[@Pas:1999fc; @Pas:2000vn].

Our approach also has some overlap with [@Babu:2001ex; @deGouvea:2007xp]. These authors write down all effective LNV operators from $d=5$ (the famous Weinberg operator [@Weinberg:1979sa]) to $d=11$. The main motivation of those papers is to identify all possible Majorana neutrino mass models via the effective LNV operators [@Babu:2001ex]. This effective operator treatment allows to estimate the scale $\Lambda$ at which new physics appears, if these operators give neutrino masses or a [$0\nu\beta\beta$ ]{}decay amplitude of the order of the current experimental sensitivity [@deGouvea:2007xp]. However, our current work is complementary to these papers, in that we list all possible [*decompositions*]{} of a particular LNV operator, that is the $d=9$ [$0\nu\beta\beta$ ]{}operator. We also go one step further than these works in the estimation of the bounds on the LNV operator, by making contact with the nuclear matrix element calculation of [@Pas:1999fc; @Pas:2000vn], instead of simply relying on dimensional arguments.[^9] Finally, there is also the recent paper [@delAguila:2012nu], where the authors study [$0\nu\beta\beta$ ]{}decay from an effective Lagrangian point of view. Operators of $d>9$ are considered, in which the Standard Model (SM) Higgs doublets are additionally inserted to the $d=9$ operator Eq. . Note, however, that [@delAguila:2012nu] considers only the case 