are aware of that a T-II contribution dominates the [$0\nu\beta\beta$ ]{}decay amplitude.[^13] Note, however, that our Tab. \[Tab:TopoII\] allows to construct a number of additional models with this property.

An example for short-range $\boldsymbol{0\nu\beta\beta}$ decay, and its test at the LHC {#sec:example}
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As mentioned above, one expects that exotic models with LNV, which lead to short-range contributions for [$0\nu\beta\beta$ ]{}decay, yield testable phenomenology at the LHC. The classical example is the LR-symmetric model, and there is also a recent paper that has made a study for trilinear RPV SUSY and [$0\nu\beta\beta$ ]{}decay [@Allanach:2009iv]. In this section we will discuss basic LHC phenomenology of one particular example in our Tab. \[Tab:TopoI\], based on the decomposition T-I-4-ii-a. We have chosen this particular case basically for two reasons: (i) it belongs to the class of models, which have not been studied in the literature before, and (ii) it leads to richer phenomenology at the LHC than either the LR-symmetric model or RPV SUSY. By using the different signals which we will discuss in the following, one could distinguish this model from the other possibilities, such as the LR-symmetric model and RPV SUSY.

For the decomposition T-I-4-ii-a one needs to introduce three new 