A Reanalysis of the Reported Observation of the

ΛΛH Hypernucleus

S. D. Randeniya & E. V. Hungerford

University of Houston

USA

October 10 -14 2006,

Mainz, Germany

4

Experiment E906

Beam : Momentum analyzed 1.8 GeV K-

Target : 9Be

K+ were detected in a magnetic spectrometer

Technique : Coincident pion decay spectroscopy

k+k-

SIDE VIEW

Cylindrical Detection System (CDS)

Coil

TOF

CDC

FRONT VIEW

Target

Coincident Pion Decay Spectrum

Motivation

Decay of ΛΛH Hypernucleus4

4 4 * 3 3(8.9)H He p H p He

~ 8.97.787.75

2.39

1.15

0.0 0+

1+

3He + Λ

ΛH+ p3

P + d+ Λ

( 0 - 2 ) -

ΛHe4 D. E. Kahana et al

PRL C 68 (2003)

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, ΔBΛΛ

Probable double Lambda Hypernuclei Produced in 9Be(K-,K+)X Reaction

BΛ(A-1) BΛΛ ΔBΛΛ MΛΛ(A) Reference

0.13 - 0.12 - 0.14 4107.78 PRL 89 172502

2.04 3.26 0.82 5037.54 NPA 754 91c

2.39 3.80 0.98 5036.98 NPA 754 91c

PRC 68 24002

3.12 7.25 1.01 5952.51 PRL 87 212502

3.12 10.9 4.7 5948.83 PRL 17 782

4.18 9.36 <1.0> 6890.86 NPA 754 103c

ΛΛYA

ΛΛH

ΛΛH

ΛΛHe

ΛΛHe

ΛΛHe

ΛΛHe

5

4

5

6

6

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.

Background Comes from quasi-free Ξ’s & quasi-free Λ’s produced in M9Be(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 Plow = Phigh was used.

J. K. Ahn, et al

PRL 87 (2002)

Background

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.

Fit to High Momentum Region

Projection on to Plow

Projection on to Phigh

2 43/ 49total dof

Results for High Momentum Region

Decay mode Normalization No. of MC events No. of counts fit

3ΛH/ 4

ΛH 0.002163 45000 97

3ΛH/ 3

ΛH 0.001608 45000 72

4ΛH/ 4

ΛH 0.002026 45000 91

Background 0.020000 25000 500

Variation of Chi Square

Case A : 3ΛH / 4

ΛH coincidence

Case B : 3ΛH / 4

ΛH with all other pairs

Chi Square drops from 75/51 DOF to 43/49 DOF

Results for Low Momentum Region

Decay mode Normalization No. of MC events No. of counts fit

3ΛH/ 4

ΛH 0.002163 45000 97

3ΛH/ 3

ΛH 0.001608 45000 72

4ΛH/ 4

ΛH 0.002026 45000 91

Background 0.020000 25000 500

All Kept constan

t

ΛΛHe 0.003197 10900 357

3-body decay of single hypernuclear modes influence the Mlow momentum region.

Decay of ΛH -ΛH in Coincidence3 4

Fit to Low Momentum Region

Projection on to Plow

Projection on to Phigh

2 48 / 51total dof

Global RepresentationProjection on to Plow

Projection on to Phigh

2 61/ 52total dof

Cuts

Plow : between 92 - 137 MeV/c

Phigh : between 101 – 143 MeV/c

Variation of Chi Square for the Global FitProjection on to

Plow

Projection on to Phigh

Case A : 7ΛΛ He

Case B : 7ΛΛ He with 3

ΛH/ 4ΛH

Case C : 7ΛΛ He with 3

ΛH/ 4ΛH, 3

ΛH/ 3ΛH

Case D : 7ΛΛ He with 3

ΛH/ 4ΛH, 3

ΛH/ 3ΛH, 4

ΛH/4 ΛH

Variation of Chi Square for the Global Fit

Decay modes / DOF

7ΛΛHe/ 3

ΛH, 4ΛH

100/50

7ΛΛHe/ 3

ΛH, 4ΛH/ 3

ΛH, 3ΛH 97/49

7ΛΛHe/ 3

ΛH, 4ΛH/ 4

ΛH, 4ΛH 67/49

7ΛΛHe / all single hypernuclei

58/48

2

Variation in Normalization for the Global Fit

Decay mode Normalization Normalization No. of MC events

(constant) (Varied)

7ΛΛHe 0.003197 0.003204 10900

3ΛH/ 4

ΛH 0.002163 0.002338 45000

3ΛH/ 3

ΛH 0.001608 0.001613 45000

4ΛH/ 4

ΛH 0.002026 0.002425 45000 Chi Square

Constant : 62/52 DoF

Varied : 58/48 DoF

Production Ratio of ΛΛHe to ΛH / ΛH coincidence

7 3 4

Assuming non-mesonic decay width is about 50%

For 2-body decay of 7

ΛΛHe

7 7 7He Li Be

0.26

1.56

0.24

No. of counts from the fit = 20

Total # of 7

ΛΛHe hypernuclei produced = 512

3ΛH / 4

ΛH Coincidence

0.34

3 3H He

0.36

4 4H He

No. of counts obtained from the fit = 27

Total # of 3ΛH / 4

ΛH coincident events produced = 221

Y. Yamamoto et al

NPA 625 (1997)

Production Ratio 7ΛΛHe to 3

ΛH / 4

ΛH coincidence = 2.32 ~ 2

Conclusions

Data can be explained without the inclusion of decay of ΛΛH.

4

More likely that ΛΛHe was observed in the experiment along Mwith a back ground of 3 single hypernuclear pairs described Mbefore.

7

Analysis supports the weak value of ΔBΛΛ , for ΛΛHe = ~ 1 MeV.

7

No evidence of any other single or double lambda hypernuclei.