Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow,...

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Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem Λ hypernuclei ( A Λ Z ) (i) s-shell hypernuclei: overbinding of 5 Λ He Contessi-Barnea-Gal, PRL 121 (2018) 102502 (ii) lifetime of 3 Λ H and 3 Λ n Gal-Garcilazo, PLB 791 (2019) 48 (iii) charge symmetry breaking ( 4 Λ H– 4 Λ He) Gazda-Gal (2016), PRL 116, 122501 & NPA 954, 161 ΛΛ hypernuclei ( A ΛΛ Z ) onset of binding, A=4 or 5? Contessi-Sch¨ afer-Barnea-Gal-Mareˇ s, submitted Review: A.Gal E.V.Hungerford D.J.Millener Rev. Mod. Phys. 88 (2016) 035004 1

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Page 1: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Recent Progress in HypernucleiINPC 2019, Glasgow, UK, July-Aug. 2019

Avraham Gal, Hebrew University, Jerusalem

• Λ hypernuclei (AΛZ)

(i) s-shell hypernuclei: overbinding of 5ΛHe

Contessi-Barnea-Gal, PRL 121 (2018) 102502

(ii) lifetime of 3ΛH and 3

Λn

Gal-Garcilazo, PLB 791 (2019) 48

(iii) charge symmetry breaking (4ΛH–4ΛHe)

Gazda-Gal (2016), PRL 116, 122501 & NPA 954, 161

• ΛΛ hypernuclei ( AΛΛZ) onset of binding, A=4 or 5?

Contessi-Schafer-Barnea-Gal-Mares, submitted

• Review: A.Gal E.V.Hungerford D.J.Millener

Rev. Mod. Phys. 88 (2016) 035004

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Single-Lambda Hypernuclei

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Page 3: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Observation of Λ single-particle states

0

20

40

60

80

100

120

140

160

180

-10 -5 0 5 10 15 20 25 30

Excitation Energy (MeV)

Cou

nts/

0.25

MeV

KEK E369

∆E=1.63 MeVFWHM

89Y(π+,K+)

Hotchi et al., PRC 64 (2001) 044302 BΛ=23.1(1) → 23.6(5) MeV

Motoba-Lanskoy-Millener-Yamamoto, NPA 804 (2008) 99:

negligible Λ spin-orbit splittings, 0.2 MeV for 1fΛ

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Page 4: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Update: Millener, Dover, Gal PRC 38, 2700 (1988)

0 0.05 0.1 0.15 0.2 0.25

0

10

20

30

Bin

din

g E

ner

gy

(M

eV)

(pi,K)

(e,e’K)

Emulsion(K,pi)

Λ Single Particle States

A−2/3

dΛfΛ

208139

8951

403228

161312

11 108 7

Woods-Saxon V = 30.05 MeV, r = 1.165 fm, a = 0.6 fm

V(MeV) = 27±3 (1964) 27.2±1.3 (1965) 27.8±0.3 (1988)

from π− decays of heavy spallation hypernuclei to (π+,K+)

Skyrme-Hartree-Fock studies suggest ΛNN repulsion.

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Page 5: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Hyperon puzzle: QMC calculationsB

[M

eV

]

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

Lonardoni et al, PRC 89 (2014) 014314

ΛNN effect on BΛ(g.s.)

PRL 114 (2015) 092301

ΛNN effect on neutron stars

• ΛN overbinds, adding ΛNN stiffens EOS of neutron stars.

• Milder overbinding keeps hyperons (Logoteta et al. 2019).

• Overbinding has been a problem in s-shell hypernuclei.5

Page 6: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Overbinding problem in s-shell

(MeV) BΛ(3ΛH) BΛ(

4ΛHeg.s.) E

x(4ΛHeexc.) BΛ(

5ΛHe)

Exp. 0.13(5) 2.39(3) 1.406(3) 3.12(2)

Dalitz 0.10 – – ≥5.16

MC(I) – 2.13(8) – 5.1(1)

MC(II) −1.2(2) 1.22(9) – 3.22(14)

LOχEFT(600) 0.11(1) 2.444 1.278 5.82(2)

LOχEFT(700) – 2.423 1.941 4.43(2)

NLO13χEFT(500) 0.135 1.705 0.915 –

NLO19χEFT(650) 0.095 1.530 0.614 –

• All models produce ΛNN terms to some extent.

• χEFT results cutoff dependent; NLO worse

than LO. Try /πEFT with contact terms only.

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Page 7: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

2-body & 3-body diagrams in /πEFTL. Contessi, M. Schafer, N. Barnea, A. Gal, J. Mares

submitted for publication

!!"# $ %& ' () ' *"+ $ %& ' *) ' (

", $ %& ' () ' *-."/ $ %& ' *) ' *-.

! 0

"1 $ %& ' () ' (

0 021 $ %& ' *-.) ' *-.

! 00

2# $ %& ' *-.) ' *-.

!! !

! 2+ $ %& ' *-.) ' (2, $ %& ' 3-.) ' (2/ $ %& ' *-.) ' *

0 !

Nuclei: C1, C2 from NN scattering lengths,fit D1 to B(3H), then ‘predict’ B(4He).

How to proceed in Λ & ΛΛ hypernuclei?

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Page 8: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

s-shell Λ hypernuclei in /πEFT 1.5

2

2.5

3

3.5

4

4.5

5

1 2 3 4 5 6 7 8 9 10

BΛ( Λ

5H

e)

[Me

V]

Cut-Off λ [fm-1

]

Alexander B

L.Contessi N.Barnea A.Gal, PRL 121 (2018) 102502

Fit 2 ΛN LECs to ΛN scattering lengths.

Fit 3 ΛNN LECs to the three known A=3,4 levels.

BΛ(5ΛHe) vs. cut-off λ in LO /πEFT SVM

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3ΛH lifetime puzzle

0

100

200

300

400

500

Life

tim

e (

ps)

PR 136 (1964) B1803

PRL 20 (1968) 819

PR 180 (1969) 1307

NPB 16 (1970) 46

PRD 1 (1970) 66

NPB 67 (1973) 269

Science 328 (2010) 58

NPA 913 (2013) 170

PLB 754 (2016) 360

PRC 97 (2018) 054909

ALICE

Pb 5.02 TeV−Pb

lifetime - PDG valueΛ

H average lifetimeΛ3

Theoretical prediction

, PRC 57 (1998) 1595et al.H. Kamada

R.H. Dalitz, M. Rayet, Nuo. Cim. 46 (1966) 786

J. G. Congleton, J. Phys G Nucl. Part. Phys. 18 (1992) 339

A. Gal, H. Garcilazo, PLB 791 (2019) 48-53

Recent heavy-ion 3ΛH production experiments yield

lifetimes shorter by ∼30% w.r.t. τΛ=263±2 ps.

STAR, PRC 97 (2018) 054909, τ=142+24−21±29 ps.

ALICE, arXiv:1907.06906, τ=242+34−38±17 ps.

Why is τ(weakly-bound Λ)≪ τΛ=263±2 ps?

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Page 10: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Brief review of lifetime calculationsReference Method R3 Γ(3ΛH,J=1

2,T=0)/ΓΛ

Experiment wo. av. 0.35±0.04 ∼1.40±0.15

Dalitz-Rayet (1966) closure – 1.05

Congleton (1992) Λd 0.33±0.02 1.12

Kamada et al (1998) Λpn Fad. 0.379 1.03

Gal-Garcilazo (2018)∗ Λpn Fad. 0.357 1.23±0.03

• R3=Γ(3ΛH→π−+3He)/Γ(3ΛH→π−+all) ⇒ J = 12.

• Closure: Γ(3ΛH,J=12,T=0)/ΓΛ = 1+0.14

√BΛ.

• A bound, isomeric 3ΛH(J=3

2,T=0) (unlikely)

would decay slower than a free Λ.

• 3Λn, if exists, lives longer by ≈40% than free Λ.

• ∗ PLB 791 (2019) 48, Pion FSI effect: 1.09→1.23.

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Page 11: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Closure approximation calculations

ΓΛ(q) =q

1 + ωπ(q)/EN(q)(|sπ|2+|pπ|2

q2

q2Λ),

pπsπ

2

≈ 0.132,

ΓJ=1/23ΛH =

q

1 + ωπ(q)/E3N(q)[|sπ|2(1+

1

2η(q))+|pπ|2(

q

qΛ)2(1−5

6η(q))].

η(q) < 1: Faddeev wavefunctions exchange integral

ΓJ=3/23ΛH =

q

1 + ωπ(q)/E3N(q)[|sπ|2(1−η(q))+|pπ|2(

q

qΛ)2(1−1

3η(q))]

ΓJ=1/23Λn ≈ q

1 + ωπ(q)/E3N(q)0.641

(

|sπ|2 + |pπ|2(q

qΛ)2)

Γ(3Λn)/ΓΛ ≈ 1.114× 0.641 = 0.714, τ(3Λn) ≈ 368 ps,

compared to 181+30−24±25 ps or 190+47

−35±36 ps from HypHI.

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Page 12: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Pion final-state interaction (FSI)

V π−

opt = − 4π

2µπN(b0[ρn(r) + ρp(r)] + b1[ρn(r)− ρp(r)])

s-wave: b0 = −0.032 fm, b1 = −0.126 fm

• Repulsive for N ≥ Z, not in π− 1H & π− 3He

as verified by observed attractive level shifts.

• Repulsive FSI in the π0 3H decay channel.

Summed FSI in total 3ΛH decay rate nearly zero.

• ∆I=1/2 rule: coherent I=1/2 (π− 3He—π0 3H),

so isovector term gives attractive −2b1.

• Γ(3ΛH)/ΓΛ: 1.09 (no FSI) ⇒ 1.23 (pion FSI);

with pion FSI: τ(3ΛH)=214±8 ps.

• Latest STAR+ALICE: τ(3ΛH)=206+15−13 ps.

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Page 13: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

4ΛH & 4

ΛHe lifetimes

Γ(4ΛH)/ΓΛ ≈ 3

2× (

2

3× 0.7 + 1× 0.3) + 0.25 = 1.40

Γ(4ΛHe)/ΓΛ ≈ 3

2× (

1

3× 0.7 + 1× 0.3) + 0.25 = 1.05

Input: 32for nuclear structure, R4=0.7

23& 1

3for π− or π0 and 4He, Γn.m./ΓΛ ≈0.25

⇒ τ(4ΛH) ≈ 190 ps, τ(4ΛHe) ≈ 250 ps

in rough agreement with measured lifetimes.

Looks like Lifetime Puzzle is limited to 3ΛH.

• For A≥12, τ(AΛZ)∼200 ps, from KEK and

very recently from HKS JLab E02-E017

NPA 973 (2018) 116. Lifetime is due to ΛN→NN.

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Page 14: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Double-Lambda Hypernuclei

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Page 15: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Ξ -

#1

#2

#3

#4

#5

#6

#7

#8

A

B

C

Nagara event, 6ΛΛHe, (KEK-E373) PRL 87 (2001) 212502

BΛΛ(6

ΛΛHeg.s.)=6.91±0.16 MeV, unambiguously determined.

• A: Ξ− capture Ξ− + 12C → 6ΛΛHe + t+ α

• B: weak decay 6ΛΛHe → 5

ΛHe + p+ π− (no 6ΛΛHe → 4He +H)

• C: 5ΛHe nonmesic weak decay to 2 Z=1 recoils + n.

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Page 16: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

The elusive H dibaryonJaffe’s H(uuddss) [PRL 38 (1977) 195] predicted stable

H ∼ A[√

1/8 ΛΛ +√

1/2 NΞ−√

3/8 ΣΣ, ]I=S=0

• To forbid 6ΛΛHe→H+4He, impose B(H)≤7 MeV.

A bound H most likely overbinds 6ΛΛHe

[Gal, PRL 110 (2013) 179201].

• Weakly bound H in Lattice QCD calculations.

SU(3)f breaking pushes it to ≈NΞ threshold,

≈26 MeV in ΛΛ continuum [HALQCD, NPA 881

(2012) 28; Haidenbauer & Meißner, ibid. 44].

• A bound H is not ruled out in ΛΛ correlationfemtoscopy (latest ALICE arXiv:1905.07209)

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Page 17: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

0

1

2

3

4

5

0 0.5 1 1.5 2 2.5 3 3.5 4

∆BΛ

Λ( Λ

Λ6H

e)

(M

eV

)

∆BΛΛ(ΛΛ5H or ΛΛ

5He) (MeV)

ΛΛ5H ΛΛ

5He

Faddeev calc. by I.N. Filikhin, A. Gal, NPA 707 (2002) 491

∆BΛΛ(6

ΛΛHe) ≡ BΛΛ(6

ΛΛHe)−2BΛ(5ΛHe) ≈ 0.7 MeV

implying that 5ΛΛH & 5

ΛΛHe are also bound.

With 4ΛΛH likely unbound, ΛΛ binding onset is 5

ΛΛH & 5ΛΛHe.

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Page 18: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Contessi et al. s-shell ΛΛ hyp. in /πEFT

A Tjon-line correlation similar to that in FG 2002.

Weak dependence on the ΛΛ LEC related to aΛΛ.

The ΛΛN LEC is fitted to ∆BΛΛ(6

ΛΛHe)

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Page 19: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Recent /πEFT ΛΛ calculations

BΛ vs. /πEFT cutoff λ5

ΛΛH bound, 4ΛΛH unlikely

minimum |aΛΛ| to bind 4ΛΛH

is over 1.5 fm, too large!

• Contessi-Schafer-Barnea-Gal-Mares, submitted.

• Neutral systems ΛΛn & ΛΛnn safely unbound.

• Argue that ΛΛ–ΞN coupling effect is minor.

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Page 20: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Binding energy consistency of ΛΛ hypernuclei

event AΛΛ Z Bexp

ΛΛ BCMΛΛ † BSM

ΛΛ † †E373-Nagara 6

ΛΛHe 6.91± 0.16 6.91± 0.16 6.91± 0.16

E373-DemYan 10ΛΛBe 14.94± 0.13 ‡ 14.74± 0.16 14.97± 0.22

E373-Hida 11ΛΛBe 20.83± 1.27 18.23± 0.16 18.40± 0.28

E373-Hida 12ΛΛBe 22.48± 1.21 – 20.72± 0.20

E176 13ΛΛB 23.4± 0.7 ∗ – 23.21± 0.21

† E. Hiyama et al., PRL 104 (2010) 212502, & refs. therein

†† A. Gal, D.J. Millener, PLB 701 (2011) 342, assuming that

< VΛΛ >≈ ∆BΛΛ(6

ΛΛHe)=0.67±0.16 MeV

‡ Assuming production in 10ΛΛBe non g.s. 2+(3.04 MeV)

∗ Assuming 13ΛΛBg.s. decay to 13

ΛC∗(5/2+, 3/2+; 4.8 MeV) + π−

• Unassigned Hida event [PTPS 185 (2010) 335]

• BSMΛΛ ≈ BCM

ΛΛ , but SM spans a wider A range

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Page 21: Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow, UK, July-Aug. 2019 Avraham Gal, Hebrew University, Jerusalem • Λ hypernuclei

Summary & Outlook

• 5ΛHe overbinding problem resolved.

• Role of ΛNN forces in AΛZ & neutron stars?

• Resolve the 3ΛH lifetime puzzle (in J-PARC ?).

• 3Λn (Λnn) is unbound.

• look for H dibaryon in (K−,K+) (J-PARC E42).

• Onset of ΛΛ binding: 4ΛΛH or 5

ΛΛZ? (E07, P75).

• 3ΛΛn (ΛΛn) and 4

ΛΛn (ΛΛnn) are unbound.

• Shell model works well for g.s. beyond 6ΛΛHe.

• Study excited states by slowing down Ξ− from

pp → Ξ−Ξ+ in FAIR (PANDA).

Thanks for your attention!

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