Neutrino mass mechanisms from a nonstandard Higgs Lagrangian and implications for flavor hierarchies

We present an alternative framework to establish the neutrino mass scale from the Higgs mechanism in a minimalist approach, which does not introduce new scalar bosons or extend the symmetry group of the standard model (SM). A nonstandard form of the Higgs Lagrangian, constructed via the inverse problem of calculus of variations, is proposed. Only one dimensionful parameter in the TeV scale is incorporated into the SM Lagrangian. The multiplicative Lagrangian model of the Higgs field plays an essential role in explaining the vast mass difference between charged fermions and Dirac neutrinos, while the Yukawa couplings for these two groups of particles naturally fall within the same scale. On the other hand, if the neutrino mass term has both Dirac and Majorana components, the mass of the mostly right-handed neutrinos in the Type-I seesaw mechanism can range from the keV scale up to slightly below the grand unification scale without requiring extremely small Yukawa couplings outside the SM regime. Furthermore, we discuss the potential of this mechanism to explain the hierarchical structure in the Yukawa couplings between first- and third-generation particles.