Αρχιμήδους Άπαντα 1970 - Ευάγγελος Σταμάτης - Τόμος Α Μέρος Β
Recent Progress in Few-Body Single- & Double–Lambda ... · NPB 16 (1970) 46 PRD 1 (1970) 66 NPB...
Transcript of Recent Progress in Few-Body Single- & Double–Lambda ... · NPB 16 (1970) 46 PRD 1 (1970) 66 NPB...
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
1
Single-Lambda Hypernuclei
2
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
3
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.
4
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
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.
6
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?
7
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.
8
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.
9
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).
10
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.
11
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.
12
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).
13
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.
14
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).
15
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
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
CSB in p-shell hypernuclei
3T
(M
eV
)Λ
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.
18
Double-Lambda Hypernuclei
19
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.
20
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).
21
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.
22
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)
23
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.
24
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
25
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!
26