We compare the discovery potential of the LHC for lepton number violating (LNV) signals with the sensitivity of current and future double beta decay experiments, assuming $0\nu \beta \beta$ decay is dominated by heavy particle exchange. We consider charged scalar, leptoquark and diquark mechanisms of $0\nu \beta \beta$ decay, covering the $0\nu \beta \beta$ decay operators with both, the smallest and largest, possible rates. We demonstrate, if $0\nu \beta \beta$ decay were found with a half-life below ${10}^{26}–{10}^{27}\mathrm{\text{years}}$ a positive signal should show up at the LHC, except for some particular cases of the leptoquark mechanism, and vice versa, if the LHC does not find any hints for LNV, a “short-range” explanation for a finite $0\nu \beta \beta$ decay half-life will be ruled out in most cases. We argue, if a positive LNV signal were found at the LHC, it is possible to identify the dominant contribution to $0\nu \beta \beta$. Two different kinds of observables which could provide such “model discriminating” power are discussed: different invariant mass peaks and the charge asymmetry.

• Received 5 March 2013

DOI:https://doi.org/10.1103/PhysRevD.88.011901