The production of Like-Sign-Di-leptons (LSD), in the high energy lepton number violating ($Delta L = +2$) reaction, p p --> 2jets + l+l+ (l=e,mu,tau) of interest for the experiments to be performed at the forthcoming Large Hadron Collider (LHC), is investigated in detail, taking up a composite model scenario in which the exchanged virtual composite neutrino is assumed to be a Majorana particle that couples to the light leptons via the $SU(2)times U(1)$ gauge bosons through a magnetic type coupling ($sigma_{mu u}$). An helicity projection method is used to evaluate exactly the tree-level amplitudes of the contributing parton subprocesses ($2to 4$), which allows to take into account all exchange diagrams and occurring interferences. Numerical estimates of the corresponding signal cross-section that implement kinematical cuts needed to suppress the Standard Model background, are presented which show that in some regions of the parameter space the total number of LSD events is well above the background. Assuming non-observation of the LSD signal it is found that LHC would exclude a composite Majorana neutrino up to 850 GeV (if one requires 10 events for discovery). The sensitivity of LHC experiments to the parameter space is then compared to that of the next generation of neutrinoless double beta decay ($betabeta_{0 u}$) experiment, GENIUS, and it is shown that they will provide constraints of the same order of magnitude and will play a complementary role.
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