A Reanalysis of the Reported
Observation of the
4 H Hypernucleus
ΛΛ
S. D. Randeniya & E. V. Hungerford
University of Houston
USA
October 10 -14 2006,
Mainz, Germany
Experiment E906
Cylindrical Detection System (CDS)
Coil
CDC
k-


Target
k+


TOF
SIDE VIEW
FRONT VIEW
Beam : Momentum analyzed 1.8 GeV KTarget :
9Be
K+ were detected in a magnetic spectrometer
Technique : Coincident pion decay spectroscopy
Coincident Pion Decay Spectrum
Motivation
Decay of
4

4
ΛΛH
Hypernucleus
H    4 He* (8.9)    p  3 H    p    3 He
~ 8.9
7.78
7.75
(0-2)P + d+ Λ
3 H+ p
Λ
2.39
3He
1.15
1+
0.0
0+
4
ΛHe
+Λ
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
apotential, ΔBΛΛ
Λ-Λ
Probable double Lambda Hypernuclei
Produced in 9Be(K-,K+)X Reaction
A
ΛΛY
BΛ(A-1)
BΛΛ
ΔBΛΛ
MΛΛ(A)
Reference
4
ΛΛH
0.13
- 0.12
- 0.14
4107.78
PRL 89 172502
5
ΛΛH
2.04
3.26
0.82
5037.54
NPA 754 91c
5
ΛΛHe
2.39
3.80
0.98
5036.98
NPA 754 91c
PRC 68 24002
6
ΛΛHe
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
6
ΛΛHe
7
ΛΛHe
 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.
J. K. Ahn, et al
PRL 87 (2002)
Background
 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.
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
 total
 43 / 49 dof
Results for High Momentum Region
Decay mode
Normalization
No. of MC events
No. of counts fit
3
ΛH/
4
ΛH
0.002163
45000
97
3
ΛH/
3
ΛH
0.001608
45000
72
4
ΛH/
4
ΛH
0.002026
45000
91
0.020000
25000
500
Background
Variation of Chi Square
Case A :
3
ΛH
/
4
Case B :
3
ΛH
coincidence
ΛH
/
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
3
ΛH/
4
ΛH
0.002163
45000
97
3
ΛH/
3
ΛH
0.001608
45000
72
4
ΛH/
4
ΛH
0.002026
45000
91
0.020000
25000
500
0.003197
10900
35
Background
7
ΛΛHe
 3-body decay of single hypernuclear modes influence the
Mlow momentum region.
All Kept
constant
Decay of
3
4
ΛH -ΛH
in Coincidence
Fit to Low Momentum Region
Projection on to Plow
Projection on to Phigh
2
total
 48 / 51 dof
Global Representation
Projection on to Plow
Projection on to Phigh
Cuts
Plow : between 92 - 137 MeV/c
Phigh : between 101 – 143 MeV/c
2
total
 61/ 52 dof
Variation of Chi Square for the Global Fit
Projection on to Plow
Case A :
7
ΛΛ He
Case B :
7
Case C :
7
Case D :
7
ΛΛ
He with 3ΛH/ 4ΛH
ΛΛ
He with 3ΛH/ 4ΛH, 3ΛH/ 3ΛH
ΛΛ He
with 3ΛH/ 4ΛH, 3ΛH/ 3ΛH, 4ΛH/4 ΛH
Projection on to Phigh
Variation of Chi Square for the Global Fit
Decay modes
 2/ DOF
7
ΛΛHe/
3
ΛH,
4
ΛH
100/50
7
ΛΛHe/
3
ΛH,
4
ΛH/
ΛH
97/49
7
ΛΛHe/
3
ΛH,
4
4
4
ΛH/ ΛH, ΛH
67/49
7
ΛΛHe
3
ΛH,
3
/ all single hypernuclei
58/48
Variation in Normalization for the Global Fit
Decay mode
Normalization
Normalization
No. of MC events
(constant)
(Varied)
0.003197
0.003204
10900
7
ΛΛHe
3
ΛH/
4
ΛH
0.002163
0.002338
45000
3
ΛH/
3
ΛH
0.001608
0.001613
45000
4
ΛH/
4
ΛH
0.002026
0.002425
45000
Chi Square
Constant :
62/52 DoF
Varied
58/48 DoF
:
Production Ratio of
7
ΛΛHe
3
to ΛH
For 2-body decay of
7

7
4
/ ΛH
coincidence
ΛΛHe
He  Li    Be    
7


 
 
0.26

 1.56

7
7
ΛΛHe

 0.24
No. of counts from the fit
Total # of

Assuming non-mesonic
decay width is about 50%
= 20
hypernuclei produced = 512
3
3

ΛH
/ 4ΛH Coincidence
H  3 He   
 

4

 0.34
H  4 He   
 

 0.36
Y. Yamamoto et al
NPA 625 (1997)
No. of counts obtained from the fit
Total # of
3
ΛH
= 27
/ 4ΛH coincident events produced = 221
Production Ratio 7ΛΛHe to 3ΛH / 4ΛH coincidence
= 2.32 ~ 2
Conclusions
 Data can be explained without the inclusion of decay of
4
ΛΛH.
7
 More likely that ΛΛHe was observed in the experiment along
Mwith a back ground of 3 single hypernuclear pairs described
Mbefore.
 Analysis supports the weak value of ΔBΛΛ , for
7
ΛΛHe
= ~ 1 MeV.
 No evidence of any other single or double lambda hypernuclei.