σ0(θ = 90 or φ = 90 )

spin singlet contributions only: ◦ (1 + Axx + Ayy − Azz )σ0(θ = 90 )

Johann Haidenbauer Hyperon-nucleon interaction + ~pp K Λp at plab = 2.70 GeV/c →

Preliminary results of a new measurement with5x higher statistics:

Λp invariant mass spectrum A0y (cos θK , mΛp) ≈ α sin θK + β cos θK sin θK ]

2 χ2 / ndf 73.43 / 36 0.3 C0 -0.2183 ± 0.0432 10000 C1 1.318e+05 ± 1.135e+04 C2 4.151e+06 ± 5.203e+03 0.25 coefficients 8000 0.2

0.15 6000 0.1 EntriesAC[1.1 / MeV/c

4000 0.05

0 2000 -0.05

0 -0.1 2060 2080 2100 2120 2140 2160 0 20 40 60 80 100 120 2 2 m Λ [MeV/c ] p mpΛ-mp-mΛ [MeV/c ]

F. Hauenstein, work in progress

Johann Haidenbauer Hyperon-nucleon interaction ΣN (I=3/2)

1 S0: test for SU(3) symmetry VNN VΣN → ≡ 1 LEC’s that are fitted to the pp S0 phase shift produce a bound state in Σ+p σ1 4 σΣ+p → S0 ≈ × simultaneous fit is possible if we assume that there is SU(3) breaking in theLO contact term only. 3 3 S1– D1: decisive for Σ properties in nuclear matter A description of YN data is possible with an attractive as well as 3 3 a repulsive S1– D1 interaction

Johann Haidenbauer Hyperon-nucleon interaction ΣN (I=3/2) phase shifts

1 ΣN S (I=3/2) Σ 3 0 N S1 (I=3/2) 50 40 40

20 30

0 20

-20 (degrees) (degrees) 10 δ δ

-40 0 LO LO NLO NLO -10 Jülich ’04 -60 Jülich '04 NSC97f NSC97f NPLQCD (2012) -20 -80 0 100 200 300 400 500 600 0 100 200 300 400 500 600 plab (MeV/c) plab (MeV/c)

(2J+1)π 2 partial cross section: σΣ+p; J = 2 sin δJ pcm

Johann Haidenbauer Hyperon-nucleon interaction Hypertriton separation energy Hypertriton separation energies

separation energies: 3 XΛH Λ separation energy 0.25 E = E(core) E(hypernucleus) ⇤

[MeV] 0.20 YN Λ dependence of χ2 Λ

2 30 E

χ 28

0.15 26 LO NLO 24

22 0.10 20

18

16 0.05 LO NLO-Idaho 500 14 NLO-Idaho 600 Exp. 12 0.00 10 450 500 550 600 650 700 450 500 550 600 650 700 Λ [MeV] Λ [MeV] • singlet scattering length for one cutoff chosen so that hypertriton binding energy is OK

• cutoff variation • is lower bound for magnitude of higher order contributions • correlation with χ2 of YN interaction ?

• long range 3BFs need to be explicitly estimated

7 September 10, 2013

Johann Haidenbauer Hyperon-nucleon interaction 4 Separation energy for ΛH

4 Separation energies for ΛH X4 H (J=0+) Λ separation energy Λ 4 + XΛH (J=1 ) Λ separation energy 2.5 2.5

[MeV]

[MeV]

Λ Λ 2.0 2.0 E

E

1.5 1.5

1.0 1.0 0.5 LO NLO-Idaho 500 Exp. 0.5 LO NLO-Idaho 500 0.0 Exp. 450 500 550 600 650 700 Λ [MeV] 0.0 450 500 550 600 650 700 Λ [MeV] • LO/NLO results: LO uncertainty in 0+ is underestimated by cutoff variation • NLO results in line with model results, implies underbinding • long range 3BFs need to be explicitly estimated

• but: for this version of NLO, results are inconsistent with experiment • note: this NLO does not allow for SU(3) breaking in contact part of YN ad-hoc p-waves • Johann Haidenbauer Hyperon-nucleon interaction September 10, 2013 8 Λp S-wave phase shifts

1 Λp S Λ 3 0 p S1 180 40

150 30

120 20 90

10

(degrees) (degrees) 60 δ δ

0 30

-10 0

-20 -30 0 200 400 600 800 0 200 400 600 800 plab (MeV/c) plab (MeV/c)

1 less repulsion in S0 at short distances – and/or 3BFs? ⇒

Johann Haidenbauer Hyperon-nucleon interaction Three-body forces

N Λ N N Λ N N Λ N

u y u u y y

N Λ N N Λ N N Λ N (a) (b) (c)

N Λ N N Λ N

Σ∗ u u Σ u u

u u u u

N Λ N N Λ N (d) (e)

(a) - (c) appear at N2LO (d) appears at NLO – in EFT that includes decuplet baryons (e) is already included by solving coupled-channel Faddeev equations

Johann Haidenbauer Hyperon-nucleon interaction Charge symmetry breaking CSB at NLO & for model interactions

Contributions to the difference of 4 H 0 + 4 He 0 + separation energies ⇤ ⇤ Λ [MeV] 450 500 550 600 650 700 Jülich Nijm Nijm Expt. 04 SC97 SC89 e ΔT [keV] 44 50 52 51 46 40 0 47 132 -

ΔVNN [keV] -3 -2 5 5 3 0 -31 -9 -9 -

ΔVYN [keV] -11 -11 -11 -10 -8 -7 2 37 228 - tot [keV] 30 37 46 46 41 33 -29 75 351 350

PΣ- 1.0% 1.1% 1.2% 1.2% 1.1% 0.9% 0.3% 1.0% 2.7% -

PΣ0 0.6% 0.6% 0.7% 0.7% 0.6% 0.5% 0.3% 0.5% 1.4% -

PΣ+ 0.1% 0.1% 0.2% 0.2% 0.2% 0.1% 0.3% 0.0% 0.1% -

• kinetic energy contribution is driven by Σ component • NN force contribution due to small deviation of Coulomb • YN force contribution: • SC89 CSB is strong • NLO CSB is zero, only Coulomb acts (Σ component)

September 10, 2013 9 Johann Haidenbauer Hyperon-nucleon interaction Λ Σ0 mixing −

Λ N Λ N Λ N

0 π δM u u u η 0 Σ0 Σ0 π 0 2 δM π uδm u u u u u

Λ N Λ N Λ N

Electromagnetic mass matrix: 0 Σ δM Λ = [M 0 MΣ+ + Mp Mn]/√3 h | | i Σ − − 0 2 2 2 2 2 π δm η = [m m + + m + m ]/√3 h | | i π0 − π K − K 0 hΣ0|δM|Λi hπ0|δm2|ηi fΛΛπ = [ 2 + 2 2 ] fΛΣπ M 0 −MΛ m −m − Σ η π0 latest PDG mass values ⇒ fΛΛπ ( 0.0297 0.0106) fΛΣπ 0.0403 fΛΣπ ≈ − − ≈ − (R.H. Dalitz & F. von Hippel, PL 10 (1964) 153)

Johann Haidenbauer Hyperon-nucleon interaction Summary

YN interaction based on chiral EFT

approach is based on a modified Weinberg power counting, analogous to the NN case The potential (contact terms, pseudoscalar-meson exchanges) is derived imposing SU(3)f constraints

Good description of the empirical YN data was achieved already atLO (only 5 free parameters!)

Excellent results at next-to-leading order(NLO) YN data are reproduced with a quality comparable to phenomenological models SU(3) symmetry for the LEC’s can be maintained in the YN system (ΛN, ΣN) but not between YN and NN

Johann Haidenbauer Hyperon-nucleon interaction