Pattern of the Approximate Mass Degeneracy of Majorana Neutrinos

In view of the recently reported evidence for a nonzero Majorana mass of the electron neutrino, together with the established phenomena of atmospheric and solar neutrino oscillations, the case of three nearly mass-degenerate Majorana neutrinos is now a distinct possibility. I show in this paper how a natural pattern of symmetry breaking in the recently proposed A4 model of Majorana neutrino masses can accommodate the data on neutrino oscillations, resulting in the predictions sin 2θatm = 1 and sin 2θsol = 2/3. In the past several years, there has been mounting evidence for neutrino oscillations [1, 2, 3]. Since they require only neutrino mass differences, the possibility of nearly degenerate neutrino masses is often considered [4]. Recently, the first positive evidence for neutrinoless double beta decay has been reported [5] which may be interpreted as an effective nonzero Majorana mass for the electron neutrino. Combined with the atmospheric and solar neutrino data, there is now a plausible argument for three nearly mass-degenerate Majorana neutrinos [6]. However, the charged-lepton masses are certainly not degenerate, so whatever symmetry is used to maintain the neutrino mass degeneracy must be broken. To implement this idea in a renormalizable field theory, the discrete symmetry A4 was proposed recently [7] where its spontaneous breaking results in charged-lepton masses and its explicit soft breaking results in neutrino mass differences. The proposed A4 model is based on a simple model of neutrino masses [8], where a leptonic Higgs doublet η = (η, η) and three right-handed neutral singlet fermions NiR are added to the minimal standard model of particle interactions. These new particles may all be at or below the TeV energy scale, so that the seesaw mechanism [9] may be tested experimentally at future accelerators. With the report of a possible discrepancy in the experimental measurement [10] of the muon anomalous magnetic moment with the theoretical prediction, this leptonic Higgs model was used [11] to constrain the masses and couplings of these new particles. However, a sign error has been discovered [12] in the theoretical calculation, hence the experimental discrepancy is now only 1.6σ, which is not much of a constraint on this model. In this paper the explicit soft breaking of the A4 symmetry is shown to allow for a natural solution with the predictions sin 2θatm = 1 and sin 2 2θsol = 2/3 which agree well with present data and may be tested more precisely in future neutrino-oscillation experiments. At the same time, the new particles NiR as well as an assortment of Higgs bosons with specific