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 $a\equiv 2\sqrt{2}{G}_{\mathrm{F}}^{}{N}_e^{}E$ 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 $\{{\tilde{\theta }}_{12}^{},{\tilde{\theta }}_{13}^{},{\tilde{\theta }}_{23}^{},\tilde{\delta }\}$ 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 $\mu$-$\tau$ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of $V$ are also obtained as a by-product.

22 pages, 8 figures, more discussions added, to be published in JHEP

References in corpus (5)

• Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity
• A review of mu-tau flavor symmetry in neutrino physics
• A partial $\mu$-$\tau$ symmetry and its prediction for leptonic CP violation
• Analytical approximations for matter effects on CP violation in the accelerator-based neutrino oscillations with E \lesssim 1 GeV
• Renormalization Group Equations for the CKM matrix

Cited by in corpus (13)

• Flavor structures of charged fermions and massive neutrinos
• The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter
• Neutrino Oscillation in Dense Matter
• Deviations from Tribimaximal and Golden Ratio mixings under radiative corrections of neutrino masses and mixings
• CP-Violation with Neutrino Disappearance Alone
• Naumov- and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos
• Interplay between the factorization of the Jarlskog Invariant and location of the Solar and Atmospheric Resonances for Neutrino Oscillations in Matter
• Evolution of Neutrino Mass-Mixing Parameters in Matter with Non-Standard Interactions
• Radiative corrections to the lepton flavor mixing in dense matter
• Continuous and Discrete Symmetries of Renormalization Group Equations for Neutrino Oscillations in Matter
• Rephasing invariance and permutation symmetry in flavor physics
• Matter Effects of Sterile Neutrino in Light of Renormalization-Group Equations