(290,90)(230,110) (290,90)(290,30)[2]{}[5]{} (290,30)(230,30) (350,30)(290,30) (130,10)(230,130) (40,25)\[t\][$\nu$]{} (100,28)\[t\][$e^-$]{} (65,60)\[r\][$W^-$]{} (100,72)\[t\][$d$]{} (100,108)\[b\][$u$]{} (320,25)\[t\][$\nu$]{} (260,28)\[t\][$e^-$]{} (295,60)\[l\][$W^-$]{} (260,72)\[t\][$d$]{} (260,108)\[b\][$u$]{} (180,58)\[b\][$0\nu\beta\beta$]{}

The Black Box theorem [@Schechter:1981bd; @Nieves:1984sn; @Takasugi:1984xr] states that since observation of [$0\nu\beta\beta$ ]{}indicates that lepton number is not conserved, it proves that neutrinos must be Majorana particles.[^5] Graphically the theorem can be depicted as shown in Fig. \[Fig:BlackBox\]: If [$0\nu\beta\beta$ ]{}decay is observed, Majorana neutrino masses are generated at least at the 4-loop order, which is a model-independent statement. This does not mean that the [$0\nu\beta\beta$ ]{}decay contribution from Fig. \[Fig:BlackBox\] is the leading contribution to neutrino mass; in fact, in specific models, neutrino mass is often generated at a lower loop order. A recent calculation [@Duerr:2011zd] indeed confirms that the neutrino mass generated through this 4-loop diagram with the [$0\nu\beta\beta$ ]{}operator of the size of the current limits is roughly $m_{\nu} \simeq {\cal O}(10^{-24})$ eV. Obviously, this number is too small to explain the neutrino masses observed in oscillation experiments, and also many orders of magnitude smaller than the current sensitivity of [$0\nu\beta\beta$ ]{}decay via the mass mechanism. The correct interpretation of the black box theorem thus is: If [$0\nu\beta\beta$ ]{}decay is observed, neutrinos are Majorana particles, whether the contribution from neutrino 