Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Running Neutrino Masses, Leptonic Mixing Angles and CP-Violating Phases:
  From $M_{\rm Z}$ to $\Lambda_{\rm GUT}$   We derive renormalization group equations for neutrino masses, leptonic
mixing angles and CP-violating phases running at energies above the seesaw
threshold, both in the Standard Model and in the Minimal Supersymmetric
Standard Model extended with three right-handed neutrinos. With these
equations, we carry out a systematic study of the radiative correction that may
arise to neutrino parameters, via their renormalization group evolution from
the electroweak scale ($M_{\rm Z}$) to the scale of Grand Unified theories
($\Lambda_{\rm GUT}$). We study in detail three typically interesting neutrino
mass patterns: normal hierarchy, near degeneracy and inverted hierarchy.
Magnitudes of possible corrections in each case are carefully investigated. We
also emphasize the significance of CP-violating phases in controlling the
evolution behavior of all neutrino parameters.

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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph