Neutrino masses in the economical 3-3-1 model

Abstract

We show that in the framework of the economical 3-3-1 model, the suitable pattern of neutrino masses arises from three quite different sources---the lepton-number conserving, the spontaneous lepton-number breaking, and the explicit lepton-number violating, widely ranging over mass scales including the GUT one: $u\ensuremath{\sim}O(1)\text{ }\text{ }\mathrm{GeV}$, $v\ensuremath{\approx}246\text{ }\text{ }\mathrm{GeV}$, $\ensuremath{\omega}\ensuremath{\sim}O(1)\text{ }\text{ }\mathrm{TeV}$, and $\mathcal{M}\ensuremath{\sim}\mathcal{O}({10}^{16})\text{ }\text{ }\mathrm{GeV}$. At the tree level, the model contains three Dirac neutrinos: one massless, and two large with degenerate masses in the range of the electron mass. At the one-loop level, the left-handed and right-handed neutrinos obtain Majorana masses ${M}_{L,R}$ in orders of ${10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{eV}$ and degenerate in ${M}_{R}=\ensuremath{-}{M}_{L}$, while the Dirac masses get a large reduction down to eV scale through a finite mass renormalization. In this model, the contributions of new physics are strongly signified, the degenerations in the masses and the last hierarchy between the Majorana and Dirac masses can be completely removed by heavy particles. All the neutrinos get mass and can fit the data. The acceptable set of the input data does not induce the large lepton flavor violating branching ratios such as $\mathrm{Br}(\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma})$.