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Interpretation of the data on $\beta\beta 0\nu$ and $\beta\beta \chi^0$.

The fair agreement between measured and calculated half lives in $\beta\beta 2\nu$ decay suggests that the same models can reasonably predict the matrix elements for the other decay modes. Table [*] lists the measured $\beta\beta 0\nu$ half life limits from several experiments. For 128Te, it was assumed that the geochemically determined half life is a lower limit for that of $\beta\beta 0\nu$ decay. The corresponding neutrino mass limits, using the QRPA calculation of Caltech as well as from two other groups, are shown. The spread between the limits for a given half life is largest for 76Ge, and relatively small for the other, heavier, nuclei. This spread can be considered a measure of the uncertainty associated with the $\beta\beta 0\nu$ matrix elements. The last column gives the limits obtained with the shell model matrix elements of Strasbourg-Madrid. One sees that the 76Ge data give the most constraining limit. In all, one may conclude that the various experiments give:
 
Table: Measured lower limits for the half-life of various $\beta\beta \chi^0$ transitions. Deduced upper limits on the effective coupling constant $\langle g_{eff}\rangle$
 
  [yr]
(90 % CL)
$\langle g_{eff}\rangle$
Caltech
direct  
> 7.91
> 5
> 1.4
 
< (3.9 - 4.4)
< (2.5 - 3.1)
< (1.2 -1.8)
 
geochem. 128Te > 2.5 - 7.7 < (2 - 5)
 
 

Table [*] shows some measured half life limits on $\beta\beta \chi^0$ decay and the corresponding limits on $\langle g_{eff}\rangle$ obtained from the more conservative Caltech matrix elements. Here the geochemical 128Te data are the most constraining. Of the direct searches the 136Xe experiment gives the most stringent limit. In any event, one may conclude that the effective coupling constant is bound by: 


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