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Λハイパー核の崩壊測定
4. Aug. 2008 サマースクール 1
ーKEK-PSの成果とJ-PARCでの将来計画理研仁科センター理研仁科センター 應田治彦應田治彦理研仁科センター理研仁科センター 應田治彦應田治彦
SKS@K6 のハイパー核崩壊実験の成果とJ-PARC の展望E278(A=5) 味村E278(A=5) 味村E307(A=12,28,56) Park, 里E369(A=12,89) Kim(Jungho)E462(A 5)/E508(A 12) K 岡田 Ki (Mij ) 亀岡 丸田
J-PARC E18 & E22
Weak decay mode of Weak decay mode of ΛΛ hypernucleushypernucleusWeak decay mode of Weak decay mode of ΛΛ hypernucleushypernucleusE462(A=5)/E508(A=12) Kang, 岡田, Kim(Mijung), 亀岡, 丸田
ΓΓππ__ (Λ→ p + π-)
ΓΓππ00 (Λ → n + π0 )
Mesonic q~100MeV/c
1/τ =ΓΓm
ΓΓpp (Λ +“p”→ n + p)ΓΓnn (Λ +“n”→ n + n)Γ (ΛNN →NNN)
Non-Mesonic(NMWD)q~400MeV/c
1/τHY =Γtot
ΓnmΓ2N (ΛNN →NNN) q 400MeV/c
Study of the mechanism of baryon-baryon weak interaction
Mesonic Weak Decay Decay mechanism is known fairly well
2
Decay mechanism is known fairly well“How to use it?”
Non Mesonic Weak Decay (NMWD)1. Γnm2 Γ /Γ 比Non-Mesonic Weak Decay (NMWD)
Decay mechanism is unknown“What is it ?”
2. Γn/Γp 比3. Asymmetry parameter
Ap = αnm×PΛ
q~400MeV/c q~100MeV/c
What is it ?
Fermi >>
p4. ΛNN→NNN ?
Massnumber
4~5
q~400MeV/cΛN→NN
• Spin/isospin dep.
Λ→Nπ
• Λ-nucleus
q 100MeV/cFermimomentum >>
4 5
~10
Spin/isospin dep.• Test of ∆I=1/2 rule
Mass number
Λ nucleuspotential
•Spin/parityassignment
50~100)( ∞→Γ Anm
Mass number dependence
assignment
Pion distortion effect in nuclei)( →nm
4
MesonicMesonic WeakWeak DecayDecay
Λ→p+π-
Λ n+π021 ∆I=1/2 ruleΛ→n+π0 1 / u e
1/2+ 1/2+ 0-
s-wave; PVL=01/2 1/2 0
L=1 p-wave; PC
I(θ)∝1-αP cosθ*
88% s-wave
22
*Re2 ps aa
+=α 12% p-wave
ps aa +
6
Spin assignment using Spin assignment using ππ-- mesonic weak decaymesonic weak decayππ-- mesonic weak decaymesonic weak decay
K- + 4He → 4ΛH + π0
0- + 0+ → 0+ + 0-
0+ + 0+ → 0+ + 0-
0- + 0+ → 1+ + 0-
0+ + 0+ → 1+ + 0-
4 H → π- + 4He
0 + 0 → 1 + 0
ΛH → π + HeJ=0 → Jz=0=s(4
ΛH)z
10
Γn/Γp ratio 19
Initial state Final state Amplitude Isospin Parity1S 1 N
If assuming 1S0
1S0 a 1 No3P0 b 1 Yes3S1 c 0 No
ginitial S state
3S1
S1 c 0 No3D1 d 0 No1P1 e 0 YesP1 e 0 Yes3P1 f 1 Yes
222 )(2 fba ++222222
)(2/fedcba
fbapn +++++
++=ΓΓ (Applying ΔΙ=1/2 rule)
∆S=2,∆L=2 ; 3S1 → 3D1 (L+S+D=odd; T=0) Λp → np T=0,1Λn → nn T=1
ΓΓn n / / ΓΓpp ratioratio3
∆S=2,∆L=2 ; 3S1 → 3D1 (L+S+D=odd; T=0)
ΓΓpp (Λ+“p”→ n + p)ΓΓnn (Λ+“n”→ n + n) Γn / Γp~0.1
One Pion Exchange
Simple theoretical modelca
l Direct Quark mechanism
Meson ExchangemechanismNN
One Pion Exchange(OPE)
eore
tic
N NNNΛ N
W Sπ
The
NΛΛ Nπ K η ρ ω K*
Tensor-dominantrequires the final Nn
pair to have isospin 0
Γ / Γ
π,K,η,ρ,ω,Kpair to have isospin 0.
10 0.5 1.5Γn / Γp
0 93±0 55 (Szymanski et al )Exp. (for 5ΛHe) 0.93±0.55 (Szymanski et al.)p ( o Λ e)
Γn / Γp ratio puzzlePhys.Rev.C43 (1991) 849-862
1. 重いハイパー核の寿命測定 (E307)
τ/1)( →Γ A τ/1)( ≈∞→Γ Anm
Merit of (π+,K+) reaction for heavy hypernuclear lifetime
56Fe target
4
measurement 56Fe target(K-,π-) K- decay background
BG from pion haloHard to produce Λ-bound statefor heavy nuclei
Λ-unbound!
(π+,K+)
for heavy nuclei
No beam-decay BG→ clean selection of Λ bound state→ clean selection of Λ-bound stateLess neutron BG
Large momentum transfer isd i bl t ffi i tl d
(stopped K- π-)
desirable to efficiently produceΛ-bound state for heavy HYP
(stopped K-,π )
K- +NN→Σ- N Σ- n + π- BG is seriousΣ- → n + π BG is seriousespecially for heavy hypernuclei
K6/SKS setup5
K+decay counter
π+
counter
π+
KEK-PS E307 experiment6
E307 Decay counterVETO
pExperimental target: C, Si and FeObservable:
RangePDC
pLifetime π- Mesonic decay branching ratio
PDCK+
SKS
Proton energy spectrumπ+
p / π separation by SKSK6p p y
dE/dx, Etot and range
Overall time resolution; σ < 100 psGood π / p separationSolid angle ~ 30%
Excitation spectra w/ coincident decay particles for Excitation spectra w/ coincident decay particles for 1212ΛΛCC 7
12ΛC 12 C 12 CΛC 12
ΛC 12ΛC
( )(in flight K- π-) (stopped K-,π-)Phys. Rev. C43 (1991) 73(π+,K+)
(in-flight K- ,π-)Phys.Rev.C43 (1991) 849
Results of lifetime measurement8
ps15231)C(12 ±=τ Λ
LifetimeTime spectra of emitted protons
14215)F(ps12206)Si(28
±±=τ Λ
(π+, pp)
ps14215)Fe( ±=τ Λ
Total decay width
ΛΛ Γ±=Γ 08.014.1)(12Ctot
y
ΛΛ
ΛΛ
Γ±=ΓΓ±=Γ
08.022.1)(08.028.1)(28
FeSitot
ΛΛ Γ±Γ 08.022.1)( Fetot
H. Bhang et al. PRL81, 4321 (1998)
9
Lifetime of very-heavy hypernuclei ? (J-PARC)
COSY-13dr Γ 2
Λ
2N
nm ϕ⋅ϕ∝ ∫ (π,K)ρ Λ
0nm ϕ∫ ( , )
at J-PARC
?KEK-E307 ?
2 Γ(Λn→nn)/Γ(Λp→np) 比の測定2. Γ(Λn→nn)/Γ(Λp→np) 比の測定
nCoincidence
NMWD
np
nΛ
pnp
n
NMWD
n npΛ
np
np
NMWD nCoincidence
NMWD
Γ測定の困難さ測定の困難さ
10
Λn → nnΛp np FSI Br(NMWD) Γ2N
NN //NN Directly TheoreticalSerious
Λp → np
NN /N/N Affected only Must to be Free
NNpp//NNnmwdnmwdDirectlyaffected input
Serious
NNnn/N/Npp in 2nd order assumed as 0Free
NN //NN Cancellation Less affectedFreeNNnnnn//NNpnpn Cancellation (back-to-back)Free
Final state interaction ΛNN→NNN
rescattering
Final state interaction (FSI) effect
ΛNN→NNN(2N-induced process)
NNn
n npp pnn
NNW π
N
np
ppnn p Λ
Nπ
N(One of the theoretical model)
The present experimentThe present experimentKEK PS E462/E508
11
KEK-PS E462/E508NMWD : ΛN→NN
Direct measurement of the Γn / Γp ratio
Select ΛN NN eventsn
pnp
CoincidenceNMWD ( ) ( ) .avnnnnnN Ω×Ω×→Λ
Select ΛN→NN events w/o FSI effect & ΛNN→NNN.
np
npΛ p
npn
( ) ( )
( ) ( )( )FSI
2n
.avnn
R1 −×ε×
p
nnp
np
NMWD
( ) ( )( )FSIpn
.avpn
R1
nppN
−×ε×ε×
Ω×Ω×→Λ
Coincidence1) Angular correlationAngular correlation( b k t b k θ 0 8 )
* cosθ<-0.8 * E(N1)+E(N2) cut
( )( back-to-back, cosθ<-0.8 )2) Energy correlationEnergy correlation( Q~E(N1)+E(N2) 〜152MeV )
( )( ) n
p
p
n
coinpairnpNcoinpairnnN
εε
×−−=
ΓΓ
Select light hypernuclei to minimize FSI effect, 5ΛHe and 12ΛC
Decay counter Setup (KEK-PS K6 & SKS)6
Decay armSolid angle: 26%9(T)+9(B)+8(S)%
π
pnn
polarizationaxis
n KpCharged particle:・TOF (T2→T3)・tracking(PDC)
N t l ti lN: 20cm×100cm×5cm
Neutral particle:・TOF (target→NT)・T3 VETO
T3: 10cm×100cm×2cm T2: 4cm×16cm×0.6cm
Decay particle identificationDecay particle identification12
Neutral PIDNeutral PIDNeutral particles from 12
ΛC Charged particles from 5ΛHe
Charged PIDCharged PID
Neutron energy resoltion7MeV(FWHM) at 75MeV
Constant backgroundbackground very small
1 / β spectra PID function1 / β spectraGood γ n separation
PID functionGood π p d separation
6Li Hypernuclear mass spectraΛ13
6Li + π+→ Λ6Li + K+inclusive 5.2×104 events
Λ6Li → Λ5He + p
18.3MeV
(Sn-1,SΛ)
π coin3.2×103 events
(P -1 PΛ)
8.3MeV
(Pn ,PΛ)p decay Λ decay
p coin 1.6×103 events
5Li0MeV
(Pn-1,SΛ)
1.6 10 events
5ΛHe
6ΛLi
Expected Spectrum14
ΛN→nN ΛNN→nNN FSI re-scattering
npnp
n
nn npp p
pnn
nn np
pp ppn
n
n p n ppn pppn p
distribute low energydistribute low energy region up to Q/2 broad peak
around Q/2 continuous
unts
distribution
cou
Q/2Energy spectra (image) Energy
Single proton/neutron spectra from Single proton/neutron spectra from 55ΛΛHe and He and 1212ΛΛCC
15
Calculation byGarbarino et al. ΛNN→NNN ??Garbarino et al. ΛNN→NNN ??
Nn~2Np
S.Okada et al.,S.Okada et al.,PLB 597 (2004) 249
np- & nn- angular distribution (5ΛHe)
16
Back-to-back Back-to-back
/Γn/Γp ∼ Νnn / Νnp = 0.45±0.11±0.03
systematic error is mainly come from efficiency for neutron (6%) + acceptance(3%)
ΓΓn n / / ΓΓpp ratioratio17
NN
One Pion Exchange(OPE)
eo.
N N
Direct Quark mechanism
Meson Exchangemechanism
NN
Λ N
NNW S
π
The
ΛΛ N
NN
Λ Nπ NΛΛ Nπ,K,η,ρ,ω…
10 0.5 1.5Γn / Γp
0.93±0.55 (Szymanski et al.) for 5ΛHe
p.
Previous exp. (at BNL)
N / N (5 He)= 0 45±0 11±0 0355 He (E462)He (E462)
Exp Nnn / Nnp ( ΛHe)= 0.45±0.11±0.0355
ΛΛHe (E462)He (E462)Kang et al. PRL 96 (2006) 062301
Γn / Γp (12ΛC)= 0.51±0.13±0.051212
ΛΛC (E508)C (E508) n p ( Λ )ΛΛ ( )( )Kim et al. PLB641 (2006) 28
Singles and Coin. Yields compared with INC(1N+2N).
0
0.025
0.05
0.075
0.1
0.125
0.15
0 50 100 150
N p/NM
WD/
10M
eV
Ep[ MeV]
dotted line : INC(Γ2n/Γnm = 0., Γn/Γp=0.51),
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150
N n/NM
WD/
10M
eV
En[ MeV]
solid line : INC(Γ2n/Γnm = 0.4, Γn/Γp=0.51)
0
0.02
0.04
0.06
0.08
-1 -0.5 0 0.5 1 cosθnp
N np(co
sθ)
0
0.01
0.02
0.03
0.04
-1 -0.5 0 0.5 1
N nn(co
sθ)
cosθnn
18
0
0.025
0.05
0.075
0.1
0.125
0.15
0 50 100 150
N p/NM
WD/
10M
eV
Ep[ MeV]
dotted line : INC(Γ2n/Γnm = 0., Γn/Γp=0.51),
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150
N n/NM
WD/
10M
eV
En[ MeV]
solid line : INC(Γ2n/Γnm = 0.4, Γn/Γp=0.51)
0
0.02
0.04
0.06
0.08
-1 -0.5 0 0.5 1 cosθnp
N np(co
sθ)
0
0.01
0.02
0.03
0.04
-1 -0.5 0 0.5 1
N nn(co
sθ)
cosθnn
proton neutron
0
0.025
0.05
0.075
0.1
0.125
0.15
0 50 100 150
N p/NM
WD/
10M
eV
Ep[ MeV]
dotted line : INC(Γ2n/Γnm = 0., Γn/Γp=0.51),
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150
N n/NM
WD/
10M
eV
En[ MeV]
solid line : INC(Γ2n/Γnm = 0.4, Γn/Γp=0.51)
0
0.02
0.04
0.06
0.08
-1 -0.5 0 0.5 1 cosθnp
N np(co
sθ)
0
0.01
0.02
0.03
0.04
-1 -0.5 0 0.5 1
N nn(co
sθ)
cosθnn
proton neutron
0
0.025
0.05
0.075
0.1
0.125
0.15
0 50 100 150
N p/NM
WD/
10M
eV
Ep[ MeV]
dotted line : INC(Γ2n/Γnm = 0., Γn/Γp=0.51),
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150
N n/NM
WD/
10M
eV
En[ MeV]
solid line : INC(Γ2n/Γnm = 0.4, Γn/Γp=0.51)
0
0.02
0.04
0.06
0.08
-1 -0.5 0 0.5 1 cosθnp
N np(co
sθ)
0
0.01
0.02
0.03
0.04
-1 -0.5 0 0.5 1
N nn(co
sθ)
cosθnn
+
0
0.025
0.05
0.075
0.1
0.125
0.15
0 50 100 150
N p/NM
WD/
10M
eV
Ep[ MeV]
dotted line : INC(Γ2n/Γnm = 0., Γn/Γp=0.51),
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150
N n/NM
WD/
10M
eV
En[ MeV]
solid line : INC(Γ2n/Γnm = 0.4, Γn/Γp=0.51)
0
0.02
0.04
0.06
0.08
-1 -0.5 0 0.5 1 cosθnp
N np(co
sθ)
0
0.01
0.02
0.03
0.04
-1 -0.5 0 0.5 1
N nn(co
sθ)
cosθnn
Indication of large
p + n n + n
0
0.025
0.05
0.075
0.1
0.125
0.15
0 50 100 150
N p/NM
WD/
10M
eV
Ep[ MeV]
dotted line : INC(Γ2n/Γnm = 0., Γn/Γp=0.51),
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150
N n/NM
WD/
10M
eV
En[ MeV]
solid line : INC(Γ2n/Γnm = 0.4, Γn/Γp=0.51)
0
0.02
0.04
0.06
0.08
-1 -0.5 0 0.5 1 cosθnp
N np(co
sθ)
0
0.01
0.02
0.03
0.04
-1 -0.5 0 0.5 1
N nn(co
sθ)
cosθnn
Indication of large contribution of Γ2N
0
0.025
0.05
0.075
0.1
0.125
0.15
0 50 100 150
N p/NM
WD/
10M
eV
Ep[ MeV]
dotted line : INC(Γ2n/Γnm = 0., Γn/Γp=0.51),
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150
N n/NM
WD/
10M
eV
En[ MeV]
solid line : INC(Γ2n/Γnm = 0.4, Γn/Γp=0.51)
0
0.02
0.04
0.06
0.08
-1 -0.5 0 0.5 1 cosθnp
N np(co
sθ)
0
0.01
0.02
0.03
0.04
-1 -0.5 0 0.5 1
N nn(co
sθ)
cosθnn
1. Singles Quenching
2. LE n enhancementNNN coincidence measurement with
much improved statistics3. Pair Quenching
are well reproduced.
much improved statistics
J-PARC E18
3 Asymmetry Parameter の測定
Ap=αNMPΛ
3. Asymmetry Parameter の測定
Ap α PΛ
Asymmetry parameter αnm19
Initial state Final state Amplitude Isospin Parity1S 1 N
If assuming 1S0
1S0 a 1 No3P0 b 1 Yes3S1 c 0 No
ginitial S state
3S1
S1 c 0 No3D1 d 0 No1P1 e 0 YesP1 e 0 Yes3P1 f 1 Yes
222 )(2 fba ++222222
)(2/fedcba
fbapn +++++
++=ΓΓ (Applying ΔΙ=1/2 rule)
)}(3{41])2(3)2([23
222222 fedcbafdcdcbaeNM
p +++++++−+−=α
We can know the interference between states withdifferent Isospin and Parity .
αNM for 5ΛHe NMWD20
・Polarization of Λ Estimated from
Aπ=απPΛε Λ
mesonic decay
Aπ:Asymmetry of Pionαπ:Asymmetry Parameter of Pion
( 0 642±0 013)(=-0.642±0.013)PΛ:Polarization of Lambdaε :Attenuation factor
α Λ
ε :Attenuation factor
・Asymmetry Parameter of ProtonAsymmetry Parameter of Proton
Ap=αNMPΛεp
We can calculate αNM without theoretical help !p
Asymmetry measurement of decay proton21
Asymmetry : Volume of the asymmetric emission from NMWD
PN(θ) = N0(1 + Acosθ) Asymmetry
ϕK >0 π/p⎝
ΛP
ΛAsymmetryparameter
= N0(1 + αPcosθ) π+ K+
ϕK
⎝
A = (R 1)(R + 1)
R =N(θ-
)
N(θ+)
parameter
ϕK <0
(R - 1) N(θ ) ,
+ 1/2π+
K+ϕK
R =N(θ+
(-ϕ))×N(θ-(+ϕ))
N(θ+(+ϕ))×N(θ-
(-ϕ)) 1/2 K
π/p⎝
ΛP
Difference of acceptance & efficiency → canceled out !!
Λ
Asymmetry parameter of 5ΛHe22
αNM=0 08±0 08+0.080 00α =0.08±0.08 0.08p -0.00
Theory: - 0.6~- 0.7
Comparison with recent calculations23
π+K OME can reproduce+2 / +2 / + +Κ+ /π+K+DQ
π+K,OME can reproduceΓn/Γp ratio but predict large negative αNM
π+2π/ρ+2π/σ+ω+Κ+ρπ/a1Calculation by Itonaga
OMEπ+K+σ
Γn/Γp and αNM can bereproduced byπ+K+σ+DQ modelOME
π+K+σ+DQ
π+K+σ+DQ model
S ki t lπ+K
π+K+σ+DQ Sasaki et al.PRC71 (2005)035502
(1) Large b(1S →3P ) and
OPE(1) Large b( S0→ P0) and
f(3S0→3P1) amplitude(2) Violation of ∆I=1/2
rule considered
)}(3{41])2(3)2([23
222222 fedcbafdcdcbaeNM
p +++++++−+−=α
rule considered
4. Mesonic Weak Decay Width4. Mesonic Weak Decay Width の精密測定
ππ00 identificationidentificationLarge plastic scintillator arrays were used as γ detector.γ detection system
Background (low energy):EM shower
m
Background (low energy): γ from nuclear decay process
EM shower
30cm
π0 emit energetic gamma. (~70MeV)
To reject the nuclear decay γ
Charged VETO
set threshold of ADC sum. The gamma cascade in many layers.
select high multiplicity event.
γ (~70MeV) In these cut conditions, It is hard toestimate gamma detection efficiency.
So we simulated with same conditions using GEANT code.
Start timing counterπ0γK+
π+5ΛHe
35
γγ efficiency estimation using GEANT simulationefficiency estimation using GEANT simulation36
Mul ≥ 4
ADC sum distribution ADC sum distribution
Mul ≥ 1* Blue histogram :
GEANT simulation20MeV
nuclear γ
u GEANT simulation * Plot (with error bar) :
Experimental data γ from π0
Mul ≥ 2 M l ≥ 5Layer multiplicity
assuming π0 momentum in GEANT simulation as 5
ΛHe : 104.9 MeV (mono)12Mul ≥ 2 Mul ≥ 5
Well agree with
12ΛC : Motoba’s calculation
PTP117(1994)
Nuclear γ is shown
gGeant simulation.
Mul ≥ 3 Mul ≥ 6Nuclear γ is shown only Mul ≥ 1.To remove it completely,we apply Mul ≥ 2 andwe apply Mul ≥ 2 andADCsum ≥ 20MeVee .
Decay Widths24
5. J-PARCにおけるハイパー核崩壊実験
残された課題:1) 1S0 initial state の寄与; ∆I=1/2則
ΛΛ ΛN 崩壊ΛΛ→ΛN 崩壊4ΛHe & 4ΛH のnp比
2) ΛNN→NNN 崩壊の寄与
NMWD of 4-, 5-body hypernucleill d i iti l ΛN t t
25
– allowed initial ΛN states
)(0 He4Λ
+)(0 H4Λ
+ He5ΛΛ
p p n Λn n p Λ p p n n Λ
0+ 0+ 0+ 0+
Λn→nn: 1S0, 3S11S0
1S0, 3S1Λp→np: 1S0
1S0, 3S11S0, 3S1
initial final amplitude isospin parity1S0
1S0 a 1 no3P b 1 )1(1 =IS3P0 b 1 yes
3S11S1 c 0 no3D1 d 0 no
)1(0 =IS
)0(13 =IS
36
assuming initial S state
1P1 e 0 yes3P1 f 1 yes
)0(1 IS)1(1
3 =IS
Status of amplitude determination26
Current statusCurrent statusOur prospectsOur prospects
new constraint from 4ΛHeConstraint from 5ΛHe dataother constraints are loose
Λnp-ratio better than 15%
error
J-PARC E22
Decay arms for J-PARC27
Decay arms for J PARC– Large acceptance and high efficiency for NN
( )( ) %30
4.0≈≈Ω
nn
ε
n n
( ) %30≈nε
( ) 25.0≈Ω pp p
G d PID bili ( / / / )
( ) %80≈pεp p
– Good PID capability (n/p/π/γ)
n/γ TOFp/π E/ΔE/rangen/p charge veto
38
n/p charge-veto
SummarySummary28
寿命寿命
重い核で Γtotal~1.2ΓΛ Γnm(A→∞)◆ Γn/Γp比
も5ΛHe, 12
ΛC ともに ~0.5◆ Asymmetry parameter
5ΛHe / 11
ΛB and 12ΛC ともに、 ~0 Λ Λ Λ
◆ Partial decay rates の精密測定
Spin-singlet initial state & ΛNN→NNN の大きな寄与Spin singlet initial state & ΛNN NNN の大きな寄与
[1] 短距離的なメカニズムの重要性が確認されたOPE ⇒ Heavy meson & DQ exchange
[2] ΛN spin-singlet 始状態からの崩壊の大きな寄与?[ ] p g 壊σ-meson exch. / ∆I=1/2 violation? ⇒ 4
ΛH 4ΛHe & ΛΛ→ΛN@J-PARC
http://ag.riken.jp/outa/summerschool.pdf
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