is simply proportional to $1/\Lambda^5$. In that case, the next generation [$0\nu\beta\beta$ ]{}decay experiments are sensitive to new physics at scales $\Lambda \gsim$ (few) TeV.

Data from the LHC will probe physics at the TeV scale, i.e., of a similar scale as the sensitivity of [$0\nu\beta\beta$ ]{}decay experiments in case of short-range contributions. In fact, first limits on particular models have already been published. Just to mention one particular example, in Left-Right (LR) symmetric models, [$0\nu\beta\beta$ ]{}decay can be generated by $W_R-N-W_R$ exchange, where $N$ is a heavy Majorana neutrino and $W_{R}$ is the charged gauge boson of the right-handed $SU(2)$ [@Riazuddin:1981hz].[^7] Using the nuclear matrix elements of [@Hirsch:1996qw], the limit on the half-life [@Auger:2012ar] corresponds to $\langle m_N\rangle = m_{W_R} \gsim
1.3$ TeV (assuming that the gauge coupling of the right-handed and left-handed $SU(2)$s are equal), while the recent analysis by the ATLAS [@ATLAS:2012ak] and the CMS collaborations [@CMS:PAS-EXO-12-017] give $m_{W_R} \ge (2.3-2.5)$ TeV for $m_N
\lsim 1.3$ TeV. [^8] Because of this complementarity of [$0\nu\beta\beta$ ]{}decay and LHC, we will pay particular attention to the short-range part of the [$0\nu\beta\beta$ ]{}decay amplitude. However, our decomposition of the $d=9$ operator, which will be shown in Sec. \[Sec:decom\], is general, 