1. A Reanalysis of the Reported Observation of the ΛΛ H Hypernucleus S. D. Randeniya & E. V. Hungerford University of Houston USA October 10 -14 2006, Mainz, Germany 4

2. Experiment E906 Beam : Momentum analyzed 1.8 GeV K - Target : 9 Be K + were detected in a magnetic spectrometer Technique : Coincident pion decay spectroscopy k+k+ k-k- SIDE VIEW Cylindrical Detection System (CDS) Coil TOF CDC FRONT VIEW Target

3. Coincident Pion Decay Spectrum

4. Motivation Decay of ΛΛ H Hypernucleus 4 ~ 8.9 7.78 7.75 2.39 1.15 0.0 0+0+ 1+1+ 3 He + Λ Λ H+ p 3 P + d+ Λ ( 0 - 2 ) - Λ He 4 D. E. Kahana et al PRL C 68 (2003)

5. Details of the Monte Carlo Simulation  Pion Decays  Simulated decays of single and double Lambda s hypernuclei starting from at rest systems.  Simulation includes decays to 2-body & 3-body afinal states.  Simulation includes decays to & from excited xstates as well as ground states.  Simulation used the new weak value for Λ-Λ apotential, ΔB ΛΛ

6. Probable double Lambda Hypernuclei Produced in 9 Be(K -,K + )X Reaction B Λ (A-1)B ΛΛ ΔB ΛΛ M ΛΛ (A) Reference 0.13- 0.12 - 0.14 4107.78 PRL 89 172502 2.043.26 0.82 5037.54 NPA 754 91c 2.393.80 0.98 5036.98 NPA 754 91c PRC 68 24002 3.127.25 1.01 5952.51 PRL 87 212502 3.1210.9 4.7 5948.83 PRL 17 782 4.189.36 6890.86 NPA 754 103c ΛΛ Y A ΛΛ H ΛΛ He 5 4 5 6 6 7

7.  Pion Decay Spectra  For the simulation pion spectra calculated in following Mreferences were used. M. Danszy, et al, PRL11 (1963), Y. Yamamoto, et al, NPA625 (1997), T. Motoba, et al, NPA534 (1991) T. Motoba, et al, NPA489 (1988)  Simulated spectra were spread by the standard deviation Mof the momentum resolution of the CDS, 4 MeV/c.  Natural decay widths for 3-body decay spectra were used Mas directly obtained from the above references.

8.  Background  Comes from quasi-free Ξ’s & quasi-free Λ’s produced in M 9 Be(K -,K + )X reaction.  Considering the statistical precision of data a background that is constant up to spectrum edges and then decrease as Gaussian with FWHM = 1.5 MeV/c at the limit P low = P high was used. J. K. Ahn, et al PRL 87 (2002) Background

9. Fits to the Experimental Data  Fit projected experimental data by the simulation Ausing Chi Square minimization Mprocedure.  This procedure equally weighted each pair of Aprojections.  Error for each experimental data point is taken Aas square root of number of events.

10. Fit to High Momentum Region Projection on to P low Projection on to P high

11. Results for High Momentum Region Decay mode Normalization No. of MC events No. of counts fit 3 Λ H/ 4 Λ H 0.002163 45000 97 3 Λ H/ 3 Λ H 0.001608 45000 72 4 Λ H/ 4 Λ H 0.002026 45000 91 Background 0.020000 25000 500

12. Variation of Chi Square Case A : 3 Λ H / 4 Λ H coincidence Case B : 3 Λ H / 4 Λ H with all other pairs Chi Square drops from 75/51 DOF to 43/49 DOF

13. Results for Low Momentum Region Decay mode Normalization No. of MC events No. of counts fit 3 Λ H/ 4 Λ H 0.002163 45000 97 3 Λ H/ 3 Λ H 0.001608 45000 72 4 Λ H/ 4 Λ H 0.002026 45000 91 Background 0.020000 25000 500 All Kept constant ΛΛ He 0.003197 10900 35 7  3-body decay of single hypernuclear modes influence the Mlow momentum region.

14. Decay of Λ H - Λ H in Coincidence 34

15. Fit to Low Momentum Region Projection on to P low Projection on to P high

16. Global Representation Projection on to P low Projection on to P high Cuts P low : between 92 - 137 MeV/c P high : between 101 – 143 MeV/c

17. Variation of Chi Square for the Global Fit Projection on to P low Projection on to P high Case A : 7 ΛΛ He Case B : 7 ΛΛ He with 3 Λ H/ 4 Λ H Case C : 7 ΛΛ He with 3 Λ H/ 4 Λ H, 3 Λ H/ 3 Λ H Case D : 7 ΛΛ He with 3 Λ H/ 4 Λ H, 3 Λ H/ 3 Λ H, 4 Λ H/ 4 Λ H

18. Variation of Chi Square for the Global Fit Decay modes / DOF 7 ΛΛ He/ 3 Λ H, 4 Λ H 100/50 7 ΛΛ He/ 3 Λ H, 4 Λ H/ 3 Λ H, 3 Λ H 97/49 7 ΛΛ He/ 3 Λ H, 4 Λ H/ 4 Λ H, 4 Λ H 67/49 7 ΛΛ He / all single hypernuclei 58/48

19. Variation in Normalization for the Global Fit Decay mode Normalization Normalization No. of MC events (constant) (Varied) 7 ΛΛ He 0.003197 0.003204 10900 3 Λ H/ 4 Λ H 0.002163 0.002338 45000 3 Λ H/ 3 Λ H 0.001608 0.001613 45000 4 Λ H/ 4 Λ H 0.002026 0.002425 45000 Chi Square Constant : 62/52 DoF Varied : 58/48 DoF

20. Production Ratio of ΛΛ He to Λ H / Λ H coincidence 7 34 Assuming non-mesonic decay width is about 50% For 2-body decay of 7 ΛΛ He No. of counts from the fit = 20 Total # of 7 ΛΛ He hypernuclei produced = 512

21. 3 Λ H / 4 Λ H Coincidence No. of counts obtained from the fit = 27 Total # of 3 Λ H / 4 Λ H coincident events produced = 221 Y. Yamamoto et al NPA 625 (1997) Production Ratio 7 ΛΛ He to 3 Λ H / 4 Λ H coincidence = 2.32 ~ 2

22. Conclusions  Data can be explained without the inclusion of decay of ΛΛ H. 4  More likely that ΛΛ He was observed in the experiment along Mwith a back ground of 3 single hypernuclear pairs described Mbefore. 7  Analysis supports the weak value of ΔB ΛΛ, for ΛΛ He = ~ 1 MeV. 7  No evidence of any other single or double lambda hypernuclei.