Renormalization-group equations of neutrino masses and flavor mixing parameters in matter.

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≡22–√GFNeE to be an arbitrary scale-like variable with N e 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 m~i (for i = 1, 2, 3). Given the standard parametrization of V , the RGEs for {θ~12,θ~13,θ~23,δ~} 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