Majorana Neutrinos and Same-Sign Dilepton Production at LHC and in Rare Meson Decays

We discuss same-sign dilepton production mediated by Majorana neutrinos in high-energy proton-proton collisions $pp\ra \ell^+ \ell^{\prime +}X$ for $\ell, \ell^\prime = e, \mu, \tau$ at the LHC energy E=14 TeV, and in the rare decays of $K$, $D$, $D_s$, and $B$ mesons of the type $M^{+}\ra M^{\prime -}\ell ^{+}\ell ^{\prime+}$. For the $pp$ reaction, assuming one heavy Majorana neutrino of mass $m_N$, we present discovery limits in the $(m_{N},|U_{\ell N}U_{\ell^\prime N}|)$ plane where $U_{\ell N}$ are the mixing parameters. Taking into account the present limits from low energy experiments, we show that at LHC one has sensitivity to heavy Majorana neutrinos up to a mass $m_{N}\leq 2$ -- 5 TeV in the dilepton channels $\mu\mu, \tau\tau$, and $\mu\tau$, but the dilepton states $e\ell$ will not be detectable due to the already existing constraints from neutrinoless double beta decay. We work out a large number of rare meson decays, both for the light and heavy Majorana neutrino scenarios, and argue that the present experimental bounds on the branching ratios are too weak to set reasonable limits on the effective Majorana masses.