The Three-body Process in the Weak Interaction Observed in the Decay of Λ hypernuclei

H. Bhang for KEK-PS SKS collaboration

(Seoul National University)

APCTP-KPS Workshop on Nuclei Far from Stability

and Their Application Chonbuk National University

Oct. 20-22, 2005

I. Issues / focus of NMWD

II. The status of Γ n/Γ p

III. Signatures of three-Body decay Process

Nonmesonic q~ 400 MeV/c

Weak Decay Modes of Λ Hypernuclei

Γ tot(=1/τ )

Γm

Γ nm

Γπ - ( Λ pπ - )

Γπ o ( Λ nπ o )

Γ p ( Λp np )

Γ n ( Λn nn )

Mesonic

q~ 100 MeV/c

Γ 2N (ΛNN NNN)

(1N)(2N)

Main focus

Focus:

• Baryon-Baryon Weak Interaction

• Long standing puzzle on Γ n/Γ p.

• 2N NMWD: 3-Body, ΛNNnNN, Interaction Process

Hyp. Nuc.

Γnm Γn/Γp

BNL

5ΛHe 0.41±0.

14.93±0.55

12ΛC 1,14±0.

21.33±1.12/0.

81

KEK’95

12ΛC 0.89±0.

181.87±0.91/1.

59

Status of Γn/Γp puzzle

Γ n/Γ pexp >> Γ n/Γ p

th(OPE)

~ 1 ~0.1

1. Γ n/Γ p Puzzle :

2. Recent Development of Γ n/Γ ptheory : 0.3 ~ 0.7

K.Sasaki, Nucl. Phys. A669 (2000) 371

D. Jido, Nucl. Phys. A694 (2001) 525

10 0.5 1.5

n / p

OPE

p n p,n singles spec p,n pair no. meas. meas. ~ 1.0 ~0.5 ~0.5 ~ 0.5

E307etc. E369 E462/E508

π+

K+

3. Recent Exp. Development at KEK-PS

Nn(> 40 MeV) =0.69

Np(> 40 MeV) =0.40

Г n/Г p(12ΛC) = 0.51±0.14

Theory Independent!! Y. Sato et al., PRC 71 (2004) 025203

J. Kim et al., PRC 68 (2003) 065201

Agrees well with the recent theoretical values, 0.3-0.7.

Then What has been the problem?

If Γ n/Γ p=1/2, one would expect (Np,Nn)=(0.67, 1.33).

[ 1 (0.5, 1.5) ]

Instead we obtained (0.40, 0.69).

Main reason of the difference ; Eth cutoff

However, the quenching was even more than what one would expect from the threshold cut.

So the quenching of proton yields were attributed to a strong neutron side strength giving us a large Γ n/Γ p ratio.

Ambiguities in Singles Measurements

E307/E369 : Г n/ Г p (12

ΛC) = 0.51± 0.14 (stat. only)

- Derived from Nn/Np ratio- Almost model independent.- agrees well with the recent theoretical values (~.5)

In order to resolve the difficulties,• Exclusive measurements

• 5ΛHe E462

• 12ΛC E508

• effect of residual final state int. • 2N induced NMWD.

However, ambiguities due to

π

K

Setup E462Setup E462/E508/E508(KEK-PS K6 beamline & SKS)

Ep

En

π

SKS

θ

inclusive

-gate

p-gate

d-gate

5He g.s.

inclusive

-gate

p-gate

d-gate

inclusive

w/ p

w/ n

w/ n+p

w/ n+n

12C g.s.

quasi free

Excitation Energy Spectra

Nn / Np (E>60MeV)~2.00±0.09±0.14

Γ n/Γ p= 0.58±0.06±0.08.

Nn / Np (60<E<110MeV) ~2.17±0.15±0.16Γ n/Γ p =0.61±0.08±0.08.

To avoid suffering from FSI effect & ΛNN→NNN,

High energy thresholdHigh energy threshold

Singles spectrum in NMWD

Okada et al., PLB 597 (2004) 249

Coincidence Observables

p

n

θ

1. Nucleon Energy sum spectrum;

Ep+En, En+En

2. Pair number per NMWD;

Nnp(cosθ),

Nnn(cosθ)

Nnp Ynp/(Ynm•εnp)

Energy Sum spectrum1. Sharp peak in Ynp(He) at Q

value. FSI negligible in He.

1. Broad spec in Ynn(He). FSI? No. π - absorption or 2N? π - can not make it broad.

Seems 2N effect!!3. Ynp(C); FSI is significant.

4. Ynn(C); Even further degraded.

Again points to 2N.

Esum = En + Ep Esum = En1 + En2

QQ

QQ

Energy Sum Spectum of the Two Nucleons

(Esum)np=12(8), (Esum)nn=16(11) MeV- ΔI=1/2 rule

- np pair absorp.

Back-to-back(bb)(cosθ≤ -0.8)

Angular Correl.of np pair

Angular Correl.of nn pair

Angular

B.Kang et al., prl submitted (’05)

NNNYNN/Ynmwd

npnn / np = 0.45±0.11±0.03

• bb dominant

• nbb; only

a few events.

• In nn, more

counts

Angular

Back-to-back(cosθ≤ -0.7)

bb ; 2-body kinematics

nbb ; ?

M. Kim et al,, Proc. of DAFNE04

(2004) 237

np= 0.50±0.11±0.03

Similar behavior

• bb dominant in np

• In nn, bb no more

major one

From the singles of E462/E508 5

ΛHe (E462) Γ n/Γ p(5ΛHe) = 0.61 ± 0.081 ± 0.082.

12ΛC (E508) Γ n/Γ p(12

ΛC) = 0.58 ± 0.06 ± 0.08.

Here no Γ2N assumed !!

5ΛHe (E462) Γ n/Γ p(5ΛHe) = 0.61 ± 0.081 ± 0.082.

12ΛC (E508) Γ n/Γ p(12

ΛC) = 0.58 ± 0.06 ± 0.08.

Here no Γ2N assumed !!

Г n/Г p from singles and coincidence data

from the coincidence pair yields,

5ΛHe (E462) Γ n/Γ p(5ΛHe) = 0.43 ± 0.12 ± 0.044

12ΛC (E508) Γ n/Γ p(12

ΛC) = 0.50 ± 0.13 ± 0.05.

Γ2N component is kinematically removed !!

Free from Г 2N Ambiguity

5ΛHe (E462) Γ n/Γ p(5ΛHe) = 0.43 ± 0.12 ± 0.044

12ΛC (E508) Γ n/Γ p(12

ΛC) = 0.50 ± 0.13 ± 0.05.

Γ2N component is kinematically removed !!

Free from Г 2N Ambiguity

diffences

Г 2N

Now we have Г n/Г p almost ambiguity free!

Then, can we determine each Γ n, Γ p itself ?

How about Г 2N(ΛNNnNN)?

Can we neglect it?

1.Large contribution of the 3-body decay process, Λ+NNNNN (Γ2N), was predicted in the theoretical calculations. Γ 2N was predicted about 1/5 of Γ nm.

(PRC 256(’91) 134, PRC 50 (’94) 2314)

2. So far no experimental identification has been made.

3. Original motivation of the experiments, E462 and E508, was to identify Γ 2N experimentally.

Status of (ΛNNNNN)

We remember that the quenching of proton singles yield was the source of the long standing confusion on Γ n/Γ p. Later we found even severer quenching in the neutron yield.

Why such severe Quenching?

1. Quenching of Singles yields ;

2. Energy sum spectrum ;

3. Quenching of Total pair yields ;

4. Enhancement of nn pair yields in the non-back-to-back angular kinematic region

5. The difference of Γ n/Γ p values derived from singles yields and coincidence pair numbers.

Signatures of Three Body Process in Weak Decay

So many places !!

In every places !!

1. Quenching of Singles Yields

Signatures of Three Body Processes

Compared to INC spectrum

(Nn+

Np)/

NM

WD

EN (MeV)

12ΛC

Significant quenching of the Nn+Np could not be explained with 1N only INC.!!

For 2N, we adopted the kinematics of uniform phase space sharing of 3 nucleons.

INC(IntraNuclear Cascade) calculation

(p,p’)

Mass Dependence

M. Kim, JKPS 46 (’05) 805

Kin. Energy Dependence

Total Pair Number is compared to that of INC

• We know that FSI(He) not strong.

Then what are those in Ynnnbb(He)?

• R(np) enhancement in C over He.

FSI

• R(nn) enhancement over R(np) both in He and C

2N? where R=Nbb/Nnbb

15 counts

8 counts

Enhancement of nn pair yields in the nbb angular region

This model tends to produce 2 HE neutron and one LE proton. Then protons are often cut off at the threshold.

No kinematic seperation With kinematic seperation

Eth SinglesQuenchin

g

NNN

Quenching

N2N;in Nnnnbb

Npn2N=0

N2NNNN

exp-

NNNINC

Γ2N/ΓNM 0.41±0.08(stat.error)No INC error included

0.37±0.14 (stat.error) No INC error

0.29±0.23(0.18±0.14)

0.28±0.12(0.30±0.19)

Rough Estimation of Γ2N

1. Consider the Nnpnbb all due to FSI. Then subtract the corresponding FSI amou

nt from Nnnnbb. The remainder would be N2N. This give us a kind of lower limit o

f Γ 2N which is about 18-19% of Γ nm.

2. Use INC calculation result to estimate the FSI component in Nnpnbb. Then it wi

ll give ~25-30% of Γ nm.

Summary

1.A series of experiments have been done for the study of NMWD of Λ hypernuclei at KEK-PS,

2. The coincidence exclusive measurement of NMWD were done for the first time for 5He and 12

ΛC and determined the Г n/ Г p to be ~0.5 almost free from the ambiguity of FSI and 2N contribution.3. The Γ n/Γ p values, ~0.5, well support the recent theoretical ratios.

4. All the signatures indicates fairly large Γ 2N comparable to Γ n, but with only a 2σ confidence level.

5. Now the accurate measurement ofГ 2N becomes so important that the decay width of each NMWD mode can be determined only after it.

6. A proposal for its accurate measurement is planned for JPARC.

KEK, RIKEN, Seoul Univ., GSI,Tohoku Univ., Osaka Univ., Univ. Tokyo

Osaka Elec. Comm. Univ.G , Tokyo Inst. Tech.

S. Ajimura, K. Aoki, A. Banu, H. Bhang, T. Fukuda, O. Hashimoto, J. I. Hwang, S. Kameoka, B. H. Kang, E. H. Kim, J. H. Kim, M. J. Kim, T. Maruta, Y. Miura,

Y. Miyake, T. Nagae, M. Nakamura, S. N. Nakamura, H. Noumi, S. Okada, Y. Okatasu, H. Outa, H. Park,

P. K. Saha, Y. Sato, M. Sekimoto, T. Takahashi, H. Tamura, K. Tanida, A. Toyoda, K.Tsukada,

T. Watanabe, H. J. Yim

KEK-PS E462/508 KEK-PS E462/508 collaborationcollaboration

Extra Slides

Total pair yields, NT:

If Γ 2N=0, Eth =0 and FSI=0, NT=1.

If Γ 2N=0, Eth =0 and FSI≠0, NT=1+α.

If Γ 2N ≠ 0 and Eth ≠ 0, NT=?.

This also has the limitation as the singles.

Quenching of Total Pair Yields

5ΛHenp pair

nn pair

np pair

nbb

nn pair

12ΛC

NT = 0.38

INC(IntraNuclear Cascade) calculation

• A nucleus as a Fermi gas.

• ρ(x) V(x)

• FSI is simulated as a cascsde free NN scattering along with Fermi blocking imposed.

• Density geometry parameters are determined fitting the reactions, (p,p’) and (p,n) data with which Mass and Energy dependence were checked

• These parameters are fixed for the decay INC calc.

(p,p’) Mass Dependence

M. Kim, JKPS 46 (’05) 805

Г 2N

1.Both singles yields (E307, E369) and coincidence yields (E462, E508) gave Γ n/Γ p ~0.5 which now agrees well with the recently enhanced theoretical ratios distributed in the range of 0.3-0.7.

2. The coincidence measurement of NMWD were done for the first time and determined the Γ n/Γ p values exclusively for the two body ΛNNN process. It is almost free from the ambiguities of FSI and 2N contribution.

Now we have Г n/Гp almost ambiguity free!

Then, can we determine each Γ n, Γ p itself ?

How about Г 2N(ΛNNnNN)?

Can we neglect it?

10 0.5 1.5

5ΛHe : 0.61±0.081±0.082 (E462)

12ΛC : 0.58±0.06± 0.08 (E508)

: (0.45~0.51)±0.15 ( E307/E369)5

ΛHe : 0.45 ±0.11 ± 0.03±(E462)12

ΛC : 0.50 ±0.13 ± (0.05) (E508) Coincidence

Exp.

OPEOME, DQ model

Singles

n / p

Γ n/Γ p Status

Energy resolution

σ ～ 8MeV( around 80MeV )

1/β spectra

5MeV< energy < 150MeV

Neutral particleNeutral particle Charged particleCharged particle

π p

d

PID spectra

Particle identificationParticle identification

Proton and neutron spectra

Nn(> 40 MeV) =0.69

Np(> 40 MeV) =0.40

E369 decay counter setup Г n/ Г p(12

ΛC) = 0.51±0.14

Obtained directly from the experimental ratio, Nn/Np,

Almost theory independently while previous ones were derived comparing to that of INC.

NnYn/Ynmwd

()

Y. Sato et al., PRC 71 (2004) 025203

J. Kim et al., PRC 68 (2003) 065201

Np/d

ecay

Proton Energy spectrum

Np/nm ~0.4

Λ+nn+nΛ+pn+p

E307 decay counter setup

where 2N ; ΛNN NNN.

2N)(1N 0.230.11

(1N) 0.210.09

0.60

0.87

pΓnΓ

Comparison to INC results gave

Angle/Energy sum Correlations

12ΛC

Preliminary Results

5ΛHe 12

ΛC

Sharp back-to-back

kinematic nature in5

ΛHe is moderated in

that of 12ΛC due to

FSI.

Comparison of 5ΛHe and 12ΛC

np pair np pair

nn pairnn pair

Preliminary Results

Estimation of pair number per NMWD

Preliminary Results

Γ n/Γ p from Nn/Np & Nnn/Nnp

Simple counting of singles yields of n,p andcoincidence yeilds of nn, np pairs gives, neglecting FSI and 2N

Nn/Np = 2•Г n/ Г p + 1,Nnn/Nnp = Г n/ Г p,

Γ n/Γ p~ (Nn/Np -1)/2 = 0.59 (5ΛHe), 0.5 (12ΛC),

Γ n/Γ p~ Nnn/Nnp = 0.45 (5ΛHe), 0.53 (12ΛC).

- Assume 1N process only ; rn + rp = 1.

- The neutron (proton) number per NMWD

Nn=Yn/NnmΩnεn = (2rn+rp)f + rpg

Np=Yp/NnmΩpεp = rpf + (2rn+rp)g,

where f, g ; FSI effects.

Correction for Cross over recoil effects

0.51,r

r1

ΓΓ

p

p

p

n

- Obtained FSI model independently, but assuming 1N process. - The INC β value is used only for second order correction.

β=0.11

Γ n/Γ p = 0.51 +-0.15

pp

pp

p

n

r)r2(

rr2

NN

INC 0.11f

gβ where

Decay counter Decay counter systemsystem

p

n

N: 20cm×100cm×5cmT3: 10cm×100cm×2cmT2: 4cm×16cm×0.6cm

Solid angle: 26%9(T)+9(B)+8(S)%

π

Comparison of Angular Correlation of He and C

We notice that

1. R(np) enhancement in C over He.

FSI?

2. R(nn) enhancement over R(np) both in He and C

2N NMWD?

where R=Nbb/Nnbb

Preliminary Results

5ΛHe 12

ΛC

np pair

nn pair

np pair

nn pair

nbb

nn pair

INC spectrum ; Fermi momentum and FSI model

Energy Sum ; EN1+EN2

Back-to-back

Uniform

Back-to-back Back-to-back(cosθ≤ -0.8)

5ΛHe

cosθnncosθnp

En+Ep(MeV) En+En

Energy Sum Correlations

Angular Correl.of np pair

Angular Correl.of nn pair

Nnn

/Nnp

cosθcut dependence

npnn / np = 0.45±0.11±0.03

Particle identificationParticle identification

Energy resolution

σ ～ 8MeV( around 80MeV )

1/β spectra

5MeV< energy < 150MeV

Neutral particleNeutral particle Charged particleCharged particle

π p

d

PID spectra

INC showing angular correlation due to Fermi Mom. Only. No FSI.

INC showing angular correlation due to Fermi Mom. Only. No FSI.

3. Enhancement of nn pair yields in the non- back-to-back angular region

R Nnbb/Nbb,

2N 2N NMWD

Suppose no 2N,

then Nnbb due to FSI and we expect

Rnp = Rnn,

R = Rnn/Rnp = 1.

But in reality,

Rnn Rnp, Rnn/Rnp ~ 2. 2N signature ! !

Estimation of Γ 2N /ΓNM

Summary on Γ n/Γ p.

1.A series of experiments have been done for the study of NMWD of Λ hypernuclei at KEK-PS. Accurate measurement of neutron spectrum finally reslove the long standing Γ n/Γ p puzzle along with the recent enhanced theoretical ratios distributed from 0.3-0.7.

2. The coincidence measurement of NMWD were done for the first time for 5He and 12

ΛC in E462/E508 and determined the pair numbers, Nnn and Nnp, exclusively for the two body ΛNNN process.3. From the pair number ratio, Nnn/Nnp, Г n/ Г p was determined to be ~0.5 almost free from the ambiguities of FSI and 2N contribution.

Then, how about the magnitude of each Γ n, Γ p itself ?

Energy Sum ; EN1+EN2

En+Ep(MeV) En+En(MeV)

En+Ep(MeV) En+En(MeV)

E sum

E sum

Two groups ; from

Integrated yields large value

the yields in nbb region smaller one

Preliminary Results

Acceptance and Efficiency correction

Back-to-Back Pair Number Ratio, Nnn/Nnp

.50

.30

.35

FSIcorr.

.53

.34

.40

b.g.Subt.

0.59-0.7

0.40-0.8

0.45-0.9

Sum cosθcut

Nnn/Nnp estimation

np

nn

12ΛC

Nnn

Nnp

Sources of Singles deficiency in the yield;

1) Weak strength of FSI;

2) 3-body 2N NMWD.

Limitation ; No way to distinguish their effects on the singles spectrum.

Quenching of Singles Yields

Compared to INC spectrum

(Nn+

Np)/

NM

WD

EN (MeV)

12ΛC

For 2N, we adopted the kinematics of uniform phase space sharing of 3 nucleons.

Significant quenching of the Nn+Np could not be explained with 1N only INC.!!

Compared to INC spectrum

(Nn+

Np)/

NM

WD

EN (MeV)

12ΛC

Non-Mesonic Weak Decay (NMWD) & Issues

1. B-B Weak Interaction ;

Λ + N N + N (ΔS=1 B-B Weak Interaction )

2. Long standing puzzle on : Γ n/Γ p (≡np ratio)

3. 2N NMWD: 3-Body, ΛNNNNN, Interaction Process,Predicted to be a significant component of NMWD, though not experimentally identified yet.

- Final State Interaction : It seems one of the important elements to understand NMWD.

4. Asymmetry :

5. ΔI=1/2 rule

apply a simple relation n / p = (Nn / Np - 1) / 2 n / p ~0.5