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

Journal of High Energy Physics, May 2018

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 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 $${\tilde{m}}_i$$ (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.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP05%282018%29015.pdf

Zhi-zhong Xing, Shun Zhou, Ye-Ling Zhou. Renormalization-group equations of neutrino masses and flavor mixing parameters in matter, Journal of High Energy Physics, 2018, 15, DOI: 10.1007/JHEP05(2018)015