Abstract
We examine the physics motivations to search for lepton number violations in the laboratory, in particular by studying the important nuclear transition called neutrinoless double beta decay, which consists in the creation of a pair of electrons. We address some major shortcomings of the Standard Model of electroweak interactions, arguing that most of them can be solved simply within extended models with Majorana neutrinos. At the same time, we discuss the difficulties of obtaining precise predictions for the neutrinoless double beta decay rate and strengthen the case of probing Majorana neutrino masses of about 10 meV.
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