Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Radiative Splitting of Three Degenerate Neutrinos   We propose a radiative origin of the two mass splittings of three degenerate
Majorana neutrinos. It can be achieved by extending the standard model to have
the usual effective dimension 5 operators generating SO(3)-invariant tree-level
masses, and a charged scalar singlet coupling with the leptons preserving the
U(1) subgroup of SO(3). The mass splittings for the atmospheric and solar
neutrino oscillations then arise from one-loop corrections due to the charged
scalar singlet coupling and the usual tau Yukawa coupling, respectively.

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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol