Lepton violating doubleβdecay in modern gauge theories

The neutrinoless lepton violating double $\beta$ decay is investigated in the context of modern gauge theories, whereby it is mediated by a Majorana neutrino. Transition operators appropriate for calculations of the relevant nuclear matrix elements are constructed. In addition, some of the approximations of the pregauge theories of double $\beta$ decay are investigated. Explicit shell model calculations are performed in the case of the $A=48\mathrm{}$ system.