Renormalization-group equations of neutrino masses and flavor mixing parameters in matter
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≡ 2√{2}{G}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 {{\tilde{θ}}_{12}, {\tilde{θ}}_{13}, {\tilde{θ}}_{23}, \tilde{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.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- May 2018
- DOI:
- 10.1007/JHEP05(2018)015
- arXiv:
- arXiv:1802.00990
- Bibcode:
- 2018JHEP...05..015X
- Keywords:
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- Neutrino Physics;
- Renormalization Group;
- High Energy Physics - Phenomenology;
- High Energy Physics - Experiment
- E-Print:
- 22 pages, 8 figures, more discussions added, to be published in JHEP