Recent Progress in Few-Body Single- & Double–Lambda ... · NPB 16 (1970) 46 PRD 1 (1970) 66 NPB...

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Recent Progress in Few-Body Single- & Double–Lambda Hypernuclei MENU 2019, CMU Pittsburgh, June 2019 Avraham Gal, Hebrew University, Jerusalem Few-body Λ hypernuclei ( A Λ Z ) (i) S-shell hypernuclei: overbinding of 5 Λ He (ii) Lifetime of 3 Λ H and 3 Λ n (iii) CSB in s-shell ( 4 Λ H– 4 Λ He) and in p-shell Few-body ΛΛ hypernuclei ( A ΛΛ Z ) (i) Onset of ΛΛ binding? NPA Topical Issues: 881 (2012) & 954 (2016) Review: A.Gal E.V.Hungerford D.J.Millener Rev. Mod. Phys. 88 (2016) 035004 1

Transcript of Recent Progress in Few-Body Single- & Double–Lambda ... · NPB 16 (1970) 46 PRD 1 (1970) 66 NPB...

Page 1: Recent Progress in Few-Body Single- & Double–Lambda ... · 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

Recent Progress in Few-BodySingle- & Double–Lambda Hypernuclei

MENU 2019, CMU Pittsburgh, June 2019

Avraham Gal, Hebrew University, Jerusalem

• Few-body Λ hypernuclei (AΛZ)

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

(ii) Lifetime of 3ΛH and 3

Λn

(iii) CSB in s-shell (4ΛH–4ΛHe) and in p-shell

• Few-body ΛΛ hypernuclei ( AΛΛZ)

(i) Onset of ΛΛ binding?

• NPA Topical Issues: 881 (2012) & 954 (2016)

• 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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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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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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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.

• YY add 0.3M⊙ to Mmax (Rijken-Schulze 2016).

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

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The lightest, s-shell, Λ hypernucleiAΛZ T Jπ

g.s. BΛ (MeV) Jπ

exc. Ex(MeV)

3ΛH 0 1/2+ 0.13(5)

4ΛH–

4ΛHe1/2 0+ 2.16(8)–2.39(3) 1+ 1.09(2)–1.406(3)

5ΛHe 0 1/2+ 3.12(2)

• No ΛN and no Λnn bound state are expected.

• ∆BΛ(4ΛHe–4

ΛH)=0.23(9) (g.s.) –0.083(94) (exc.) in MeV.

• Recent A = 3, 4 few-body calculations:

• A. Nogga, NPA 914 (2013) 140

Faddeev & Faddeev-Yakubovsky (chiral LO & NLO).

• E. Hiyama et al., PRC 89 (2014) 061302(R)

Jacobi-coordinates Gaussian basis (Nijmegen soft-core).

• R. Wirth et al., PRL 113 (2014) 192502 (chiral LO).

D.Gazda, A.Gal, (2016): PRL 116 122501, NPA 954 161.

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

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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,D1 fitted to B(3H)

How to proceed in Λ & ΛΛ hypernuclei?

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Overbinding problem in s-shell(MeV) BΛ(

3ΛH) BΛ(

4ΛHg.s.) E

x(4ΛHexc.) BΛ(

5ΛHe)

Exp. 0.13(5) 2.16(8) 1.09(2) 3.12(2)

Dalitz 0.10 2.24 0.36 ≥5.16

NSC97f(S) 0.18 2.16 1.53 2.10

AFDMC(I) – 1.97(11) – 5.1(1)

AFDMC(II) −1.2(2) 1.07(8) – 3.22(14)

LOχEFT(600) 0.11(1) 2.31(3) 0.95(15) 5.82(2)

LOχEFT(700) – 2.13(3) 1.39(15) 4.43(2)

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

Resolving the overbinding problem in /πEFT

• Fit 2 ΛN LECs to ΛN scattering lengths.

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

• Calculate in SVM 5ΛHe binding.

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Contessi et al. s-shell Λ hyp. 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

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

Solid line: a two-paraneter fit a+b/λ, λ ≥ 4 fm−1.

Gray horizontal band: λ → ∞ extrapolation uncertainties.

Dashed horizontal line: Bexp.Λ (5ΛHe)=3.12±0.02 MeV.

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3ΛH lifetime puzzle

Lifetim

e (

ps)

0

50

100

150

200

250

300

350

400

450

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 Prel. SQM2017

lifetimeΛPDG value - free

Statistical uncertainties

Systematical uncertainties

Average hypertriton lifetime

, Phys. Rev. C 57 (1998) 1595et al.Expected lifetime H. Kamada

Expected lifetime J. G. Congleton, J. Phys. G 18 (1992) 339

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

Expected lifetime A. Gal, H. Garcilazo, arXiv:1811.03842

The weakly-bound 3ΛH, BΛ=0.13±0.05 MeV, expected

to have lifetime within a few % of the free Λ lifetime.Recent heavy-ion 3

ΛH production experiments yieldlifetimes shorter by ≥ 30%. ALICE, PLB 754 (2016) 360.

STAR, PRC 97 (2018) 054909: τ=142+24−21±29 ps (0.54+0.09

−0.08τΛ).

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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 (2018) 48, Pion FSI effect.

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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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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).

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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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The 4ΛH–4

ΛHe complex & CSB since 2015MAMI’s A1, 4

ΛH→4He+π−, PRL 114 (2015) 232501J-PARC’s E13, 4He(K−, π−γ), PRL 115 (2015) 222501

CSB due to Λ-Σ0 mixing, strongly spin dependent,

dominantly in 0+g.s., large w.r.t. ≈−70 keV in 3H-3He.

Re-measure 4ΛHeg.s. (E13 → E63).

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Relating Λ-Σ0 CSB mixing to ΛΣ SI coupling

Λ

N

Λ

N

VΛN−ΣN

δM

Σ0

Dalitz-von Hippel (1964): “applies to any isovector meson

exchange, π, ρ...” & also to χEFT contact interactions.

〈NΛ|V CSBΛN |NΛ〉 = −0.0297 τNz

1√3〈NΣ|V SI|NΛ〉.

Applied systematically by A. Gal, PLB 744 (2015) 352

A=4: D.Gazda A.Gal (2016), PRL 116 122501; NPA 954 161.

Latest summary: J. Phys. Conf. Series 966 (2018) 012006.16

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NCSM HO hω dependence of ∆BΛ(4ΛHe–4

ΛH) for 0+ & 1+.

Note ± sign pattern resulting from 1S0 Λ-Σ contact term

dominance at LO [see OPE discussion NPA 954 (2016) 161].

Λ=600 MeV: ∆Eγ=∆(∆BΛ)=0.33±0.03 MeV compared to

a measured ∆Eγ=0.32±0.02 MeV.17

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CSB in p-shell hypernuclei

3T

(M

eV

­ B

5.9−

5.8−

5.7−

5.6−

5.5−

5.4−

5.3−

5.2−

5.1−

5−

He7Λ

JLab

*Li7

Λ

FINUDA

*Li7

Λ

SKS rev.

*Li7

Λ

emuls

Be7Λ

emuls

­1 0 0 0 +1

17

0 k

eV

±3

90

17

0 k

eV

±2

70

E. Botta, T. Bressani, A. Feliciello, NPA 960 (2017) 165-179

CSB appears to be much weaker in the A=7 isotriplet

than in the A=4 isodoublet provided counter experiments

are not compared directly with old emulsion results.

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Double-Lambda Hypernuclei

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

H ∼ A[√

1/8 ΛΛ+√

1/2NΞ−√

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].

• ΛΛ correlation femtoscopy in pp at√s=7 TeV

(ALICE exp. at the LHC, arXiv:1805.12455)

rules out a bound H (Laura Fabbietti @HYP18).

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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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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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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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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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Summary & Outlook

• Role of ΛNN forces in AΛZ & neutron stars?

• Resolve the 3ΛH lifetime puzzle from HIC.

• 3Λn (Λnn) is unbound.

• Re-measure the 4ΛH–4

ΛHe complex (E13→E63).

• Search for n-rich AΛZ; (6ΛH not seen in E10).

• Onset of ΛΛ binding: 4ΛΛH or 5

ΛΛZ? (E07).

• 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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