The super-weak interaction includes three simple extensions of the standard model: gauge extension, fermionic extension, and scalar extension. All of these extensions are strongly influenced by their complex phenomenology. They can explain a number of unresolved questions in particle physics and cosmology, including the genesis of dark matter, cosmic inflation, asymmetry of matter and antimatter, neutrino masses, and vacuum stability, if combined into a single structure. This is an extension of the gauge group of the standard model $G_{\rm SM}$ by $G_{\rm SM}\otimes U(1)_Z$ without any anomalies. We investigate the implications of the development of a general Majorana mass renormalization group for neutrinos with masses in the range of 0.03 $eV$ and 0.1 $eV$, which fall within the recently published range as well as the range to be explored in future planned experiments.