Transcript Weak Decay of Λ Hypernuclei; - Status and Prospects - H. Bhang

Weak Decay of Λ Hypernuclei;
- Status and Prospects -
H. Bhang
(Seoul National University)
2007 APCTP workshop on
“Frontiers in Nuclear and Neutrino Physics”
APCTP, Postech
Feb. 26-28, 2007
I. Current Status of NMWD study
II. Experimental Signatures of the 3-body process in NMWD
III. Final State Interaction and 3-body process 2N-NMWD.
IV. Summary
The Decay Modes of Λ Hypernuclei
Γm
Γπ- ( Λ  pπ- )
Mesonic
Γπo ( Λ  nπo )
q~ 100 MeV/c
Γp ( Λp  np )
Previous Searches;
Гn/Гp puzzle
Γtot(=1/τ)
Γnm
Γn ( Λn  nn )
Γ2N (ΛNN nNN)
(1N)
Nonmesonic
(2N)
q~ 400 MeV/c
3-Body Process
decay observables;
Γn, Γp, nm, Г2N etc.
Non-Mesonic Weak Decay (NMWD) & Issues
1. B-B Weak Interaction ;
Λ + N -> N + N (ΔS=1 B-B W.I. )
- The fundamental importance of NMWD is that it is practically
the only place to study the strangeness changing baryonic
ΛN->NN weak interaction.
2. Г; Long standing puzzle on : Γn/Γp (≡np ratio)
3. Asymmetry ; Decay asymmetry wrt the polarization axis of Λ.
It is due to the interference of PC and PV amplitudes of weak
interaction. Provides the information on the composition of the
amplitudes.
4.ΔI=1/2 Rule ; Its validity not well established yet. Can be tested
in light hypernuclei.
5.Final State Interaction : It is an important element in order to
understand NMWD.
6. The 3-body interaction process, 2N NMWD:Current
indication is a large Г2N. The enhancement of 3-Body processHYP03
in Conf.
Гn/Гp puzzle and the previous searches
1. Γn/Γp Puzzle :
Γn/Γpexp >> Γn/Γpth(OPE)
~1
Hyp.
Nuc.
Γnm
Γn/Γp
ΛHe
0.41±0.14
.93±0.55
12 C
Λ
1,14±0.2
1.33±1.12/0.81
5
~0.1
BNL
KEK’95
12 C
Λ
0.89±0.18 1.87±0.91/1.59
OPE
Gn / Gp
0
0.5
1
1.5
All these derived from p spectra
Recent Experiments at KEK-PS
p
meas.
~ 1.0
n
meas.
~0.5
p,n singles spec
np,nn pair no.
~0.5
~ 0.5
E307etc. E369
E462/E508
Nn(> 40 MeV) =0.69
12C(π+,K+)12 C
Λ
Np(> 40 MeV) =0.40
Гn/Гp(12ΛC) =0.51±0.14
π
+
K
+
- Residual FSI effects
Ambiguity
- No 2N NMWD assumed!!
Sources!!
Models of ΛNNN interaction (I)
I. Meson Exchange Models; ΔI=1/2 rule
adopted.
• OPE model(1967) ; Vπ by Adams.
• Vπ+V ;McKellar&Gibson(’84), Bando(’85)
 very small Γn/Γp
• Heavy meson exchange(HME) model;
Dubach, Oset, Ramos, Parreno. .
- Due to large momentum, they involve
short distance behaviors.
- pseudo-scalar and vector mesons;
π,K,. . .
- No drastic effect.
• 2π(σ,  channel) Exchange Model;
Itonaga, Schmatikov
- 2π exchange is important in nuclear
force.
- found its contribution important.
N
N
N
π
N
N
π
N
Λ
N
Models of NMWD and the Γn/Γp puzzle (II)
II. Hybrid quark-hadron Model
• 6-q Bag model + Vπ; Cheung et al.,
• Direct Quark(DQ) Mechanism; VDQ + VME
- ΔI=1/2, 3/2 both allowed.
- Oka, Sasaki, . .
- considerable improvement on Γn/Γp
• Phase problem in K exchange amplitude; Sasaki,
III. Contact four fermion interaction model
N
N
• Block and Dalitz; prl 11 ('63) 96
• Jun J., prc 63 ('01) 044012
• Parreno A.; prc 70 ('04) 051601.
Λ
N
Resolution of the Γn/Γp puzzle (II)
Upgraded Γn/Γp theoretical values
• After the correction of the phase error in K exchange term, the
n/p ratio was enhanced significantly. Since the K exchange term was
employed in most of the calculations, the correction also improved the
n/p ratios of HME model calculations.
• Now the theoretical n/p ratios of various models agree with the
recent exp. ratio quite well. The n/p ratio puzzle was finally resolved.
5 He
Λ
Γnm(ΓΛ)
Γn/Γp
nm(p)
OBE(all)
0.32
0.46
-0.68
Parreno et al.
π+K+DQ
0.52
0.70
-0.68
Sasaki et al.
π+K+w+2π(,)
0.42
0.39
-0.33(0.12)
Itonaga et al.
Experiment
0.42
0.03
0.45 
0.110.03
0.11 
0.080.04
KEK-PS E462
Comparison with recent results
p+K+DQ
p+K+
OME
p+K++DQ
p+K
OPE
 Theoretical models,
such as π+K and
OME, can explain
our Гn/Гp ratio, but
not pNM.
 At present, only
π+K+σ+DQ model
is reproduced both
Гn/Гp ratio and 
aNM.
ΔI=1/2 rule in Nonmesonic Weak Decay.
- It is well known that the strangeness changing weak decay strongly
favors ΔI=1/2 transition, though it is not well understood yet.
- The OBE models for NMWD adopt it while DQ and 4 point
interaction models do not.
This becomes one of the most urgent issues of NMWD.
Its test can be done in decay of light Hypernuclei, 4ΛH, 4ΛHe.
This will be one of the main theme of J-PARC Hypernuclear
decay experiments.
Proposal 10-2.
How to measure partial decay widths (Γp, Γn, Γ2n)
• Γ = 1/τ= Γm + Γnm
= (Γπ-+ Γπ0) + (Γp + Γn)
Γm
Γnm (?)
 Decay widths; the strategy to determine the decay width of each
channel of NMWD is
1st ; Determine Γnm (= Γ - Γm).
2nd ; Determine r=Γp/Γn, then,
3rd ; Γp = Γnm /(1+r), Γn = Γnm r/(1+r),
 This does not work if Γ2n is large.
Γn ( Λn  nn )
3-body Interaction
“A three-body force arises when two nucleons interact to produce a
virtual excited state which contains some entity other than nucleons
and while this state exists one of its constituent parts interacts with a
third nucleon. The effect cannot be attributed to a succession of of
two-nucleon interactions.” – M.A. Preston -
Which ones are 3-B interaction?
Δ
X
O
Δ
X
X
It is known that the Δ is by far the most important in the nucleus.
Ex. • Pot. En. ; V2N ~ 1-2 MeV
• Nuclear matter energy; ~ few % of 2-body contribution.
• Binding En. of 3H, 3He ; only 1%.
Theoretical Prediction of 3-body process (Γ2N) of NMWD.
• Absorption of virtual pion by 2p-2h states.
• The real pion has a large width in nuclear medium
due to the coupling to 2p-2h.
• The strength of the real pion becomes a BreitWigner distribution and the part of the tail becomes
Pauli-unblocked.
• However, this pion is almost on-shell and absorbed
via 2p-2h state. It is well established that pions
are absorbed dominantly on the pn pair. In the
process 3 nucleons are emitted.
- Yield Characteristics ; 1p(LE) + 2n (HE)
 practically 2n  n enhancement
N
π
- Γ2N ~ 0.2 Γ1N
But it is not yet experimentally confirmed.
Λ
Ramos-Oset Model
Exclusive Measurements (KEK E462/E508) for
5 He/12 C
Λ
Λ
To exclude FSI effect and 3-body decay in Гn/Гp
and to identify 2N channel,
 Exclusive meas. of each decay channel.
π
Ep
+
θ
En
K+
π
SKS
Quenching of Singles Yield/ LE n enhancement
INC(1N)
INC(1N)
1. Observed Quenching in both p and n spectra from that of INC.
2. What would be the mechanism for the nucleon Quenching?
 FSI & 3-Body process.  different yield characteristics.
3. FSI ; n & p are indistingushable (isospin indep.)  HE similarity.
4. LE behavior ; Channel Cross-over  LE p enhancement.
Instead, What observed  LE n enhancement.
5. What would be the source of the LE n enhancement???
Broad Esum spectrum in NN correlations (5ΛHe)
5 He
Λ
1. Sharp peak in Ynp(He)
at Q value(Λpnp).
 FSI negligible in He.
2. Broad spec in Ynn(He).
FSI? No.
Energy resolution? No,
 Seems 3-Body phace space!!
3. bb dominance
4. Nbb(nn)/Nbb(np)  Γn/Γp
np
Broad Esum spectrum in NN correlations (12ΛC)
1. No more sharp peak at Q
value(Λpnp).
 FSI significant in C.
2. Ynn(C); Even further degraded.
 Again points to 3B decay.
3. bb dominance in np pairs,
but not anymore in nn pairs.
4. Nnbb/Nbb(R) is much enhanced
in nn pair over that of np.
 Rnn/Rnp ~ 2.3±0.93
attribute this  2N NMWD
5. Г2N/ГNM ; 0.15 ~ 0.27,
depending on methods.
Strategy to measure 3-body NMWD
1.Quenching (Singles and pair nucleons) observed.
- Two mechanisms for quenching ; FSI and 3-body  (how)
- FSI characteristics ; n and p are indistinguishable (HE spec..)
- LE behavior; quite different due to the imbalance of cross over.
 p enhancement expected in LE.
 However, what observed in LE is n enhancement.
 3-B enhances n ! ! !
2. Broad Energy sum spec. of nn ;  show 3-B phase space dist..
3.
Enhancement of nn pair
in non-back-to-back kinematic region;
Most direct identification;
 i. 2-body events seperated kinematically.
ii. FSI events can be removed by the exp. reference (pp events).
.
However, the current statistics are very much limited at the moment.
4. INC incooperated with 3-B process reproduced both singles and coincidence
yields well, but only with a large
Г2N.
Enhancement of nn in nbb region  Г2N
1. Enhancement of Nnn in nbb,
over that of Nnp, by a factor,
Rnn/Rnp~(2.30.93).
8 counts
15 counts
 Assign it to Г2N.
2. Just Rough Estimation;
1) Nnp(nbb)  all FSI eff.
 Same FSI on Nnn
 Г2N ~ The residual Nnn
after FSI sub.
 Г2N / ГNM ~0.150.09±
2) Similarly,
but using INC for FSI
 Г2N / ГNM ~0.270.12
RNN=NNN(nbb)/NNN(bb);
Ratio of N(nbb) to N(bb)
Quenching of Pair Yields.
INC(1N)
- Quenching of pair yields
INC(1N)
 Quenching of singles.
- Enhancement of Nnn in non-back-to-back region.
What is this enhancement?
FSI? No, np and nn should have similar ang. distribution
INC(1N+2N) Reproduction of Singles yields
INC(1N)
INC(1N)
INC(1N+2N)
INC(1N+2N)
1. INC calculation included 2N-NMWD with
2. 3-body kinematics of equal phase space sharing.
3. In order to explain the quenchings, we need Г2N~0.4Гnm.
Singles and Coin. Yields Reproduction with INC(1N+2N).
Г2N=0.4Гnm
1. Singles Quenching
2. LE n enhancement
3. Pair Quenching
are reasonably well reproduced.
Motivation of the proposal (P18)
1. Though the limitation of statistics of data and INC uncertainty, all
the current aspects indicate the large Γ2N.
2. The first road block toward the decay widths, the Γn/Γp puzzle, has
been finally removed.
3. Now the only road block is the determination of the contribution of
the 3-body NMWD process, 2N-NMWD. ,
4.  We absolutly need to determine the contribution of the 3-body
process in NMWD before the main observables, Γn and Γp
 Proposal for J-PARC (P18)
Non-Mesonic Weak Decay (NMWD) & Issues
1. B-B Weak Interaction ;
Λ + N -> N + N
(ΔS=1 B-B W.I. )
2. Long standing puzzle on : Γn/Γp (≡np ratio)
3. Asymmetry ; The relative phase concern of PC and PV part of
NMWD interaction.
4.ΔI=1/2 Rule ;
5.Final State Interaction : It seems one of the most important
element to understand NMWD.
6. The 3-body interaction process, 2N NMWD: Predicted to
be a significant component of NMWD, though not experimentally
identified yet.
HYP03 Conf.
N
N

N
N


N
N
Γ2N ~ Γ1N
N

N
Why enhancements?
Why do we expect such enhancements of 3-body process in
NMWD?
•
In the nucleus ; π highly off shell.
•
In hypernuclear decay ; almost on shell
 this might be, at least, one reason of the large
enhancement.
N
N
N
N
π
N
N
N
N
N
π
N
Nucleus
N
Λ
Nonmesonic W.D.
The Implication of the Enhancement of the 3-B process
• The mechanism of the enhancement is very interesting.
• The enhancement of the 3-B interaction process in the
weak interaction in ΔS=1 sector could be global in the
nucleus.
• Its implication could be profound.
I would like to call your attention,
especially those of young theorists,
to this problem ! ! ! Thanks.
IV. Summary
1. Discussed the NMWD, the only window to study ΔS=1 Baryonic weak
interaction. The long stood Гn/Гp puzzle has finally been resolved.
However, there remains important issues remained to be solved.
2. The Гn and Гp, remain to be measured. However, it seems that Г2N
comparabel to Г1N and has to be determined beforehand. Its
enhancement may not be an isolated one in NMWD, but could be
global one of ΔS=1 weak interaction in nuclear medium.
3. Asymmetry parameter; Large discrepancy remained between the
exp.(small) and theoretical values(large neg.). It remains to be
cleared yet, but it leaves more homework to theorists.
4. ΔI=1/2 rule ; This is an empirical rule. Though it holds very well in
the strangeness changing weak decay, it is not well understood yet.
Its validity in the baryonic weak interaction has not been
established. Its experimental test is considered one of the most
important one in the baryonic weak interaction study.
5. Two proposals for J-PARC experiments (P10-2 and P18) are
proposed focused on these issues. We expect these can be answered
with the high intensity J-PARC beam.
EXTRA
INC (IntraNuclear Cascade) calculation
(p,p’)
• A nucleus as a Fermi gas.
Mass Dependence
• ρ(x)  V(x)
• FSI is simulated as a cascade
free NN scattering along with
Fermi blocking imposed.
• Density geometry parameters are
adopted from 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.
M. Kim, JKPS 46 (’05) 805
Enhancement of nn in nbb region
• 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
8 counts
This model tends to produce 2 HE
neutron and one LE proton. Then
protons are often cut off at the
threshold.
15 counts