1. Soongsil University, Seoul, Korea
Nuclear Matrix Elements (NME) for Double Beta Decay (DBD) (based on Quasi-particle RPA)
Myung-Ki Cheoun
Department of Physics,
Soongsil University, Seoul, Korea
K.S.Kim, E. Ha, W.Y.So, C. Ryu…
A.Faessler, F. Simkovic..
Int. Workshop on DBD, SNU

2. Contents 0. Motivation for DBD 1. Brief Introduction of QRPA
2. Ambiguities in NME for DBD
3. Uncertainties and their Correlations by NME in the analysis of DBD
4. Summary and Remarks
Int. Workshop on DBD, SNU

3. 0. Motivation for DBD
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4. But, DBD occurs in Nucleus.
Mayoron contribution ?
But, DBD occurs in Nucleus.
Ambiguities from the Structure should be pinned down !!
Int. Workshop on DBD, SNU

5. Half lives for DBD can be factored by 3 ingredients !!
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6. 3 Main Transitions (Fermi, GT and Tensor) in the NME for DBD !!
Various Multipolarities
High momentum transfer
Int. Workshop on DBD, SNU
1 - 2 fm

7. Experimental Status No overlap !! => HM data ? More sensitive test
Experimental Results
Range expected
By Theo. NME
and HM data
Int. Workshop on DBD, SNU

8. 1. Brief Introduction of QRPA
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9. 2. Ambiguities in NME for DBD
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10. Even
Even
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11. Quasi Boson Approx. ??
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12.
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13.
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14. other multipole states ?
But How about
other multipole states ?
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15.
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16.
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17.
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18.
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19. 3. Uncertainties and their Correlations by NME in the analysis of DBD
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20.
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21.
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22. Most 24 theo. Data are included Strong and positive Correlations !!
in 1 sigma error eclipse
Strong and positive Correlations !!
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23. Estimation of neutrino mass
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24.
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25. Comparison of half-lives in coupled nuclei
76Ge HM result
Phase space and Theo. NME
Theo. Error bars
With correlations
Int. Workshop on DBD, SNU

26. More sensitive test are
No overlap !!
=>
HM data ?
More sensitive test are
necessary
Int. Workshop on DBD, SNU

27. Prospective Sensitivities for DBD in future project !!
Reliable limits for DBD,
if DBD exists !! !!
Int. Workshop on DBD, SNU

28. 4. Summary and Remarks
Most of uncertainties from the nuclear structure in DBD could be pinned down, but parts of them are inescapable because of the original problem in the many body system of nucleons.
Allowing the ambiguities as the error bars theoretical data for NME are strongly correlated within 1-3 sigma, even if include other model calculations.
Mayorana neutrino mass can be deduced from HM data, but the lower limit masses by other data are not reached to the upper limit of HM data.
Int. Workshop on DBD, SNU

29. 4. By the correlation method in NME results and HM data, one can estimate half lives of other nuclei. Their results are dislocated from the present data.
5. Prospective half lives in promising future projects could allow reliable limits to this DBD problem, if DBD exists.
6. Not only DBD but also other related reactions could be very helpful for pinning down the ambiguities from NME.
7. Theoretical studies for NME should be go on not only for DBD but also for unstable nuclei playing important roles on the nucleosynthesis in the Universe.
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30. Thanks for your attention !!
감사합니다 !!
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31.
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32.
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33.
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34.
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35.
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36.
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37. The formula for computing the covariance of the variables X and Y is
with  and  denoting the means of X and Y, respectively. 
Mean vector and variance-
covariance matrix for sample data matrix  The results are:
Thus, is the variance of the length variable, is the covariance
between the length and the width variables, is the covariance between the
length and the height variables, is the variance of the width variable,
is the covariance between the width and height variables and
is the variance of the height variable.
Int. Workshop on DBD, SNU

38. Although the variance is intended to be an overall measure of spread,
The variance is roughly the arithmetic average of the squared distance from the mean.
Squaring the distance from the mean has the effect of giving greater weight to values
that are further from the mean. For example, a point 2 units from the mean adds 4
to the above sum while a point 10 units from the mean adds 100 to the sum.
Although the variance is intended to be an overall measure of spread,
it can be greatly affected by the tail behavior
Int. Workshop on DBD, SNU