Hyperon interactions from Lattice QCD
and Ξ hypernuclei

Tetsuo Hatsuda(RIKEN iTHEMS)

ΞClustering as a Window on the Hierarchical Structure of Quantum Systems (CLUSHIQ2022)(Oct. 31, 2022)

1

J-PARC@KEK

Monte Carlo method for
109-10 dim. QCD Integral

Single Baryon

3

Hadron masses from LQCD

Review: Fodor and Hoelbling, Rev. Mod. Phys. 84 (2012) 449

4

Baryon Interactions

Femtoscopy
Hypernuclei
Neutron stars

5Scattering of composite particles
・ Haag-Nishijima-Zimmermann reduction formula (1958)
・ Borchers Theorem (1960)
r0τ

HAL QCD MethodIshii, Aoki & Hatsuda, PRL 99 (2007) 022001
Ishii+ [HAL QCD Coll.], PLB 712 (2012) 437

R (r,τ)  LS equation (T =U +GUT )  phase shift, binding energy6

Large scale LQCD simulations for BB interactions(KEK)

T. Aoyama(RIKEN) T. Doi, T. Hatsuda, T. Sugiura(Nihon)

T. Inoue(YITP)

Y. Akahoshi, S. Aoki, K. Murakami(RCNP)T. M. Doi, N. Ishii, K. Murano, H. Nemura(Osaka) Y. Ikeda, K.Sasaki(Birjand) F. Etminan(Beijing) Yan Liu, Hui Tong

V=(8.1 fm)3 , mπ=146 MeV

V=(8.1 fm)3 , mπ=138 MeVK@RIKEN: 11PFlops (2011-2019)

FUGAKU@RIKEN: 440 PFlops (2020-)

7

Large scale LQCD simulations for BB interactions(KEK)

T. Aoyama(RIKEN) T. Doi, T. Hatsuda, T. Sugiura(Nihon)

T. Inoue(YITP)

Y. Akahoshi, S. Aoki, K. Murakami(RCNP)T. M. Doi, N. Ishii, K. Murano, H. Nemura(Osaka) Y. Ikeda, K.Sasaki(Birjand) F. Etminan(Beijing) Yan Liu, Hui Tong

V=(8.1 fm)3 , mπ=146 MeV

V=(8.1 fm)3 , mπ=138 MeVK@RIKEN: 11PFlops (2011-2019)

FUGAKU@RIKEN: 440 PFlops (2020-)

8Coupled Channel S=-2 system

Short-rangeNΞ-ΛΛ coupling

Small ΛΛattraction
I=0, JP=0+

K. Sasaki+ [HAL QCD Coll.]
Nucl. Phys. A998 (2020)

Large NΞ
attraction

Short-rangeNΞ-ΛΛ coupling9ΞN scattering phase shifts
ΞN phase shift in HAL QCD
I=0, S=0: moderate attraction
I=0, S=1: weak attraction
I=1, S=0: weak repulsion
I=1, S=1: weak attraction

I=0, JP=0+10← Lattice QCD force(⊄⊄ renormalized)

Phenomenological force↓Femtoscopy: NΞ pair in pp collisions
LHC ALICE Coll., Nature 588 (2020) 232(pp, √s = 13 TeV)

11

E07 Coll. at J-PARC,Phys.Rev.Lett. 126 (2021) 062501

Ξ hypernuclei at J-PARC

5 He
Λ

Λ

Ξ-14N
10

Λ Be

Attraction in NΞ
Weak NΞ- ΛΛ coupling12Ξ hypernuclei found so far
Yoshimoto+, PTEP 2021 (2021) 073D02

13

Q1. What is the lightest
Ξ hypernuclei?

Ξpn n

Q2. Can we test thespin-isospin dependenceof ΞN int.?
Ξααn14

Q1. What is the lightest Ξ hypernuclei?
Hiyama, Sasaki, Miyamoto, Doi, Hatsuda, Yamamoto, Rijken,
Phys.Rev.Lett.124 (2020) 092501

Gaussian expansion method(Hiyama et al., 2003)

Γ ~ 60 keV

15

Q2. Can we test the spin-isospin dependence of ΞN int.?
Hiyama, Isaka, Doi, Hatsuda, arXiv:2209.06711 [nucl-th]ΞααnGaussian expansion method (Hiyama et al., 2003)

16

Inversion of spin-doublets in ΞNαα system
Hiyama, Isaka, Doi, Hatsuda,arXiv:2209.06711 [nucl-th]ΞααnΓ=20-40 keV17Q3. How to create bound ΞNαα systems

K+,0KpααnΞαα10Be(K-,K+) [ΞNαα]T=110Be(K-,K0) [ΞNαα]T=0n1818

Conclusions
1. LQCD simulations for YN and YY interactions at
mπ=146MeV (K) and at 138 MeV (FUGAKU). [HAL QCD Coll.]
2. LQCD data vs. and femtoscopy data.

[ALICE Coll. at LHC]

3. Hypernuclei using few-body method (GEM) + LQCD.
-- What is the lightest Ξ hypernuclei ?
NΞ, NNΞ none, NNNΞ possible

Hiyama et al.,PRL 124 (2020) 092501-- Can we test the spin-isospin dep. of ΞN int.?
Ξ hypernuclei wirh α cores
Hiyama, Isaka, Doi, Hatsuda,-- Possible expt. to study ΞNαα.
K- induced reactions

arXiv:2209.06711 [nucl-th]19

19Thank you !

20

Hyperon embedded in cold nuclear matter (HAL QCD + BHF)

Inoue [HAL QCD Coll.], Few-body Syst. 62 (2021) 106
21
Hiyama, Sasaki, Miyamoto, Doi, Hatsuda, Yamamoto, and Rijken, PRL 124 (2020) 092501 21

SU(3)F classification of BB system

x8 x 8 = 27 + 8s + 1 + 10* + 10 + 8aNN(1S0)Η (1S0)

NN(3S1)

Jaffe (1977)xdeuteron8 x 10 = 35 + 8 + 10 + 27(1987)NΩ (5S2) Goldman+Oka (1988)x

10 x 10 = 28 + 27 + 35 + 10*1S )ΩΩ(Kopeliovich+ (1990)
0∆∆(7S3) Dyson+ (1964)
22

23

HAL QCD Lattice data
CP-PACS @Tsukuba
0.6 Tflops(1996-2005)

K computer@ RIKEN
10 PFlops(2011-2019)

PACS-CS @Tsukuba
14 TFlops(2006-2011)3-flavor & (2+1)-flavor
V~(3 fm)3 , mπ > 400 MeV
BB
HBB

Inoue+, PTP 124 (’10)
Inoue+, PRL 106 (’11)
NPA 881 (’12)
Sasaki+, PTEP 2015 (’15)

NΩΩΩ

Etminan+, NPA 928 (’14)
Yamada+, PTEP 2015 (’15)

KN, πΣ
KNTcc
Zc

Dbar-NJ/ψ-N
Λc-N

Ikeda+, PoS Lat (’11)
Murakami+, PTEP 2020 (’20)
Ikeda+, PLB 729 (’14)
Ikeda+, PRL 117 (’16)
Ikeda+, HAL internal rep. (’16)
Sugiura+, PoS Lat (’18)
Miyamoto+, NPA 971 (’18)

Phase I: exploratory studies(2+1)-flavor
V=(8.1 fm)3 , mπ=146 MeV
S=-1 (ΛN, ΣN)
Nemura+, EPJ conf. 175 (’18)
S=-3 (ΞΣ, ΞΛ-ΞΣ) Ishii+, EPJ conf. 175 (’18)
S=-4 (ΞΞ)
Doi+, EPJ conf, 175 (’18)
SU(3) basis
Inoue+, AIP conf. 2130 (’19)
S=-2 (ΛΛ, NΞ)
S=-3 (NΩ)
S=-6 (ΩΩ)
C=+6 (ΩcccΩccc)
φN

Sasaki+, NPA 998 (’20)
Iritani+, PLB 792 (’19)
Gongyo+, PRL 120 (’18)
Tong+,
PRL 127 (‘21)
Lyu+, 2205.10544 (‘22)

Phase II: almost physical point

Fugaku@RIKEN
440 PFlops(2020-)(2+1)-flavor
V=(8.1 fm)3 , mπ=138 MeV
BB: Octet x Octet
BB: Octet x Decuplet
BB: Octet x Charmed
BB: LS force
MB: KN, φN , DN, J/ψ-N, …
MM: ππ, πK, DD*, J/ψ-J/ψ, …
BBB

Phase III: physical point

24

2019

2020

J-PARC

2030s

2022

2021

YN, YY, (YNN)
Exotic hypernuclei

J-PARC ExHEF (2028(?)-)
HIAF (2024-)

NICER

LIGO/Virgo
KAGRA

GW in NS merger
NS radius

RIBF

3NF (I=1/2, 3/2)
r-process in NS merger

LHC/RHIC

Femtoscopy
Exotic hadrons

Belle II EoS
FRIB (2022-)
FAIR (2025(?)-)
LHC RUN3 (2022-24)

Exotic hadrons
K-computer

11 PFlopsFUGAKUBB, MB
strange, charm

440 PFlops

LS, BBBcharm,bottom

25