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.
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