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 studyII. Experimental Signatures of the 3-body process in NMWDIII. Final State Interaction and 3-body process 2N-NMWD.IV. Summary

Nonmesonic q~ 400 MeV/c

The 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)

3-Body Process

Previous Searches; Гn/Гp puzzle

decay observables;

Γ n, Γ p, nm, Г 2N etc.

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 : Γ n/Γ p (≡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 Г 2N. 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.

Non-Mesonic Weak Decay (NMWD) & Issues

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

Г n/Г p puzzle and the previous searches

Γ n/Γ pexp >> Γ n/Γ p

th(OPE)

~ 1 ~0.1

1. Γ n/Γ p Puzzle :

10 0.5 1.5

n / p

OPE

All these derived from p spectra

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

E307etc. E369 E462/E508

π+

K+

Recent Experiments at KEK-PS

Nn(> 40 MeV) =0.69

Np(> 40 MeV) =0.40

Г n/ Г p(12ΛC) =0.51±0.14

- Residual FSI effects

- No 2N NMWD assumed!!

Ambiguity

Sources!!

12C(π +,K+)12ΛC

Models of ΛNNN 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 Γ n/Γ p

• 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.

NN

NN

π

NΛ

NN

π

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 Γ n/Γ p

• 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. Λ N

NN

5ΛHe Γ nm(ΓΛ) Γ n/Γ p 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 0.420.03

0.45 0.110.03

0.11 0.080.04

KEK-PS E462

Upgraded Γ n/Γ p 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.

Resolution of the Γ n/Γ p puzzle (II)

Comparison with recent results

OPE

+K+DQ

+K+

+K++DQ

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

+K

OME

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

p

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, 4

ΛH, 4ΛHe.- This will be one of the main theme of J-PARC Hypernuclear decay experi

ments.- Proposal 10-2.

How to measure partial decay widths (Γ p, Γn, Γ2n)

• Γ = 1/τ = Γm + Γ nm = (Γπ -+ Γπ 0) + (Γ p + Γn)

Γm Γ nm (?)

Decay widths; the strategy to determine the decay width of each channel of NMWD is

1st ; Determine Γ nm (= Γ - Γm).

2nd ; Determine r=Γ p/Γ n, then,

3rd ; Γ p = Γ nm /(1+r), Γ n = Γ nm r/(1+r),

This does not work if Γ 2n is large.

Γn ( Λn nn )

“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?

X O X X

3-body Interaction

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%.

Δ Δ

Theoretical Prediction of 3-body process (Γ 2N) of NMWD.

Ramos-Oset Model Λ

N

π

• 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

- Γ 2N ~ 0.2 Γ 1N

But it is not yet experimentally confirmed.

Exclusive Measurements (KEK Exclusive Measurements (KEK E462E462/E508) for /E508) for 55ΛΛHe/He/1212

ΛΛCC

Ep

En

π

θ

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

Exclusive meas. of each decay channel.

π+

SKS

K+

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???

Quenching of Singles Yield/ LE n enhancement

np

Broad Esum spectrum in NN correlations (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 dominance4. Nbb(nn)/Nbb(np) Γ n/Γ p

5ΛHe

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

5. Г 2N/ Г NM ; 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 wel

l, but only with a large Г 2N.

15 counts

8 counts

Enhancement of nn in nbb region Г 2N

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

Assign it to Г 2N.

2. Just Rough Estimation;

1) Nnp(nbb) all FSI eff.

Same FSI on Nnn

Г 2N ~ The residual Nnn

after FSI sub.

Г 2N / Г NM ~0.150.09±

2) Similarly,

but using INC for FSI

Г 2N / Г NM ~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)

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 Г 2N~0.4Г nm.

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

Г 2N=0.4Г nm

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 Γ 2N.

2. The first road block toward the decay widths, the Γ n/Γ p puzzle, has been finall

y 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, Γ n and Γ p

Proposal for J-PARC (P18)

1. B-B Weak Interaction ;

Λ + N -> N + N (ΔS=1 B-B W.I. )

2. Long standing puzzle on : Γ n/Γ p (≡np ratio)3. Asymmetry ; The relative phase concern of PC and PV part of NMWD intera

ction.

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.

Non-Mesonic Weak Decay (NMWD) & Issues

J-PARC P10(2)

J-PARC P18

N

N

N

N

N

N

N

N

Γ 2N ~ Γ 1N

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 enhancemen

t.

N

N

π

N

N

N

N

Nucleus

Λ

N

π

N

N

N

N

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 int

eraction 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 Г n/ Г p puzzle has finally been resolved. However, there remains important issues remained to be solved.

2. The Г n and Г p, remain to be measured. However, it seems that Г 2N comparabel to Г 1N 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

• 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.

(p,p’) Mass Dependence

M. Kim, JKPS 46 (’05) 805

• 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 in nbb region

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