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