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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. - PowerPoint PPT Presentation
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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
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