when new physics is confined to the leptonic part of the [$0\nu\beta\beta$ ]{}decay amplitude.

The rest of this paper is organised as follows. In the next section, as a preparation for our approach, we will first recapitulate the characteristics of the long-range and short-range contributions to [$0\nu\beta\beta$ ]{}decay. Then, in Sec. \[Sec:decom\] we will focus on the decomposition of effective operators to find all possible models generating the $d=9$ [$0\nu\beta\beta$ ]{} operator. Through an example, we will study the crucial role that the LHC can play in discriminating such models in Sec. \[sec:example\]. The relations between the list of particle models and the general decay rate of [@Pas:1999fc; @Pas:2000vn] are given in tabular form in the appendix for the short-range part for the case of scalar exchange. The corresponding relations for the other parts of the decay rate can be easily derived from the recipes spelled out below and in the appendix.

Model-independent parametrisation of the $\boldsymbol{0\nu\beta\beta}$ decay rate
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A general Lorentz-invariant parametrisation of new physics contributions to [$0\nu\beta\beta$ ]{}has been developed in [@Pas:1999fc; @Pas:2000vn]. This formalism allows to derive limits on any LNV new physics contributing to [$0\nu\beta\beta$ ]{}decay without recalculation of nuclear matrix elements. In order to 