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Naumov- and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos
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abstract
In an analytical way of studying matter effects on neutrino oscillations, the Naumov and Toshev relations have been derived to respectively link the Jarlskog invariant of CP violation and the Dirac phase in the standard parametrization of the $3\times 3$ flavor mixing matrix to their matter-corrected counterparts. Here we show that there exist similar relations for Dirac neutrinos and charged leptons evolving with energy scales via the one-loop renormalization-group (RG) equations in the tau-dominance approximation, and for the running behaviors of up- and down-type quarks in the top-dominance approximation, provided a different parametrization is taken into account.
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Cited by 1 Pith paper
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On the Properties of the Effective Jarlskog Invariant for Three-flavor Neutrino Oscillations in Matter
The ratio of the matter-changed CP violation measure to its vacuum value is approximately the product of two two-flavor resonance factors, now derived more accurately and used to locate its peaks and dip.
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