Non- Mesonic Weak Decay Λ Hypernuclei - Results at KEK-PS and open problems at J-PARC

1. Weak decay mode of Lhypernucleus Γπ_(L→ ｐ + π－) Γπ0(L → ｎ + π０ ) Mesonic q～100MeV/c Γm 1/tHY =Γtot Γp(L +“ｐ”→ ｎ + ｐ) Γn(L +“ｎ”→ ｎ + ｎ) Γ2N (ΛNN →NNN) Non-Mesonic(NMWD) q～400MeV/c Γnm Workshop on Strangeness Nuclear Physics(SNP2013), Xiamen Dec. 13, 2013 RIKEN H. Outa Non-Mesonic Weak Decay ΛHypernuclei- Results at KEK-PS and open problems at J-PARC Study of the mechanism ofbaryon-baryon weak interaction 1. Results of NMWD experiments at KEK-PS 2. Λ Hypernuclear weak decay experiments at J-PARC E18 and E22 experiments E18: ΛNN → NNN for 12ΛC E21: Γ（Λn→nn)/Γ(Λp→np) for 4ΛHe 1

2. Γn/Γp ratio and Asymmetry parameter αnm If assuming initial S state OPE: ΔS=2, ΔL=2 3S1 → 3D1 (L+S+T=odd; T=0) Λn→nn is suppressed (Applying DI=1/2 rule) We can know the interference between states with differentIsospin and Parity . ２

3. Direct Quark mechanism Meson Exchange mechanism One Pion Exchange (OPE) N N Theo. N Λ N N π,K,η,ρ,ω… S W π N Λ Gn / Gp 1.5 0.5 1 0 N N 5LHe (E462) Nnn / Nnp (5LHe)= 0.45±0.11±0.03 Kang et al. PRL 96 (2006) 062301 12LC (E508) Γn / Γp (12LC)= 0.51±0.13±0.05 Λ N Kim et al. PLB641 (2006) 28 Gn/ Gp ratio ΔS=2,ΔL=2 ； 3S1 → 3D1 (L+S+T=odd; T=0) OPE: Λn→nn is suppressed Previous exp. (at BNL) 0.93±0.55 (Szymanski et al.) for 5LHe Exp. ３

4. LN→nN LNN→nNN FSI re-scattering n n n n n n n n p p p p p p p p p p p p p p n n n n n n n Expected Spectrum distribute low energy region up to Q/2 broad peak around Q/2 continuous distribution counts Energy Energy spectra (image) Q/2

5. Γn/Γp ratio measurement Coincidence Select ΛN→NN events w/o FSI effect & ΛNN→NNN. NMWD L NMWD Coincidence * cosθ<－0.8 * E(N1)+E(N2) cut p p p p p p n n n n n n n n KEK-PS E462/E508 Direct measurement of the Gn/ Gp ratio NMWD : ΛN→NN 1) Angular correlation ( back-to-back, cosq<-0.8 ) 2) Energy correlation ( Q～E(N1)+E(N2) ～152MeV ) Select light hypernuclei to minimize FSI effect, 5LHeand12LC ５

6. ６ Charged PID Charged particles from 5LHe Constant background very small PID function Decay particle identification @E462/E508 Neutral PID Neutral particles from 12LC Sensitive to all the decay modes 1 / b spectrum Good p p d separation Good g n separation

7. 7 Excitation spectra w/ coincident decay particles for 12LC 12LC 12LC 12LC (in-flight K- ,π-) Phys.Rev.C43 (1991) 849 (stopped K-,π-) (π+,K+)

8. ８ Lifetime & Decay Widths

9. ? Lifetime of very-heavy hypernuclei ? COSY-13 KEK-E307 ９

10. Coincidence Measurement(E462/E508) nn-pairs np-pairs 10

11. Ap=apPLe Ap:Asymmetry of Pion ap:Asymmetry Parameter of Pion (=－0.642±0.013) PL:Polarization of Lambda e :Attenuation factor We can directly measure aNM p aNMfor 5ΛHe NMWD Estimated from mesonic decay ・Polarization ofL α Λ ・Asymmetry Parameter of Proton Ap=aNMPLe p 11

12. Asymmetry parameter of 5ΛHe Theory: －0.6～0.7 pcontami statistical aNM=0.08±0.08+0.08 -0.00 p 11

13. 12 p+K,OME can reproduce Gn/Gp ratio but predict large negative aNM p+2p/r+2p/s+w+K+rp/a1 Calculation by Itonaga p+K+DQ Gn/Gpand aNM can be reproduced by p+K+s+DQ model p+K+s OME p+K+s+DQ Sasaki et al. PRC71 (2005)035502 p+K (1) Large b(1S0→3P0) and f(3S0→3P1) amplitude (2) Violation of ΔI=1/2 rule considered Comparison with recent calculations OPE

14. NMWD of Λ-hypernuclei- achievement and open problems - N N N Λ π,K,η,ρ,ω… N N N N N W π Λ Λ N N N ✔ Gn/ Gp～0.5 Meson Exchange mechanism Direct Quark mechanism × OPE ✔ Heavy meson exch./DQ Spin/isospin dependence ?? ✔ αNM～0 ×Hard to be explained w/ large Gn / Gp ✔ Some cancellation mechanism LNN→NNN (2N-induced process) Large contribution of 1S0 ΛN initial state?? ✔ G２Ｎ/ Gnmwd～0.3 ? E18 ✔ Gnm (A～56）～1.2ΓΛ

15. 15 n n p n W p π- Λ n p 4 Λn→nn like n p n p n n W π0 Λ 1 n p n Λp→np like ΛNN→NNN consideration Larger contribution in n+n-pair ? Seen as…. n p n

16. Theoretical prediction of 3-body process (Γ2N) of NMWD. •First proposed by Alberico-Ericson for Nuc. Matter (‘91) and Ramos-Oset extended to finite nuclei (‘94). • Coupling of virtual π- to 2p-2h correlations. - Λpπ- is dominant at the weak vertex and - π- absorbed dominantly on the pn pair. In the process 3 nucleons are emitted; 1p(LE) + 2n (HE) • Γ2N/Γnm= 0.20 (12ΛC) • Bauer and Garbarino; Recently, extended the model to include K, ,  mesons and other nucleon pairs. Γ2N/Γnm→ 0.37 (12ΛC) [E. Bauer, plb 698 (‘11)] n p n n p n Extended to K, ρ,ω. . 16

17. Nn+Npand(Nnn+Nnp) back-to-back yield ✔　When we summed up Nnn+Nnp (back-to-back) and Nn+Np the spectra becomes free from Γn/Γp ratio ✔　Both of Nnn+Nnp and Nn+Np yields are smaller than those of INC calculation withonly ΛN→NN process (1N) ✔ΛNN → NNN decay is assumed to occur uniformly in three-body phase space. ✔　Good agreement obtained when we assume Γ2N/Γnmwd = 0.29±0.13 M. Kim et al., PRL103 (2009) 182502 N-N pair number distribution Nucleon number distribution 17

18. 11 Hypernuclear decay experiments at J-PARC OPEN PROBLEMS : 1) Large ΛNN→NNN contribution 2) 1S0 initial state contribution; ΔI=1/2rule 4ΛHe & 4ΛH : np-ratio (E22 experiment at J-PARC) ΛΛ→ΛN decay of double Λ hypernuclei 18

19. E18 Setup T4 p+ Side Veto T3 PDC T2 K+ y 20cm x z 19

20. Comparison of acceptance enn enp np nn E18 E18 n qnp E508 E508 cosqnp cosqnn eNN epp E18 pp Double coincidence eff. at EN=75MeV → Much increased!! E18 pp np beam p E508 nn cosqpp cosqNN 20

21. Statistics of the Two-step Plan Λp→np Λn→nn FSI ΛNN→NNN & FSI @20% stat. ✔ Much improved statistics in non b-t-b region ✔　With the similar analysis as E508, can establish the existence of ΛNN→NNN with ～4σ-level @100% stat. ✔ Dalitz plot analysis for NNN-final state ✔　FSI-free(or less affected) analysis can be tried ✔ 10% error can be reached for both of Γn/Γp & Γ2N/ΓNM ✔　Also all the mesonic/non-mesonic widths will be updated with much improved accuracy. 21

22. NMWD of 4-, 5-body hypernuclei • allowed initial LN states p p n Λ p p n n Λ n n p Λ 0+ 0+ 0+ 0+ Ln→nn: 1S0, 3S11S01S0, 3S1 Lp→np: 1S01S0, 3S11S0, 3S1 22 assuming initial S state

23. Status of amplitude determination Our prospects new constraint from 4LHe np-ratio better than 15% error Current status Constraint from 5LHe data other constraints are loose J-PARC E21 23

24. Indication of Γ2N in 4ΛHe decay ?? 26 PRC 76,035511 (2007) EN1+EN2 Opening angle p+n p+n n+n n+n ? p p n Λ J-PARC E21 proposed by Osaka/RCNP 0+ 0+

25. Summary ◆Γn/Γpratio 5ΛHe, 12ΛC ～0.5 ◆ Asymmetry parameter 5ΛHe / 11ΛB and 12ΛC ～0 ◆ Lifetime Heavy hypernucleiΓtotal～1.2ΓΛΓnm(A→∞) ◆ ΛNN→NNN process Γ2N/Γnmwd= 0.29±0.13 Suggesting possible large contribution of spin-singlet initial state & ΛNN→NNN [1] High statistics/wide acceptance run of 12ΛC at J-PARC (E18) － NN non-back-to-back & NNN coincidence ：　Stage-2 approved [2] Spin/isospin dependence of NMWD : np-ratio for 4ΛHe (E21) －Stage-1 approved [3] Lifetime measurement of very heavy hypernuclei σ-meson exch. / ΔI=1/2 violation? ⇒ 4ΛH 4ΛHe & ΛΛ→ΛN@J-PARC

26. ６ p p n n Rare NMWD of 4ΛHe (Bｒ～1/1300) 4He(K－,d) Inclusive ? ～105 events ～1% of stopped K % of stopped K－/(10MeV/c) (1)　Ｐｄ>500 MeV/c > 2×PFermi Hard to explain the origin of such high momentum deuterons (2)Observation of back-to-back dd pair from stopped 4ΛHe → d + d (Ｐｄ = 571.8MeV/c ) 800 600 700 500 MeV/c 4He(K－,dd) Back-to-Back Coincidence d !! 30 cosθ < -0.9995 20 d Counts / 0.0005 Counts / (10MeV/c) 10 0 ー0.96 ー0.92 ー0.9 ー1 ー0.94 ー0.98 500 600 700 cosθ(dd) MeV/c

27. Spare OHPs

28. Oka’sTheorem for NMWD Nucl.Phys. A754 (2005) 117-126

29. Our strategy to control FSI effect ✔On most of the observables we are not “free” from FSI effect. But its effect is NOT the major part of error source in E508. We have already achieved the control of strength of FSI in 4% level. ✔　KEK-PS E508 setup is NOT optimized for non back-to-back coincidence measurement where TN-NWWD & FSI becomes dominant. Measurement of (1) 3N Dalitz plot and (2)Nnn/Nnp/Npp measurement in whole cosθNN region and also for (3)singles proton/nucleon spectra/NMWD will give good control data for FSI effect ✔We are now seriously considering the method of analysis free from (or less affected by) FSI. By artificially changing FSI strength in SNU cascade simulation, Nnn/Nnp ratio analysis coupled with precise Γn/Γpratio measurement seems to be promising. ✔　To measure the TN-NMWD with different mass number is the way to check FSI. Most of E18 member also joins the proposal E21 for 4ΛHe, which will take sufficient data for TN-NMWD at A=4 15

30. Γπ/Γnm and Λ-Nucleus Potential Mesonic decay rate Γπ(YNG) > Γπ(ORG) Non-mesonic decay rate Γnm(ORG) >Γnm(YNG) Calculation using two types of a-L potential, ORG and YNG(Motoba et al. NPA577) Central repulsion in a-L potential ? Can be directly checked by the mesonic decay width! 12

31. Mesonic decay widths?? ＊ Important to study the NMWD widths Br(NMWD) = 1 － Br(π－) － Br(π0) Γnm= 1/τ× Br(NMWD) σ=119ps ADC sum w/ Geantsim  20 MeVee 5LHe g.s. quasi free inclusive N (inc) = 42040 w/ gamma bp0 = N (w/ g) / N (inc) × eff = 0.212±0.008 N (w/ g) = 848 • = 217 ± 6 ps for 12ΛC 13

32. 14 Gp- and Gp 0 for 5LHe GL GL Gp0 Gp- 0.207±0.013 GL Isle SG Isle 0.322±0.018 GL SG Measured with much improved accuracy Λ-nucleus potential with inner repulsive core can reproduce present experimental results

33. Γ2N of 11ΛB (preliminary) Nnn+Nnp (≤300MeV/c) • Fitting with the known 12ΛC and 11ΛB structure information. • Side band subtraction of Continuum contribution. Γ2N/Γnm (%) 18

34. Neutron random background; - E508 Neutral particle TOF spectrum Beam rate at E508 ～ 5×106 π+/spill = 3Mπ+/sec (thanks to the good duty factor of 0.8～0.9) n singles ~2% nn background @E508 … This number need to be controlled less than 8% in order to obtain n+n results in non b-t-b region. 2% → 4% by Ωnbut some room for higher beam rate if D.F.=1 nn pair Neutron background level is beam-line dependent … need to be checked with beam 23

35. Nn+Npand(Nnn+Nnp) back-to-back yield ✔　When we summed up Nnn+Nnp (back-to-back) and Nn+Np the spectra becomes free from Γn/Γp ratio ✔　Both of Nnn+Nnp and Nn+Np yields are smaller than those of INC calculation withonly ΛN→NN process (1N) ✔　ΛNN → NNN decay is assumed to occur uniformly in three-body phase space. ✔　Good agreement obtained when we assume Γ2N/Γnmwd = 0.29±0.13 N-N pair number distribution Nucleon number distribution 19

36. 7 N+N momentum sum analysis INC N1 •E508 Exp. p12 PRL103(2009) 182502 N3 N2 *INC(IntraNuclear Cascade) - -- - 1N ーー 2N ● E508 - -- - 1N ーー 2N ● E508

37. 3. Comments on FSI ー“Even though a triple coincidence is detected, there is no clear way to separate TN-NMWD from a NMWD (LN-NN) with final state interactions (FSI). One will have to rely on the inter-nuclear cascade (INC) calculations or equivalent procedures, which may limit the precision that can be reached to that of the previous KEK-PS experiment. Meanwhile FINUDAshowed a new result based on mass number dependence where TN-NMWD was derived in a way related directly to the experimental spectra.” (PAC2011Jan. )

38. INC strength effect control data Inelastic scattering(p,p’) Charge exchange reaction(p,n) Confirmed the validity of the INC parameters for the FSI over the nuceon energy region of 45-160MeV and the mass region of A=12-90 within 4% accuracy for its strength 16

39. Ｓｔａｔｉｓｔｉｃａｌ error ～10% >> Systematic error ～ 3% at least at E508 17

40. 1２ Status of amplitude determination Our prospects new constraint from 4LHe np-ratio better than 15% error Current status Constraint from 5LHe data other constraints are loose J-PARC E22

41. FSI independent observables to extract G2N In the left figure the E508 data is compared with those of INC whose FSI istoo weak. However in the ratio Nnn/Nnp, the weakness of FSI is cancelled out so that the predicted branching ratio is about 0.2 but with a large error. We need to reduce this error bar in the main run.

42. FSI strength renormalization factor a determination a = 1.09±0.04

43. 3 K6/SKS setup K+ decay counter π+

44. INC calculation p p n Flow Chart Target nucleus At first, we develop scattering and reaction process to check its range of validity by comparing experimental data * included important features 1)Pauli-effect and Fermi momentum 2)Woods-saxon type density fix the strength of FSI on the nucleons. Then, applied in the calculation of decay particle propagation

45. Applying INC to a Λ hypernuclei decay process 1N- induced NMWD process: Λ+N N + N + 176MeV according to the momentum distribution of 1s –state in the harmonic oscillation potential Primary energy dis. from 1N Initial Count/MeV Count/MeV/c EN1[MeV] Count/MeV PL[MeV/c] PN[MeV/c] (in the nucleus) EN2[MeV]

46. 1N-induced NMWD process INC results proton neutron before FSI Counts/10MeV Counts/10MeV Λp np after FSI Ep[MeV] En[MeV] proton neutron Counts/10MeV Counts/10MeV Λn nn Ep[MeV] En[MeV] After FSI suffering, recorded at outside of nucleus

47. 2N-induced NMWD process Λ+N+N N+N+N+176MeV In a 2n NMWD process, three nucleons were produced at a point interaction site with the kinematics of uniform phase space sharing LNN→nNN(Using Dalitz Plot)-uniform phase space sharing proton Counts/10MeV neutron EN[MeV] EN[MeV] energy dis. after FSI including, outside nucleus Primary energy dis. in the nucleus before FSI

48. Comparison of INC results and Data Inelastic scattering(p,p’) Charge exchange reaction(p,n) Confirmed the validity of the INC parameters for the FSI over the nuceon energy region of 45-160MeV and the mass region of A=12-90

49. Signature of the 3-body process -- Measured results are compared with those of INC(only 1N process) • The quenching of the yields are universal for both proton and neutron and accordingly also for np,nn pair and momentum sum

50. Renormalized INC method Г2N (ΛNN nNN) INC reproductions including the 3-body process INC • E508 Exp. G2N= 0.29±0.13Gnm