Abstract
We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter \( a\equiv 2\sqrt{2}\kern0.5em {G}_{\mathrm{F}}{N}_eE \) to be an arbitrary scale-like variable with Ne being the net electron number density and E being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix V and the effective neutrino masses \( {\tilde{m}}_i \) (for i = 1, 2, 3). Given the standard parametrization of V , the RGEs for \( \left\{{\tilde{\theta}}_{12},\kern0.5em {\tilde{\theta}}_{13},\kern0.5em {\tilde{\theta}}_{23},\kern0.5em \tilde{\delta}\right\} \) in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial μ-τ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of V are also obtained as a by-product.
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Xing, Zz., Zhou, S. & Zhou, YL. Renormalization-group equations of neutrino masses and flavor mixing parameters in matter. J. High Energ. Phys. 2018, 15 (2018). https://doi.org/10.1007/JHEP05(2018)015
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DOI: https://doi.org/10.1007/JHEP05(2018)015