1Study of hyperon-nucleon interactions
for understanding the hierarchicalstructure of matter with hyperons
Koji Miwa (Tohoku Univ.)
on behalf of J-PARC E40 collaboration, HEF ex TF
B01 group : Hierarchy of matter studied via strange hadron clusters

CLUSHIQ2022, Oct. 31st – Nov. 3rd, 2022

Hypernuclear physics

2

Baryon-Baryon interaction Study of light Λ, Ξ hypernuclei Spectroscopy of heavy hypernuclei
Density at Λ orbitp3

ΛHΛ

deuteronΛΛΛΛΛsΛpΛdΛfΛ

gΛ

EnergyhΛfΛΞ hypernucleidΛTwo-body YN int.

pΛ

ΛN-ΣN coupling, ΛNN int., ΛΛ, ΞN int.

sΛDensity dependent ΛN int., ΛNN int.

Neutron star?

pnΞΛ

3Contents• Introduction• Σp scattering experiment (J-PARC E40)

• Σ−p channels (Differential cross sections)• Σ+p elastic scattering (Differential cross sections and phase-shiftanalysis)• Future project : J-PARC HEF extension project• Λp scattering with polarized Λ beam
• High-resolution Λ hypernuclear spectroscopy at HIHR

• SummaryRealistic nuclear force : base for nuclear physics
Realistic Nucleon-Nucleon Potential (CD Bonn, AV18, Nijmegen I, II)
Updated based on a lot of scattering observables of NN scattering

Solid base for nuclear studies
3 Nucleon Force

Nucleon-Deuteron scattering

Nuclear binding energy

K. Sekiguchi et al.
Phys. Rev. C 65, 034003 (2002)

Equation of State of Nuclear Matter4

NN scattering and hyperon-nucleon (YN) scattering
Clearly there is a big difference in data quality between NN and YN scatterings

Λp scattering
np scattering

YN scattering experiment was regarded as impossible experimentΣ+p scatteringNN scattering and hyperon-nucleon (YN) scattering
Clearly there is a big difference in data quality between NN and YN scatterings

Λp scattering
np scattering

YN scattering experiment was regarded as impossible experimentΣ+p scattering

7

Recently, many achievements in two-body BB interaction
study has been realized both theoretically andexperimentally.

Lattice QCD

K. Sasaki et al., Nucl. Phys.
A 998 (2020) 121737

ΞN potential close to physical point
11S ΞN is most attractive among spin-isospin configurations
0Slide from Doi-sanT. Iritani et al. Phys. Lett. B
792 (2019) 284

Attractive potential w/ NO Pauli exclusion
Decay suppression to ΛΞ, ΣΞ with D-wave

S=-1 system
Theoretical improvement with Misner’s method (T. Miyamoto et al. Phys.Rev. D 101 (2020) 074514) is ongoing.

BB interaction from femtoscopy
𝒄𝒄 𝒌𝒌∗

𝟐𝟐
𝑵𝑵 (𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔)∗∗∗= � 𝑺𝑺(𝒓𝒓 ) 𝜳𝜳(𝒌𝒌 , 𝒓𝒓 ) 𝒅𝒅𝟑𝟑 𝒓𝒓∗=𝑵𝑵(𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔)

Fix source size(S(r*))  Study interaction from wave function (Ψ(𝑘𝑘 ∗ , 𝑟𝑟 ∗ ))Powerful method to test BB int. theoriesp-Ξ− correlationp-Ω− correlation

ALICE Collaboration, Nature 588 (2020) 232

and more correlation data !

Chiral EFT in strangeness sector• Underlying chiral symmetry in QCD• Power counting feature to improve calculation systematically by going to higher order• Multi baryon force appear naturally and automatically
YN interaction at NLO
S. Petschauer et al. Nucl. Phys.
A 957 (2017) 347

Density-dependent effective potential
w/ 2π-exchange ΛNN and ΛNN-ΣNN
3BF

Promoted to NLO
B*J. Haidenbauer et al., Eur. Phys. J. A (2020) 56:91
J. Haidenbauer et al., Nucl. Phys. A 915 (2013) 24

M. Kohno, Phys. Rev. C 97 (2018) 035206

ΛN+ ΛNN+ ΛNN-ΣNN

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New and accurate YN scattering data are alsoessential to construct realistic BB interaction models.

J-PARC E40 : Measurement of dσ/dΩ of Σp scatterings
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Verification of quark Pauli repulsion

Constraint for BB int. theories

Lattice QCD calculation

Σ+p scatterng

T. Inoue, AIP Conf. Proc. 2130, 020002 (2019)

Quark Cluster model (FSS, fss2)
Nijmegen model
Chiral EFT (NLO)

Very repulsive interaction
6 quarks can stay in s state innormal case𝑑𝑑𝜎𝜎⁄𝑑𝑑Ω (mb⁄sr)

Σ+p (0.5 < p (GeV/c) < 0.6)

Pauli Forbidden !
Phase-shift measurement
𝑙𝑙=0s u uu u dΣ+pSystematic measurements of dσ/dΩ
Σ+p elastic scattering•• Σ−p elastic scattering• Σ−p  Λn inelastic scatteringcos 𝜃𝜃

J-PARC E40 experimental setup
Two successive two-body reactions• Σ production by πpK+Σ reaction• Σp scattering reaction@ J-PARC K1.8 beam line

CATCHπ−LH2 targetp13KURAMA spectrometer• Identification of K+• Momentum analysis

Σ−Κ+
Momentum tagging of Σ beamπ+Beam-line spectrometer• Momentum analysis ofπ beam

J-PARC E40 experimental setup
Two successive two-body reactions• Σ production by πpK+Σ reaction• Σp scattering reaction@ J-PARC K1.8 beam line

CATCH

π−

LH2 targetpΣ−

KURAMA spectrometer• Identification of K+• Momentum analysispn
π−14Κ+
Momentum tagging of Σ beamπ+Beam-line spectrometer• Momentum analysis ofπ beam

dσ/dΩ of Σ−p scattering channels

15np

Σ−p elastic scattering
K. Miwa et al., PRC 104, 045204 (2021)

Σ−

Σ−

Σ−

Λ

Σ−pΛn inelastic scattering

Clear forward peaking angular dependence
Comparison with theories

K. Miwa et al., PRL 128, 072501 (2022)

Moderate forward peaking dependence• fss2, Chiral EFT show a reasonable angular dependence.
• Nijmegen ESC models clearly underestimate the forward angle.

dσ/dΩ of Σ+p elastic scattering

16T. Nanamura et al., Prog. Theor. Exp. Phys. 2022 093D01

Σ+p scatterng
6 quarks can stay in s state
in normal casePauli Forbidden !
l=0s u uu u dΣ+pThe more repulsive potential in 3S1
 The larger dσ/dΩ (like fss2)

Comparison with theories

E40 data : much smaller than fss2 prediction and E289 results• fss2, FSS (quark model) are too large compared to data
• Chiral EFT’s momentum dependence does not match with data
• Nijmegen (ESC) models are rather consistent.

Phase shift analysis
Phase shift analysis for Σ+p dσ/dΩ• Two parameters : δ(3S1), δ(1P1)• Other phase shifts up to D wave :fixed on NSC97f, ESC16, pp scat

Fitting dσ/dΩ with sum of partial waves
0.44<p(GeV/c)<0.55

0.55<p(GeV/c)<0.65

17T. Nanamura et al., Prog. Theor. Exp. Phys. 2022 093D01

Phase shift analysis
Phase shift analysis for Σ+p dσ/dΩ

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T. Nanamura et al., Prog. Theor. Exp. Phys. 2022 093D01• Two parameters : δ(3S1), δ(1P1)• Other phase shifts up to D wave :fixed on NSC97f, ESC16, pp scat

Comparison with HAL QCD ΣN potential

First experimental derivation of phase shift of 3S1
E40 data

NSC97f

ESC16

δ(3S1)

fss2H. Nemura et al., EPJ Web of Conf., 175, 05030 (2018)

Derived phase shift suggest that the 3S1 interaction is moderately repulsive.

Chiral EFT is in progress w/ E40 data
Development of Chiral EFT at NNLO have got started with E40 datareactionelastic scattering

elastic scatteringdatachiral EFT calc.

But, still …

Slide of J. Haidenbauer at HYP2022

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Future project at J-PARC

J-PARC Hadron Experimental
Facility Extension ProjectHadron Experimental Facility
Extension (HEF-EX) project
K1.8BR（~1.0 GeV/c K− ）Kbar N interaction

K10HIHRCP violation in K0L decay

high-pCOMET

KL2

K1.8KL (KOTO)

KLT1Ω baryon spectroscopy

K1.8（~1.8 GeV/c K− ）K1.8
K1.8BR

Ultra precise Λ hypernucler
spectroscopy

BB interaction(focusing on S=-2)

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K10 (~10 GeV/c K-)

HIHR (~2 GeV/c π)

K1.8BR

T1

T2

Test-BLCOMET
K1.1BR (~0.8 GeV/c π/K)

high-p （30GeV primary proton beam）
π20（20GeV/c secondary beam）
Hadron property in nuclear medium
Baryon spectroscopy

Physics using alow energy Kaon

K1.1
K1.1BR
high-pKL2 (KOTO step2)

Search for CP violation
beyond the SM sensitivity
K1.1 (~1.2 GeV/c π/K)
BB interaction(focusing on S=-1)

Perform physics not accessible in the present hadron hall
Perform physics programs in parallel with twice more beam lines

Hyperon puzzle in neutron star
Strange Hadronic Matter in neutron star ?

Hyperon’s appearance is reasonable scenario because of
the huge Fermi energy of neutrons in the inner core.

ds

ΞHigh density
D. Gerstung et al., Eur. Phys.
J. A(2020) 56:175

un ps

How can we reconcile ?
Hyperon appearance  soften EOS
Two-solar-mass NS  require stiff EOS

Repulsive

Λ3 Baryon Force (3BF):
Significant repulsive contribution at high density
LowHyperonss22

YN(ESC)+3BF(MPa)YN (ESC) only

Y. Yamamoto et al.
PRC90, 045805(2014)We have to understand the density dependence of ΛNinteraction from Λ binding energy data in hypernuclei.
 determine the strength of the ΛNN force

23Toward Λp scattering
Reliable ΛN two-body interaction :key to deepen Λ hypernuclear physics

Λ hypernuclei

key to reveal ΛNN int.

p nΞ Neutron starΛ?

Femtoscopy from HIC
New cross section datafrom Jlab CLAS

New project at J-PARC
Λp scattering w/ polarized ΛpΛ• Feasibility test w/ E40 data
• Expected results in new experiment

ALICE Collaboration, arXiv:2104.04427

J. Rowley et al. (CLAS), Phys. Rev. Lett. 127 (2021) 272303

Λp scattering experiment with polarized Λ beam
Λ beam identification
Tagged by π−p  K0Λ reaction at p=1.05 GeV/cJ-PARC P86 (J-PARC EX project)
at K1.1 beam line
Almost same setup with E40To SKS spectrometer
SKS spectrometerΛp scattering identification
Detected by CATCH

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Λp scattering experiment with polarized Λ beam
Analyzing power

High spin polarization of ΛΛ beam polarization (PΛ)Λ polarization in the π-p→K0Λ reaction

Left/Right asymmetry of Λp scattering
Right scattered event

Left scattered eventΛp’Λ
*E40 data*R. D. Baker et al (1978)
cosθCM, K0

Realize spin observable measurement

25pp’

Λ

Depolarization (Dyy)pΛChange the spin polarization after the Λp scattering

dσ/dΩ and Spin observables in Λp scattering
J-PARC P86 (J-PARC EX project) at K1.1 beam line

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Analyzing power

Depolarization (Dyy)

Simulation

Simulation

Differential cross section

Simulationcosθcosθ

No differential observables of Λp scattering SO FAR
Simulated results w/ 108 Λ--> Large uncertainty in P-wave and higher-wave interaction.
Theoretical prediction shows quite different angular dependence in dσ/dΩ, Ay and Dyy
These new scattering data become essential constraint to determine spin-dependent ΛN interaction

Λ binding energy measurement deep inside of nucleus : Unique for Λ hypernuclei
Nuclear density is different for each Λ orbital state
Density at Λ orbit

Energy spectra of 13ΛC, 16ΛO, 28ΛSi, 51ΛV, 89ΛY,139 La, 208 Pb with Nijmegen ESC16 modelΛΛ
M.M. Nagels et al. Phys. Rev. C99, 044003 (2019)

ΛΛ

Λ

ΛsΛ

pΛ

dΛ

fΛ

gΛ fΛ

EnergydΛpΛsΛTwo directions for study of the density
dependence of ΛN interaction• Mass number dependence of BΛ• Λ orbital dependence of BΛ

Accurate BΛ measurementw/ ΛN int. w/o ΛNN int.
w/ ΛN int. w/ ΛNN int.

DifferenceCalculation w/ only ΛN int : Over boundEffect of density dependence ΛNN repulsive interaction is introduced toof ΛN interaction
explain Λ hypernuclear binding energy

This density dependence should be explained from ΛNN force.
 Predict ΛN int. in higher density nuclear matter.

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High-resolution Λ hypernuclear spectroscopy at HIHR
HIHR : Dispersion-matching beam line Realize high-resolution spectroscopy without beam intensity limit

High intensity π beam of > 108 /pulse(~100 times stronger than KEK-PS)

Focal plane• Thin target can be used High resolution and various target options
Impossible to separate peaks

with a few MeV resolution

208 Pb (KEK-PS)
ΛBΛ=0 MeV

0.4 MeV (FWHM) resolutionBΛ=−5 MeV
BΛ=−10 MeV

Clear separation of sub-major as well as major peaks

ΔE=2.3 MeV (FWHM)

BΛ=−15 MeVhΛ

Each peak cannot be separated

gΛ

HIHR
fΛ
dΛ

T.Hasegawa etal., Phys. Rev. C
53 (1996) 1210.

pΛsΛPrecise Λ binding energies
for wide-mass range

Density dependence of ΛNinteraction (ΛNN interaction)
Calculate UΛ at high density region
Untangle hyperon puzzle in neutron starSummary and future prospects• Many progresses have been obtained in the BB interactions study.
• Lattice QCD, Chiral EFT, …
• Femtoscopy is successfully used for the hadron-hadron interaction study.
• YN scattering experiment gets possible!

• Systematic measurements of Σp scattering at J-PARC• dσ/dΩ for Σ+p, Σ−p, Σ−pΛn scatterings with ~10% level accuracy for fine angular pitch (dcosθ=0.1)• Momentum dependence of Σ+p δ(3S1) channel was derived (−20 ~ -35 degrees)• Future project : Λp scattering w/ polarized Λ beam
• dσ/dΩ and spin observables (analyzing power, depolarization)•  reinforce the current ΛN interaction for deepening hypernuclear physics.

• High-resolution spectroscopy up to medium and heavy Λ hypernuclei• New HIHR beam line with dispersion-matching technique will open new era of unprecedent
resolution of 400 keV (FWHM)• By using this high resolution, the ΛNN 3body interaction will be examined.

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