1

Introduction to Hypernuclear (and Kaon-nucleus) Physics

Outline:• What is a hypernucleus?• BB interaction and hypernuclei structure• Formation of Λ-hypernuclei• Weak decay of Λ-hypernuclei• Search for Σ−hypernuclei• K-N, K-A and Deeply bound kaonic nuclei• An experimental approach to low-energy kaon

physics and some recent results

3

Hyperons and hypernuclei

Λ=(uds), Σ(qqs), Ξ=(qss),… � Hyperons Hyperon = strange baryon (s≠0); notation: YWeak decay: τ~10-10 s, [Σ0�Λγ (∼10-19 s)];cτ=τ=τ=τ=OOOO(10(10(10(10cm)

u c td s b

•There are six quark flavors in nature:

Spin=1/2

p π−

n π0Λ

p π0

n π+Σ+

Σ− n π−

Σ0 Λ γ

4

The First HypernuclearEvent (1953)

P – Cosmic trackA - Nuclear InteractionB – Hypernuclear Decay

at Rest

Ordinary baryons are stable: p, n both targets or projectiles (NN, eN, πN…scattering)

But nuclear interaction not limited to the u,d sector…

Since Hyperons have very short lifetime, low energy YN scattering is difficult.

� extension to strange sector via hypernuclear studies

5

What is a hypernucleus?

• Normal nucleus: composed of nucleons (proton, neutron)At the quark level: p=(uud), n=(udd)

• Hypernucleus: not only nucleons but hyperons (one or more) s quarks beside u andd

- Extension of the strong int. to strange sector- Probing the interior of the nucleus- Short rangestrong YN interaction- New light on NN interaction- A new dimensionto world of nuclei: no Pauli p., new symmetries,

selection rules,…- medium modifications- Four fermion weak vertex(Λ N � NN), quark-gluon effects,…- Tool to match nuclear and particle physics

Knowledge of elementary hyperon-nucleon (YN) andhyperon-hyperon (YY) interaction crucial to fully understand the nuclear force!

6

Notation

ZΛAZΛA • A: Total number of baryons (nucleon & hyperon)

• Z: Total charge• Λ: hyperon (other examples --Σ, Ξ, …)

• Some examples:1. 3p + 3n + 1Λ �

2. 2p + 2n + 2Λ �3. 1p + 2n + 1Σ+

2p + 1n + 1Σ0 �

3p + 0n + 1Σ−

Li7Λ

He6ΛΛ

ΣHe4ΣHe4

•Known hypernuclei (strangeness only): ΛΛΛΛ-hypernuclei (~50 species),

ΣΣΣΣ-hypernucleus (only 1), ΛΛ-hypernuclei (a few events) and probably one

anti-hypernucleus (@RHIC)

7Gang Wang (UCLA) QM2009

Observation of and @ RHICH3Λ

H3Λ

[1] R. H. Dalitz, Nuclear Interactions of the Hyperons (1965).[2] R.H. Dalitz and G. Rajasekharan, Phys. Letts. 1, 58 (1962).[3] H. Kamada, W. Glockle at al., Phys. Rev. C 57, 1595(1998).

ps4330153±=τ

World data

180ps

256ps

STAR Preliminary

� First ever observation of an anti-hypernucleus(4σ signal of )

� The hypertriton and anti-hypertriton signal : 244±35

� The hypertriton and anti-hypertriton lifetime:

H3Λ

STAR Preliminary

Details!! (in that mess...)

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Baryon-Baryon interaction and the structure of hypernuclei

• GOAL: unified understanding of NN, YN and YY interactions• Flavor SU(3) symmetry (symmetry in u, d, s quarks) • NN interaction -- experimentally well known from elastic

scattering data� phenomenologically well reproduced by meson-exchange

(ME) and quark-cluster models (short range repulsion).• YN, YY interaction: poor scattering data (short lifetime)� information from hypernuclei is important

(mostly Λ-hypernuclei� ΛN interaction)In Λ-hypernuclei: No Pauli effect, weak coupling

� simpler structure� extraction of ΛN interaction is rather straightforward

Extension of ME description to strange sector: long history, but notover yet(one, two-ME potentials[Julich, Nijmegen], quark-clusters…)

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Some features of the ΛΛΛΛN interaction (1)

• ΛN and NN One meson exchange models

OME

Λ: I=0Σ: I=1

NΛ

π(ρ)

NΛ

π(ρ)

Σ NNΛ

ω,η

NΛ

NN

π,ρ,ω,η

NN

strong vertex

Λ(I=0)

Λ

ππππ(I=1)

N

N

•One pion exchange is forbidden (ΛΛΛΛ≠≠≠≠>>>>ΛπΛπΛπΛπ)(Violates isospin symmetry)

OPE forbidden in ΛN interaction� two π exchange dominant�ω,η, 2ρ …allowed

Main difference:

CONSEQUENCES…

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Some features of ΛΛΛΛN interaction (2)

Also allowed:

Strangeness exchangeN Λ N

π

π

Σ

Important to study structure of Λ-hypernuclei. It is due to the sizeable ΛN-ΣN coupling inside nuclear medium (OPE enters at 2nd order)

ΛΝ

Κ

NΛ

-weakness of ΛΝΛΝΛΝΛΝ interaction (no OPE)e.g., no two body bound state (no hyperdeuteron!)

- ΛΝΛΝΛΝΛΝ is a short range interactiontwo π, heavier mesons (K, η, ω, σ, ...) exch.quark-gluon picture (manifestation of q.-g. degreees of f.?)

More later…

3-body ΛΛΛΛNN interaction

3-body forces much less importantIn ordinary nuclei (m∆-mN~293 MeV,mΣ-mΛ~78 MeV!)

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• No experimental data so far from scattering experiments� All information is from hypernuclei

• Data are mostly for light (s- and p-shell) hypernuclei•Spin dependent terms ΛN effective potential in hypernuclei

Vσ(r) σσσσΛ• σσσσN ‥‥ spin-spinVΛ(r) σσσσΛ • LΛN ‥‥ spin-orbit (Λ-spin dependent)VN(r) σσσσN • LΛN ‥‥ spin-orbit (N-spin dependent)VT(r){3(σσσσΛ • r)(σσσσN • r)/r2 − σσσσΛ • σσσσN} ‥‥ tensor

• Λ-N spin-spin interaction: usually weak

~0.1MeV for p-shell hyp. (except 7LLi(g.s.) �0.6MeV)Some data show that ΛN interaction more attractive in spin-singlet (J=0) state than in spin-triplet state (J=1) but situation not clear.

Some features of ΛΛΛΛN interaction (3)

Spin-dependence

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ΛΛΛΛ-N spin-orbit interaction: small

Note: Λ-nucleus spin-orbit potential < 1/10 N-nucleus

potential.

Probably related to missing contribution of one body π π π π (ρ)(ρ)(ρ)(ρ) exchange (strong in ordinary nuclei) which suggests

that Spin-orbit potential in ordinary nuclei mediated by

single π (ρ) exchange.

Some features of ΛΛΛΛN interaction (4)

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Experiments with high energy resolution essential to study spin dependence

Spin-dependence

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Hyperons in nuclei

• Y as an impurity• Influence of the medium on the hyperon:

Single particle behaviour (mean field)appropriate (althoughdeviations from e.g. 3-body forces, ΣN-ΛN,…)

•A hyperon influences the nuclear medium: may change some properties of nuclei(size, shape, energy levels …)

Theoretical prediction: - A Λ makes a loosely-bound light nucleus, such as 6Li , smaller� glue-like role (Motoba et al., PTP70 (1983) 189)

α d

6Li

+ Λ α dΛ�

ΛLi7

• Recent experiment gives evidence for such shrinkage5He & 8Be unstable BUT and stable!!ΛHe6

ΛBe9

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As in Nuclear Physics, Baryons in the Hypernucleus can be treated as Fundamental Objects.

The ΛΛΛΛ mantains its identity in the nuclear medium because the interaction with the nucleus is “weak”.

The Structure is discussed in the particle-hole formalism

An elementary potential form inserted into the hadronicmany-body problem yields a one-body effective potential

The Λ resides in the 1s shell for the hypernuclear ground state (probes nuclear core!). No Pauli blocking!

Hypernuclei (and Λ-nucleus interaction)

p shell: 4 radial integrals for pN,sΛ w.f.

3(σ1 r)(σ2 r)−σ1σ2, spin-tensor operator

General hyperon-nucleus potential

120 )(sl)(sl)(ss)()()( SrVrVrVrVrVrV TNN +⋅+⋅+⋅+= ΛΛ NNNNNNNNΛΛΛΛΛΛΛΛNNNNΛΛΛΛΛΛΛΛNNNNrrrvrv

σ

∆ SΛ SΝ Τ

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Overall binding energy of hypernuclei

• from A=3 to 208• UΛΛΛΛ ~ 27 MeV ~ 2/3 UN

well reproduces data� weakness of ΛN interaction• Single particle picture

works even for deep states unlike for nucleons

Λ can occupy any single p. state: Yg.s. always 1s.�good probe of nucleus interior!

BΛ (ΑΛΖ) = Μ (Α

ΛΖ) − Μ (Α−1Ζ) −mΛ

(D. J. Millener et al., PRC38 (1988) 2700)

Density-dependent Woods-Saxon potential

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• BΛ Λ Λ Λ monotonically increses up to ~27 MeVfor 208208208208

ΛΛΛΛPb (BΝ Ν Ν Ν saturates @ ∼8Μ∼8Μ∼8Μ∼8ΜeV (A ≤≤≤≤10) )• ΛΛΛΛ-nucleus mean field depth ~30 MeV (N-nucleus m.f.d. ~50-55 MeV)• Weakness & smaller range of ΛΛΛΛN w.r.t. NN interaction

BΝ Ν Ν Ν and BΛ Λ Λ Λ very different

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Test of single-particle states at the center of nucleus

• Hyperons are free from Pauli blocking- can stay at the center of the nucleus - good probe of nucleus interior

• KEK-PS E369 observed clear and narrow peaks for sΛ and pΛ states of (H. Hotchi et al., PRC64 (2001) 044302)� There are single-

particle states in thenuclear interior

sΛ

pΛ

ΛY89

Textbook example of

Single-particle orbits in nucleus

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Light hypernuclei (1) --overbinding problem and charge symm. breaking

• Binding energy of hypernuclei, A=3~5 [exp. Values]: BΛ = 0.13 ± 0.05 MeV (lightest bound state!): BΛ = 2.04 ± 0.04 MeV (ground state, 0+)

1.00 ± 0.06 MeV (excited state, 1+): BΛ = 2.39 ± 0.03 MeV (0+)

1.24 ± 0.06 MeV (1+): BΛ = 3.12 ± 0.03 MeV

• If we use ΛN interaction(centr.pot)which reproduces A=3,4 bindingenergies, overbinds by ~1 MeVin calculations

� overbinding problem of 5ΛHe

ΛHe4

ΛH4ΛΛΛΛH3

ΛHe5

ΛHe5

• First pointed out by Dalitz et al. in 1972 NPB47 109 ,but not solved for nearly 30 years.

27

Solution to the overbinding problem? (1)

• Quark Pauli effect?

baryon level

p n Λ

no pauli blocking

quark level

u d s

partial Pauli blocking

• Is this significant? � seemingly no(H. Nemura et al., PTP 101 (1999) 981, Y. Suzuki et al., PTP 102 (1999) 203)

If Λ and N partially overlap…

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Solution to the overbinding problem? (2)

N Λ N

π

π

Σ

• importance of ΛNN three body force

ΛN-ΣN coupling (+ structure) Seems to explain the binding anomaly

ΛHe5

N1Λ

π(ρ)

N1Λ

π(ρ)

Σ N

2ΛNN 2π-exch. component

Medium-modifiedΛN 2π-exch. component

3-body forces much less importantIn ordinary nuclei (m∆-mN~293 MeV,mΣ-mΛ~78 MeV!)

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Light hypernuclei (2) -- charge symmetry breaking

• Λ has no charge, no isospin� difference of ΛΛΛΛp and ΛΛΛΛn interaction is CSB (ΛΛΛΛp more attractive)• Λ in is more strongly bound than by 0.35 ± 0.05 MeV(~15%)• Coulomb force correction makes the difference larger!• After Coulomb force correction, this difference is ~5 timeslarger than in 3H -- 3He case (i.e. for neutron energies)

• The reason is not yet fully understood, possibilities include- Λ/Σ0 mixing in free space �π0 exchange force (tensor) ??- ΛΛΛΛN-ΣΣΣΣN coupling sensitive to mass difference of initial/final state

∆m(Λp�Σ+n)~75MeV< ∆m(Λn�Σ-n) ~ 80.5MeV � three-body forceas well as two body force.- K0 and K± mass difference (~1%), also in K*

- ρ/ω mixing � spin-orbit• These are strongly spin dependent •� spin/state dependence is important

ΛHe4ΛH4

33

ΛΛ interaction

• Unique channel in SU(3) BB interaction classification• Repulsive core may vanish in this channel� possibile existence of H-dibaryon (uuddss, J=I=0)

• Original prediction by Jaffe (PRL38 (1977) 195)- H is 80 MeVbound from ΛΛ

• No experimental evidence so far- at least, deeply bound H is rejected

• ΛΛ − ΞΝ (− ΣΣ) coupling important• ΛΛ interaction study performed by

- ΛΛ hypernuclei- ΛΛ final state interaction in (K−,K+) reaction

(J. K. Ahn et al., PLB444 (1998) 267 )• Present data suggests ΛΛΛΛΛΛΛΛ interaction is weakly attractive

35

ΣN interaction and Σ-hypernuclei

• Different and more difficult to investigate than ΛΛΛΛN

• ΣΣΣΣ has isospin 1 (mΣ~1190 MeV)� (long range) OPE component allowed� ΣΣΣΣN interaction both in T= 3/2, 1/2 (only ½ for Λ)

• Central part weaker than ΛΛΛΛN (strength of averaged potentials: NN/ΛN ~3/2 NN/ΣN~3) but still poorly known

• Strong spin-isospin dependence(due to exchange of isoscalar (ω,η) and isovector (π,ρ) mesons)

Potential form similar to Λ except Vi terms are isospin dependent(1S0,T=3/2), ( 3S1,T=1/2): strong attraction, (3S1,T=3/2), (1S0,T=1/2): weak repulsion

• Spin-orbit strength comparable to NN (0.5-1.MeV)

In Vacuum: Σ±�NπIn nuclei: ΣΝ�ΛΝ

37

• ΣΣΣΣN potential weaker than NNDo ΣΣΣΣ−−−−Hypernuclei bind?

• The potential has a strong imaginary component due to the ΣΣΣΣN-ΛΛΛΛN Interaction (ImV~10-15MeV)

�large width (Γ~20-30MeV)

ΣN interaction and Σ-hypernuclei

Do ΣΣΣΣ−−−−Hypernuclei have Narrow Structure ?

Exp: 20 years ago narrow (<8MeV) peaks seen at CERN.Theory:20÷÷÷÷30 MeV expected in nuclear matter (ΣΣΣΣN����ΛΛΛΛNconversion creates a Λ with ~40MeV, which can escape the nucleus)

Exp. Situation very confusing; finally KEK exp.:4He(K-, ππππ±±±±) (PRL 80(1998)1605)

: 4.4 MeV Bound State; 7.0 MeV Width ΣΣΣΣHe4

38

Possible width suppressing mechanisms- Σ�Λ conversion less efficient (width decrease) because S-wavew.function considerably out of the nucleus due to shallow Σ-nucleus

potential (especially in T=3/2 ch.)- Pauli blocking effect on final nucleon in ΣN�ΛN- suppression of particular spin-isospin transitions - medium polarization effects

Clear peak only in 4He(K-, π−)No bound state in 4He(K-, π+)

PK=600MeV/c

4He(K-, π−): populates T=1/2,3/2 states4He(K-, π+): populates T=3/2 states

Since no bound state in 4He(K-, π+)�ΣΣΣΣ

4He b.s. has T=1/2 and T=1/2 attractive, T=3/2 strongly repulsive

ΣN interaction and Σ-hypernuclei

39

Σ-nucleus potential still ambiguously known:(K-, ππππ±±±±): Σ single particle potential (for hypn.

beyond s-shell) ~10 MeVΣ- atoms: ~20MeV (but not sensitive to nuclei interior)

The existence of Σ-hypernuclei heavier than ΣΣΣΣ4He is still an open question.

Data on medium-heavy Σ-hypernuclei useful to better understand Σ-nucleus potential, crucial for the study of Σ- hypernuclei in dense nuclear matter (neutron stars)

ΣN interaction and Σ-hypernuclei

40

Impact on other fields: YN interaction and astrophysical objects

Strange matter not in everyday life but most likelyhyperons in neutron stars (Neutron star =“giant hypernucleus” [SchaffnerBielichNPA804(‘08)])

hyperons populate deep lying states (no Pauli blocking)� presence of hyperons energetically favoured

1. YN and YY interactions determine neutron stars E.o.S(�max N.S. mass)2. Non Mesonic Weak Decays control core viscosity(macroscopic effects!)

42

Strongly interacting matter in neutron stars

45

How to produce

−− +Λ→+ πnK

++ +Λ→+ Knπ

++′+Λ→+ Kepe )()(γ

Different production mechanisms can be used to form an hypernucleus:

strangeness exchangestrangeness exchange reactionreaction

(in flight, stopped) σ 100 mb; Ibeam = 104 s-1

associated productionassociated productionσ 1 mb ; Ibeam = 107 s-1

real and virtual photo- production

σ b ; Ibeam = 1010 s-1

− →+ −+Λ πnK−+Σ0 π0+Σ− π

− →+ 0+Λ πpK −+Σ+ π++Σ− π0+Σ0 π++ +Λ→+ Knπ

++Σ0 K 0+Σ+ K

In order to produce a hypernucleus, the hyperon emerging from the reaction has to remain inside the nuclear system. The formation probability of a hypernucleus depends on the energy transferred in the production.

When the momentum transferred to the hyperon is much larger than the nuclear Fermi momentum , the hyperon has a very small sticking probability and it leaves the nucleus. If it is smaller the hyperon is created, with a high probability, in a bound state. H

yper

on r

ecoi

l mom

entu

m [M

eV/c

] L= 0o

++ +Λ→+ Knπ

++′+Λ→+ Kepe )()(γ

π+Λ→+− NK

Projectile momentum pLab [GeV/c]

46

Quark Flow Diagrams

47

•• Strangeness exchange Strangeness exchange (K(K−−,,ππ±±) reactions) reactions- Transforms a nucleon in a Λ/Σ with emission of a π± (hypn.

levels from π spectrum)- reaction is esoenergetic�hyperon can be created at rest (if pion

emitted at θ=00 and pK~530 MeV/c)- in general mom. transfer can be quite small

• at θ=00 hyperon produced predominantly with same quantum n. of nucleon (substitutional reaction,∆l=0). Increasing θ, the importance of∆l 1,2,… increases (access to hyp. with higher spin)

• K−,π± strongly absorbed by nucleus � preferentially populate less bound Λ-levels (used mostly for s,p-shell nuclei)

How to produce

48

•• Strangeness exchange Strangeness exchange ((stoppedstoppedKK−−,,ππ±±) reaction) reaction

stopped K− captured into atomic level � cascades to inner levels� absorbed at nuclear surface creating Λ (Σ). Momentum transferred≅ kF (Λ:∼Λ:∼Λ:∼Λ:∼250MeV/c)-large production yield. High background

AK- ππππ

ΛΛΛΛA

How to produce

49

•• n(n(ππ++,K,K++))ΛΛ strangeness associated production reactionstrangeness associated production reaction

- production ofss pair- large momentum transfer (q > 350 MeV/c @ 00scatt)����hyperon can be produced above emission threshold. Some hypn. state in continuum may be quasi-bound states (they emit [clusters of] nucleons)

-well suited for studying deeply bound states in medium-heavy hypernuclei (populates states with high (n-1,Λ) spin configurations)

- small cross section, but intense π beam available

How to produce

53

[In general decays with γ,N,clusters… possible if highly excited hypn.]

Mesonic decayOnce a Λ is formed, regardless the capture shell level, it quickly cascades to (1S1/2) state (emitting γ’s).• In free space n, Λ unstable (weak decay):

n → p + e + ν (τn∼103s)Λ → N + π (101MeV/c) (τΛ=2.63 10−10s) mesonic

decay• Inside nuclei:

mn-mp= 1.3 MeV < nucleon b. energy BN~ 8MeV/NmΛ-(mN - mπ) ~ 40 MeV >> Λ b. energy BΛ (<28MeV)

�while neutron is stable inside nuclei, Λ eventually decays.The decay nucleon momentum (energy) in free space is ~100MeV/c (~5MeV) which is below the Fermi momentum �Nπ decay is Pauli blocked (strictly forbidden in infinite N.M. (kF~270MeV/c))

Weak decay of hypernuclei.

54

Mesonic decay

- MD dominant only in very light hypernuclei(A<6)-Well described by (phase space)*(Pauli effect)*(π distortion)

π− decay partial width

free Λ • Exp. data fromH. Outa et al., NPA639

(1998) 251cV. J. Zeps et al., NPA639

(1998) 261cY. Sato, Doctor thesis

(Tohoku Univ., 1998)

Still, in finite nuclei can occur because (medium effects)• Hyperon has momentum distribution (confined) →larger final nucleon momenta

• Binding of final pions→ given momentum means less energy

(ω(q) <sqrt(q2+mπ2) → more energy to the nucleon

�mesonic width increased (factor2 @A=16, 2 o.of m. @ A=200 ))Mesonic decay � info on pion-nucleus optical potential (ΓM very

sensitive to π self-energy)

55

Mesonic decay•In free space... (∆s=1)

Λ � p + - (63.9%, Q = 38 MeV) = Γπ− / ΓΛn + 0 (35.8%, Q = 41 MeV) = Γπ0 / ΓΛ

ΓΓΓΓΛ Λ Λ Λ ==== ΓΓΓΓππππ−−−− ++++ ΓΓΓΓπ0π0π0π0 ΓΓΓΓππππ−−−−/Γ/Γ/Γ/Γπ0 π0 π0 π0 ~2 – initial state: I=0, final state: I=1/2 or 3/2 ∆I=1/2 or 3/2 theor. equivalent (weak hamiltonian)

if If = 1/2, Γπ−/Γπ0 = 2:1 3/2, Γπ−/Γπ0 = 1:2

Exp.lly ΓΓΓΓππππ−−−−/Γ/Γ/Γ/Γπ0 π0 π0 π0 ~2 which is consistent with pure I=1/2 ( I=1/2 amplitude enhaced by~20)

I=1/2 rule holds is general rule in strangeness decay, but not clearly understood•Inside nuclei the I=1/2 (for closed shell, symmetric n.) holds,but strongly dependent on hypernuclear structure.

**Note: ∆I=1/2 rule holds for all strangeness-changing non-leptonic processes

56

Non-mesonic decay• Mesonic decay is suppressed in hypernucleidue to Pauli blocking for the final state nucleon.

• Therefore, non-mesonic (NM) decay dominates in hypernucleiΛ p � n p,) (ΓΓΓΓpΛ n � n n, (ΓΓΓΓn)

Λ NN �nNN (ΓΓΓΓ2) Total weak decay rate is ΓΓΓΓT= ΓΓΓΓM+ ΓΓΓΓNM τ = τ = τ = τ = /ΓΓΓΓNM decay can be interpreted as a M decay where the virtual pionis absorbed by one (a pair of) nucleon(s).

Weak decay of hypernuclei

Q~mΛ-Mn~176 MeV , i.e. pN~420 MeV/c(340 MeV/c for 2-nucleon induced)

Pauli-blocked Not Pauli-blocked

High mom. Transf. �short distances probe (quark-gluon d.of f.)

57

NM decay is only possible in nuclei and can be mediated by the exchange of more massive mesons.

Study of weak interaction between nucleons difficult (PC part masked by strong int.).

NMWD only practical way to study weak interaction between barions.

NM mechanism dominates over M for all but s-shell hyp.

Non-mesonic decay

d

s

u

W u

d

dnΛ

u

u

d

u

u

d

pp

One-nucleon two-nucleon induced Λ decay.

sw

59

observables:observables:h

τ Λ

= Γtot = Γπ − + Γπ 0 + Γp

+ Γn

+ Γ3N

non- mesonicDecay ΓNM

mesonicDecay ΓM

NM channel �large momentum tranfer�details of hypn. structure negligible (except very light hypn.)�ΛN, NN short range correlation very important

Anticorrelation between M and NM decay modes �τΛ (ΓΓΓΓtot) quite stable from light to heavy hypn. (except few cases).

This is because NM rate rather constant in heavy hypn.(in a zero-range approx. Γn +Γp proportional to overlap of Λ and nuclear densities,which saturates for A>65)

Non-mesonic decay

60

Weak decay

• Almost constant for A > 10 • non-mesonic decaydominant (short range nature of nonmesonicdecay)

• exp. data fromH. Park et al., PRC61 (2000) 054004H. Outa et al., NPA639 (1998) 251cV. J. Zeps et al., NPA639 (1998) 261cJ. J. Szymanski et al., PRC43 (1991) 849R. Grace et al., PRL55 (1985) 1055

Lifetime measurements

61

Non-mesonic decay: Γn/Γp puzzle

• Simplest diagram for non-mesonic weak decay-- one pion exchange • Virtual mesonic decay +absorption

- (ΛN)3S1 � (NN)3D1 tensorcouplin∆L=2, ∆S=2 has the largestamplitude, but this is forbidden for (nn) final state.

• This model predictsΓn (nΛ�nn) << Γp(pΛ�pn)Λ

Νπ

N

N

Weak Strong

• However, experimental data (before ~2003) indicate Γn/Γp ~ 1(e.g., H. Hashimoto et al., PRL88 (2002) 042503)

OPE : ΓΓΓΓn / ΓΓΓΓp 0.1 Exp. : ΓΓΓΓn / ΓΓΓΓp 1with large error

This was the situation till ~2003…..

64

ExperimentallyExperimentally very challengingHuge (60% for 5ΛΛΛΛHe) data error on n / p

Non-mesonic decay: Γn/Γp puzzle

Experimental problems:Experimental problems:

••high proton threshold (usually~30MeV)high proton threshold (usually~30MeV)

••Low neutron efficienciesLow neutron efficiencies

••Large error barsLarge error bars

Problems in determination method of Problems in determination method of ΓΓΓΓΓΓΓΓnn//ΓΓΓΓΓΓΓΓpp ratio ratio from datafrom data

1)model dependent1)model dependent

2) Effects of FSI (low en. protons from FSI) and 2) Effects of FSI (low en. protons from FSI) and 2N proces2N processs((if if ΛΛΛΛΛΛΛΛNNNN��������NNN large, then NNN large, then ΓΓΓΓΓΓΓΓnn overestimatedoverestimated if thresh. on if thresh. on low energy protons present)low energy protons present)

65

Non-mesonic decay: Γn/Γp puzzle.Theory

Several attempts made to solve the puzzle:• Additional meson exchange?� K (+ η, ρ, ω, K*,....) meson

Λ

Ν

K

N

N

Strong Weak

• Improve the situation, butstill below exp. data.(e.g., E. Oset et al.,

NPA691 (2001) 146c)• Some models also incorporate

2π exchange processes(e.g., K. Itonaga et al.,

NPA639 (1998) 329c)

• Direct quark mechanism?- s-quark decays directly without meson propagation

(e.g., M. Oka, NPA691 (2001) 364c)

• Two nucleon induced processes? (ΛNN � NNN)

66

Γn/Γp puzzle: towards a solution?

Recent Exp. Development: eeee ~ 0.5Recent Development of eeee 0.3 ~ 0.7

5ΛΛΛΛHe : 0.61±±±±0.081±±±±0.082 (E462)

12ΛΛΛΛC : 0.58±±±±0.06±±±±0.08 (E508)

: ( ±±±±0.15 (E307/E369)

10 0.5 1.5ΓΓΓΓn / ΓΓΓΓp

Exp.

OPEOME, DQ model

5ΛΛΛΛHe : 0.43 ±±±±0.12 ±±±±0.044±±±±(E462)

12ΛΛΛΛC : 0.34 ±±±±0.13 ±±±±0.05 (E508)

Singles

Coincidence

MESON2008-Krakow-5/10 June 2008 Paolo CameriniMESON2008-Krakow-5/10 June 2008 Paolo CameriniMESON2008-Krakow-6/10 June 2008 Paolo Camerini

NMWD: study of baryon-baryon weak interaction (and 3-baryons ΛNN int.)Slightly affected by nuclear structure (mom. Tranfer ~400MeV/c), test of short range correlations, ∆I=1/2 rule, quark d.o.f., rare decays…

Strong disagreement between exp. and theory until recentlyГn/Гp puzzle: OPE: Гn/Гp ~0.1; EXP : Гn/Гp.~ 1

■ Experimentally difficult -Hyp.nucleus identification (π)+ p/n detection necessary.High proton thresholds: low energy region missing ( FSI and 2-N induceddecays), model dependent data analysis→ Гn/Гp puzzle unsolved for several years

■ Theory: OPE + kaons + heavier mesons exch.+ direct quark mechanisms

Гn/Гp puzzle solved in correlated p/n back-to-back kinematics +non-trivial data interpretation(no FSI, no 2N abs)

12ΛC: OME Гn/Гp ~0.4 [Garbarino,PRC69(04)]; EXP(KEK) : Гn/Гp.~ 0.4 [Kang,PRL96(’06)]

NM Weak decay of Λhypernuclei

Single proton spectra still incompatible with theor. predictions (Bauer et al,nucl-th/0602066)

More in the next lessons…