Recent Progress in Hypernuclei - Eventsforce · Recent Progress in Hypernuclei INPC 2019, Glasgow,...
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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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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
sΛ
pΛ
dΛ
sΛ
fΛ
∆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
sΛ
pΛ
dΛfΛ
gΛ
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.
• Milder overbinding keeps hyperons (Logoteta et al. 2019).
• Overbinding has been a problem in s-shell hypernuclei.5
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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2-body & 3-body diagrams in /πEFTL. Contessi, M. Schafer, N. Barnea, A. Gal, J. Mares
submitted for publication
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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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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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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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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);
with pion FSI: τ(3ΛH)=214±8 ps.
• Latest STAR+ALICE: τ(3ΛH)=206+15−13 ps.
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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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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 +√
1/2 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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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
• 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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