The extension of the Standard Model of electroweak interactions, to accommodate massive neutrinos and/or right-handed currents, is one of the fundamental questions to answer in the cross-field of particle and nuclear physics. The consequences of such extensions would reflect upon nuclear decays, like the very exotic nuclear double-beta-decay, as well as upon high-energy proton-proton reactions of the type performed at the LHC accelerator. In this talk we shall address this question by looking at the results reported by the ATLAS and CMS collaborations, where the excitation and decay of a heavy-mass boson may be mediated by a heavy-mass neutrino in proton-proton reactions leading to two jets and two leptons, and by extracting limits on the left-right mixing, from the latest measurements of nuclear-double-beta decays reported by the GERDA and EXO collaborations.