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Weak Decay of Λ Hypernuclei; - Status and Prospects -

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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 process2N-NMWD.

IV. Summary

The Decay Modes ofΛHypernuclei

Mesonic

q~ 100 MeV/c

Γπ- ( Λ pπ- )

Γπo ( Λ nπo )

Γm

Γnm

Γtot(=1/τ)

Previous Searches;

Гn/Гp puzzle

Γp ( Λp np )

Γn ( Λn nn )

(1N)

Nonmesonic

q~ 400 MeV/c

(2N)

Γ2N (ΛNN nNN)

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.

- ΔI=1/2 Rule ; Its validity not well established yet. Can be tested in light hypernuclei.
- 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 process in ΔS=1 weak interaction is very interesting and it could be global phynomena in nuclear medium.

HYP03 Conf.

Гn/Гp puzzle and the previous searches

OPE

Gn / Gp

1.5

0.5

1

0

All these derived from p spectra

1. Γn/Γp Puzzle :

Γn/Γpexp>> Γn/Γpth(OPE)

~ 1 ~0.1

Recent Experiments at KEK-PS

Nn(> 40 MeV) =0.69

Np(> 40 MeV) =0.40

K+

π+

p n p,n singles spec np,nn pair no.

meas. meas.

~ 1.0 ~0.5 ~0.5 ~ 0.5

E307etc. E369 E462/E508

12C(π+,K+)12ΛC

- Residual FSI effects
- No 2N NMWD assumed!!

Ambiguity

Sources!!

Гn/Гp(12ΛC) =0.51±0.14

N

N

N

N

π

π

N

N

Λ

N

I. Meson Exchange Models; ΔI=1/2 rule adopted.

- OPE model(1967) ; Vπby 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

Λ

N

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

- Block and Dalitz; prl 11 ('63) 96
- Jun J., prc 63 ('01) 044012
- Parreno A.; prc 70 ('04) 051601.

Resolution of the Γn/Γppuzzle (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.

- Theoretical models, such as π+K and OME, can explain our Гn/Гp ratio, but not NM.

p+K+DQ

p

p+K+s

- At present, only π+K+σ+DQ model is reproduced both Гn/Гp ratio and aNM.

OME

p+K+s+DQ

p+K

OPE

- 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.

- 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 Γ2nis large.

Γn ( Λn nn )

3-body Interaction

X

X

X

O

“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

Δ

It is known that the Δis 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.

N

π

Λ

•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 Breit-Wigner 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

- Γ2N ~ 0.2 Γ1N
But it is not yet experimentally confirmed.

Ramos-Oset Model

Ep

π+

θ

En

K+

SKS

π

To exclude FSI effect and 3-body decay in Гn/Гpand to identify 2N channel,

Exclusive meas. of each decay channel.

Quenching of SinglesYield/ LE n enhancement

INC(1N)

INC(1N)

- Observed Quenching in both p and n spectra from that of INC.
- 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)

np

5ΛHe

1. Sharp peak in Ynp(He)

at Q value(Λpnp).

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

Broad Esum spectrum in NN correlations (12ΛC)

1. No more sharp peak at Q value(Λpnp).

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

- Г2N/ГNM; 0.15 ~ 0.27,
depending on methods.

- 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 ; show3-B phase space dist..

3. Enhancement of nn pairin 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

15 counts

8 counts

- Enhancement of Nnn in nbb, over that of Nnp, by a factor, Rnn/Rnp~(2.30.93).
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~0.150.09±

2) Similarly,

but using INC for FSI

Г2N/ ГNM~0.270.12

RNN=NNN(nbb)/NNN(bb);

Ratio of N(nbb) to N(bb)

Quenching of Pair Yields.

INC(1N)

INC(1N)

- Quenching of pair yields 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)

INC(1N+2N)

- INC calculation included 2N-NMWD with
- 3-body kinematics of equal phase space sharing.
- In order to explain the quenchings, we need Г2N~0.4Гnm.

Singles and Coin. Yields Reproduction with INC(1N+2N).

Г2N=0.4Гnm

- Singles Quenching
- LE n enhancement
- Pair Quenching
are reasonably well reproduced.

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/Γppuzzle, 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.

- ΔI=1/2 Rule ;
- 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.

J-PARC P10(2)

J-PARC P18

HYP03 Conf.

N

N

N

N

N

N

N

N

Γ2N ~ Γ1N

N

N

N

N

N

N

π

π

N

Λ

N

N

N

N

Nucleus

Nonmesonic W.D.

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.

- 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 beglobal 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

- 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.
- 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.
- 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.
- 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.
- 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.

INC (IntraNuclear Cascade) calculation

(p,p’)

Mass Dependence

• A nucleus as a Fermi gas.

• 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

15 counts

8 counts

• 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

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