The Three-body Process in the Weak Interaction Observed in the Decay of Λ hypernuclei H. Bhang for KEK-PS SKS collaboration (Seoul National University) APCTP-KPS Workshop on Nuclei Far from Stability and Their Application Chonbuk National University Oct , 2005 I. Issues / focus of NMWD II. The status of Γ n /Γ p III. Signatures of three-Body decay Process

Nonmesonic q~ 400 MeV/c Weak Decay Modes of Λ Hypernuclei Γ tot (=1/τ) Γ m Γ nm Γ π- ( Λ  pπ - ) Γ πo ( Λ  nπ o ) Γ p ( Λp  np ) Γ n ( Λn  nn ) Mesonic q~ 100 MeV/c Γ 2N (ΛNN  NNN) (1N) (2N) Main focus Focus: Baryon-Baryon Weak Interaction Long standing puzzle on Γ n /Γ p. 2N NMWD: 3-Body, ΛNN  nNN, Interaction Process

Hyp. Nuc. Γ nm Γ n /Γ p BNL 5 Λ He0.41± ± Λ C1,14± ±1.12/0.81 KEK’ Λ C0.89± ±0.91/1.59 Status of Γ n /Γ p puzzle Γ n /Γ p exp >> Γ n /Γ p th(OPE) ~ 1 ~ Γ n /Γ p Puzzle : 2. Recent Development of Γ n /Γ p theory : 0.3 ~ 0.7 K.Sasaki, Nucl. Phys. A669 (2000) 371 D. Jido, Nucl. Phys. A694 (2001)  n /  p OPE

p n p,n singles spec p,n pair no. meas. meas. ~ 1.0 ~0.5 ~0.5 ~ 0.5 E307etc. E369 E462/E508 π+π+ K+K+ 3. Recent Exp. Development at KEK-PS N n (> 40 MeV) =0.69 N p (> 40 MeV) =0.40  Г n /Г p ( 12 Λ C) = 0.51±0.14 Theory Independent!! Y. Sato et al., PRC 71 (2004) J. Kim et al., PRC 68 (2003)

 Agrees well with the recent theoretical values, Then What has been the problem? If Γ n /Γ p =1/2, one would expect (N p,N n )=(0.67, 1.33). [ 1 (0.5, 1.5) ] Instead we obtained (0.40, 0.69). Main reason of the difference ; E th cutoff  However, the quenching was even more than what one would expect from the threshold cut.  So the quenching of proton yields were attributed to a strong neutron side strength giving us a large Γ n /Γ p ratio.

Ambiguities in Singles Measurements E307/E369 : Г n /Г p ( 12 Λ C) = 0.51± 0.14 (stat. only) - Derived from N n /N p ratio - Almost model independent. - agrees well with the recent theoretical values (~.5) In order to resolve the difficulties, Exclusive measurements 5 Λ He  E Λ C  E508 effect of residual final state int. 2N induced NMWD. However, ambiguities due to

π K Setup E462/E508 (KEK-PS K6 beamline & SKS) EpEp EnEn π SKS θ

inclusive  -gate p-gate d-gate 5  He g.s. inclusive  -gate p-gate d-gate inclusive w/ p w/ n w/ n+p w/ n+n 12  C g.s. quasi free Excitation Energy Spectra

N n / N p (E>60MeV) ~2.00±0.09±0.14  Γ n /Γ p = 0.58±0.06±0.08. N n / N p (60<E<110MeV) ~2.17±0.15±0.16  Γ n /Γ p =0.61±0.08±0.08. To avoid suffering from FSI effect & ΛNN→NNN, High energy threshold Singles spectrum in NMWD Okada et al., PLB 597 (2004) 249

Coincidence Observables p n θ 1. Nucleon Energy sum spectrum; E p +E n, E n +E n 2. Pair number per NMWD; N np (cosθ), N nn (cosθ) N np  Y np /(Y nmε np )

Energy Sum spectrum 1.Sharp peak in Y np (He) at Q value.  FSI negligible in He. 1.  Broad spec in Y nn (He). FSI? No. π - absorption or 2N? π - can not make it broad.  Seems 2N effect!! 3. Y np (C); FSI is significant. 4. Y nn (C); Even further degraded.  Again points to 2N. E sum = E n + E p E sum = E n1 + E n2 QQ Q Q Energy Sum Spectum of the Two Nucleons  (E sum ) np =12(8),  (E sum ) nn =16(11) MeV - ΔI=1/2 rule - np pair absorp.

Back-to-back(bb) (cosθ≤ -0.8) Angular Correl. of np pair Angular Correl. of nn pair Angular B.Kang et al., prl submitted (’05) N NN  Y NN /Y nmwd  n  p  nn /  np = 0.45±0.11±0.03 bb dominant nbb;  only a few events. In nn,  more counts

Angular Back-to-back (cosθ≤ -0.7) bb ; 2-body kinematics nbb ; ? M. Kim et al,, Proc. of DAFNE04 (2004) 237  n  p  = 0.50±0.11±0.03 Similar behavior bb dominant in np In nn, bb no more major one

From the singles of E462/E508 5 Λ He (E462)  Γ n /Γ p ( 5 Λ He) = 0.61 ± ± Λ C (E508)  Γ n /Γ p ( 12 Λ C) = 0.58 ± 0.06 ± Here no Γ 2N assumed !! 5 Λ He (E462)  Γ n /Γ p ( 5 Λ He) = 0.61 ± ± Λ C (E508)  Γ n /Γ p ( 12 Λ C) = 0.58 ± 0.06 ± Here no Γ 2N assumed !! Г n /Г p from singles and coincidence data from the coincidence pair yields, 5 Λ He (E462)  Γ n /Γ p ( 5 Λ He) = 0.43 ± 0.12 ± Λ C (E508)  Γ n /Γ p ( 12 Λ C) = 0.50 ± 0.13 ± Γ 2N component is kinematically removed !! Free from Г 2N Ambiguity 5 Λ He (E462)  Γ n /Γ p ( 5 Λ He) = 0.43 ± 0.12 ± Λ C (E508)  Γ n /Γ p ( 12 Λ C) = 0.50 ± 0.13 ± Γ 2N component is kinematically removed !! Free from Г 2N Ambiguity  diffences

Г 2N Now we have Г n /Г p almost ambiguity free! Then, can we determine each Γ n, Γ p itself ?  How about Г 2N (ΛNN  nNN)? Can we neglect it?

1.Large contribution of the 3-body decay process, Λ+NN  NNN ( Γ 2N ), was predicted in the theoretical calculations. Γ 2N was predicted about 1/5 of Γ nm. ( PRC 256(’91) 134, PRC 50 (’94) 2314) 2. So far no experimental identification has been made. 3. Original motivation of the experiments, E462 and E508, was to identify Γ 2N experimentally. Status of (ΛNN  NNN) We remember that the quenching of proton singles yield was the source of the long standing confusion on Γ n /Γ p. Later we found even severer quenching in the neutron yield. Why such severe Quenching?

1. Quenching of Singles yields ; 2. Energy sum spectrum ; 3. Quenching of Total pair yields ; 4. Enhancement of nn pair yields in the non-back-to-back angular kinematic region 5. The difference of Γ n /Γ p values derived from singles yields and coincidence pair numbers. Signatures of Three Body Process in Weak Decay So many places !! In every places !!

1. Quenching of Singles Yields Signatures of Three Body Processes Compared to INC spectrum (N n +N p )/NMWD E N (MeV) 12 Λ C Significant quenching of the N n +N p could not be explained with 1N only INC.!! For 2N, we adopted the kinematics of uniform phase space sharing of 3 nucleons.

INC(IntraNuclear Cascade) calculation (p,p’) Mass Dependence M. Kim, JKPS 46 (’05) 805 Kin. Energy Dependence

Total Pair Number is compared to that of INC

We know that FSI(He) not strong. Then what are those in Y nn nbb (He)? R(np) enhancement in C over He.  FSI R(nn) enhancement over R(np) both in He and C  2N? where R=N bb /N nbb 15 counts 8 counts Enhancement of nn pair yields in the nbb angular region This model tends to produce 2 HE neutron and one LE proton. Then protons are often cut off at the threshold.

No kinematic seperation With kinematic seperation E th Singles Quenching N NN Quenchin g N 2N ;in N nn nbb N pn 2N =0 N 2N  N NN exp - N NN INC Γ 2N /Γ NM 0.41±0.08 (stat.error) No INC error included 0.37±0.14 (stat.error) No INC error 0.29±0.23 (0.18±0.14) 0.28±0.12 (0.30±0.19) Rough Estimation of Γ 2N 1.Consider the N np nbb all due to FSI. Then subtract the corresponding FSI amount from N nn nbb. The remainder would be N 2N. This give us a kind of lower limit of Γ 2N which is about 18-19% of Γ nm. 2. Use INC calculation result to estimate the FSI component in N np nbb. Then it will give ~25-30% of Γ nm.

Summary 1.A series of experiments have been done for the study of NMWD of Λ hypernuclei at KEK-PS, 2. The coincidence exclusive measurement of NMWD were done for the first time for 5 He and 12 Λ C and determined the Г n /Г p to be ~0.5 almost free from the ambiguity of FSI and 2N contribution. 3. The Γ n /Γ p values, ~0.5, well support the recent theoretical ratios. 4. All the signatures indicates fairly large Γ 2N comparable to Γ n, but with only a 2σ confidence level. 5. Now the accurate measurement ofГ 2N becomes so important that the decay width of each NMWD mode can be determined only after it. 6. A proposal for its accurate measurement is planned for JPARC.

KEK, RIKEN, Seoul Univ., GSI, Tohoku Univ., Osaka Univ., Univ. Tokyo Osaka Elec. Comm. Univ. G, Tokyo Inst. Tech. S. Ajimura, K. Aoki, A. Banu, H. Bhang, T. Fukuda, O. Hashimoto, J. I. Hwang, S. Kameoka, B. H. Kang, E. H. Kim, J. H. Kim, M. J. Kim, T. Maruta, Y. Miura, Y. Miyake, T. Nagae, M. Nakamura, S. N. Nakamura, H. Noumi, S. Okada, Y. Okatasu, H. Outa, H. Park, P. K. Saha, Y. Sato, M. Sekimoto, T. Takahashi, H. Tamura, K. Tanida, A. Toyoda, K.Tsukada, T. Watanabe, H. J. Yim KEK-PS E462/508 collaboration

Extra Slides

Total pair yields,N T : If Γ 2N =0, E th =0 and FSI=0, N T =1. If Γ 2N =0, E th =0 and FSI≠0, N T =1+α. If Γ 2N ≠ 0 and Eth ≠ 0, N T =?. This also has the limitation as the singles. Quenching of Total Pair Yields 5 Λ He np pair nn pair np pair nbb nn pair 12 Λ C N T = 0.38

INC(IntraNuclear Cascade) calculation A nucleus as a Fermi gas. ρ(x)  V(x) FSI is simulated as a cascsde free NN scattering along with Fermi blocking imposed. Density geometry parameters are determined fitting 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

Г 2N 1.Both singles yields (E307, E369) and coincidence yields (E462, E508) gave Γ n /Γ p ~0.5 which now agrees well with the recently enhanced theoretical ratios distributed in the range of The coincidence measurement of NMWD were done for the first time and determined the Γ n /Γ p values exclusively for the two body ΛN  NN process. It is almost free from the ambiguities of FSI and 2N contribution. Now we have Г n /Гp almost ambiguity free! Then, can we determine each Γ n, Γ p itself ?  How about Г 2N (ΛNN  nNN)? Can we neglect it?

Λ He : 0.61±0.081±0.082 (E462) 12 Λ C : 0.58±0.06±0.08 (E508) : ( 0.45~0.51)± 0.15 (E307/E369) 5 Λ He : 0.45 ±0.11 ±0.03 ± (E462) 12 Λ C : 0.50 ±0.13 ±(0.05) (E508) Coincidence Exp. OPE OME, DQ model Singles  n /  p Γ n /Γ p Status

Energy resolution σ ～ 8MeV ( around 80MeV ) 1/β spectra 5MeV< energy < 150MeV Neutral particle Charged particle π p d PID spectra Particle identification

Proton and neutron spectra N n (> 40 MeV) =0.69 N p (> 40 MeV) =0.40 E369 decay counter setup  Г n /Г p ( 12 Λ C) = 0.51±0.14  Obtained directly from the experimental ratio, N n /N p,  Almost theory independently while previous ones were derived comparing to that of INC. N n  Y n /Y nmwd () Y. Sato et al., PRC 71 (2004) J. Kim et al., PRC 68 (2003)

N p /decay Proton Energy spectrum N p /nm ~0.4 Λ+n  n+n Λ+p  n+p E307 decay counter setup where 2N ; ΛNN  NNN. Comparison to INC results gave

Angle/Energy sum Correlations 12 Λ C Preliminary Results

5 Λ He 12 Λ C Sharp back-to-back kinematic nature in 5 Λ He is moderated in that of 12 Λ C due to FSI. Comparison of 5 Λ He and 12 Λ C np pair nn pair Preliminary Results

Estimation of pair number per NMWD Preliminary Results

Γ n /Γ p from N n /N p & N nn /N np Simple counting of singles yields of n,p and coincidence yeilds of nn, np pairs gives, neglecting FSI and 2N N n /N p = 2Г n /Г p + 1, N nn /N np = Г n /Г p, Γ n /Γ p ~ ( N n /N p -1)/2 = 0.59 ( 5 Λ He), 0.5 ( 12 Λ C), Γ n /Γ p ~ N nn /N np = 0.45 ( 5 Λ He), 0.53 ( 12 Λ C).

- Assume 1N process only ; r n + r p = 1. - The neutron (proton) number per NMWD N n =Y n /N nm Ω n ε n = (2r n +r p )f + r p g N p =Y p /N nm Ω p ε p = r p f + (2r n +r p )g, where f, g ; FSI effects. Correction for Cross over recoil effects - Obtained FSI model independently, but assuming 1N process. - The INC β value is used only for second order correction. β=0.11  Γ n /Γ p =

Decay counter system p n N: 20cm×100cm×5cm T3: 10cm×100cm×2cm T2: 4cm×16cm×0.6cm Solid angle: 26% 9(T)+9(B)+8(S)% π

Comparison of Angular Correlation of He and C We notice that 1.R(np) enhancement in C over He.  FSI? 2. R(nn) enhancement over R(np) both in He and C  2N NMWD? where R=N bb /N nbb Preliminary Results 5 Λ He 12 Λ C np pair nn pair np pair nn pair nbb nn pair

INC spectrum ; Fermi momentum and FSI model

Energy Sum ; E N1 +E N2 Back-to-back Uniform Back-to-back (cosθ≤ -0.8) 5 Λ He cosθ nn cosθ np E n +E p (MeV)E n +E n Energy Sum Correlations Angular Correl. of np pair Angular Correl. of nn pair

Nnn/Nnp cosθ cut dependence

 n  p  nn /  np = 0.45±0.11±0.03

Particle identification Energy resolution σ ～ 8MeV ( around 80MeV ) 1/β spectra 5MeV< energy < 150MeV Neutral particle Charged particle π p d PID spectra

INC showing angular correlation due to Fermi Mom. Only. No FSI.

3. Enhancement of nn pair yields in the non- back-to-back angular region R  N nbb /N bb, 2N  2N NMWD Suppose no 2N, then N nbb due to FSI and we expect Rnp = Rnn, R = Rnn/Rnp = 1. But in reality, Rnn  Rnp, Rnn/Rnp ~ 2.  2N signature ! !

Estimation of Γ 2N /Γ NM

Summary on Γ n /Γ p. 1.A series of experiments have been done for the study of NMWD of Λ hypernuclei at KEK-PS. Accurate measurement of neutron spectrum finally reslove the long standing Γ n /Γ p puzzle along with the recent enhanced theoretical ratios distributed from The coincidence measurement of NMWD were done for the first time for 5 He and 12 Λ C in E462/E508 and determined the pair numbers, N nn and N np, exclusively for the two body ΛN  NN process. 3. From the pair number ratio, N nn /N np, Г n /Г p was determined to be ~0.5 almost free from the ambiguities of FSI and 2N contribution. Then, how about the magnitude of each Γ n, Γ p itself ?

Energy Sum ; E N1 +E N2 E n +E p (MeV)E n +E n (MeV) E n +E p (MeV)E n +E n (MeV) E sum

 Two groups ; from  Integrated yields  large value  the yields in nbb region  smaller one

Preliminary Results Acceptance and Efficiency correction

Back-to-Back Pair Number Ratio, N nn /N np FSI corr b.g. Subt Sum cosθ cut N nn /N np estimation np nn 12 Λ C N nn N np

Sources of Singles deficiency in the yield; 1) Weak strength of FSI; 2) 3-body 2N NMWD.  Limitation ; No way to distinguish their effects on the singles spectrum. Quenching of Singles Yields Compared to INC spectrum (N n +N p )/NMWD E N (MeV) 12 Λ C For 2N, we adopted the kinematics of uniform phase space sharing of 3 nucleons. Significant quenching of the N n +N p could not be explained with 1N only INC.!!

Compared to INC spectrum (N n +N p )/NMWD E N (MeV) 12 Λ C

Non-Mesonic Weak Decay (NMWD) & Issues 1. B-B Weak Interaction ; Λ + N  N + N (ΔS=1 B-B Weak Interaction ) 2.Long standing puzzle on : Γ n /Γ p (≡np ratio) 3. 2N NMWD: 3-Body, ΛNN  NNN, Interaction Process, Predicted to be a significant component of NMWD, though not experimentally identified yet. - Final State Interaction : It seems one of the important elements to understand NMWD. 4. Asymmetry : 5. ΔI=1/2 rule

apply a simple relation  n /  p = (N n / N p - 1) / 2   n /  p ~0.5