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

• Main Authors: Zhi-zhong Xing, Shun Zhou, Ye-Ling Zhou
• Format: Article
• Language: English
• Published: SpringerOpen 2018-05-01
• Series: Journal of High Energy Physics
• Subjects: Neutrino Physics; Renormalization Group
• Online Access: http://link.springer.com/article/10.1007/JHEP05(2018)015

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≡22GFNeE $$ a\equiv 2\sqrt{2}\kern0.5em {G}_{\mathrm{F}}{N}_eE $$ 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 m˜i $$ {\tilde{m}}_i $$ (for i = 1, 2, 3). Given the standard parametrization of V , the RGEs for θ˜12,θ˜13,θ˜23,δ˜ $$ \left\{{\tilde{\theta}}_{12},\kern0.5em {\tilde{\theta}}_{13},\kern0.5em {\tilde{\theta}}_{23},\kern0.5em \tilde{\delta}\right\} $$ 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.