Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter

Abstract

Recently, a complete set of differential equations for the effective neutrino masses and mixing parameters in matter have been derived to characterize their evolution with respect to the ordinary matter term $a\equiv 2\sqrt{2}{G}_{\mathrm{F}}^{}{N}_e^{}E$, in analogy with the renormalization-group equations (RGEs) for running parameters. Via series expansion in terms of the small ratio ${\alpha }_{\mathrm{c}}^{}\equiv {\Delta }_{21}^{}/{\Delta }_{\mathrm{c}}^{}$, we obtain approximate analytical solutions to the RGEs of the effective neutrino parameters and make several interesting observations. First, at the leading order, ${\tilde{\theta }}_{12}^{}$ and ${\tilde{\theta }}_{13}^{}$ are given by the simple formulas in the two-flavor mixing limit, while ${\tilde{\theta }}_{23}^{}\approx {\theta }_{23}^{}$ and $\tilde{\delta }\approx \delta$ are not changed by matter effects. Second, the ratio of the matter-corrected Jarlskog invariant $\tilde{\mathcal{J}}$ to its counterpart in vacuum $\mathcal{J}$ approximates to $\tilde{\mathcal{J}}/\mathcal{J}\approx 1/({\hat{C}}_{12}^{}{\hat{C}}_{13}^{})$, where ${\hat{C}}_{12}^{}\equiv \sqrt{1-2A_{\ast }^{}\cos 2{\theta }_{12}^{}+A_{\ast }^2}$ with $A_{\ast }^{}\equiv a/{\Delta }_{21}^{}$ and ${\hat{C}}_{13}^{}\equiv \sqrt{1-2A_{\mathrm{c}}^{}\cos 2{\theta }_{13}^{}+A_{\mathrm{c}}^2}$ with $A_{\mathrm{c}}^{}\equiv a/{\Delta }_{\mathrm{c}}^{}$. Finally, after taking higher-order corrections into account, we find compact and simple expressions of all the effective parameters.

arXiv comment20 pages, 8 figures. More discussions added, to be published in JHEP

References in corpus (20)

• Global analysis of three-flavour neutrino oscillations: synergies and tensions in the determination of theta_23, delta_CP, and the mass ordering
• Golden measurements at a neutrino factory
• Analytic Approximations for Three Neutrino Oscillation Parameters and Probabilities in Matter
• Series expansions for three-flavor neutrino oscillation probabilities in matter
• Flavor Mixing and CP Violation of Massive Neutrinos
• CP and T Violation in Neutrino Oscillations and Invariance of Jarlskog's Determinant to Matter Effects
• Compact Perturbative Expressions For Neutrino Oscillations in Matter
• New Formulation of Matter Effects on Neutrino Mixing and CP Violation
• Simple and Compact Expressions for Neutrino Oscillation Probabilities in Matter
• What is $\Delta m_{ee}^2$ ?
• Analytical approximations for matter effects on CP violation in the accelerator-based neutrino oscillations with E \lesssim 1 GeV
• Three Neutrino Oscillations in Matter
• Rotations Versus Perturbative Expansions for Calculating Neutrino Oscillation Probabilities in Matter
• More Straightforward Extraction of the Fundamental Lepton Mixing Parameters from Long-Baseline Neutrino Oscillations
• Renormalization-Group Equations of Neutrino Masses and Flavor Mixing Parameters in Matter
• Neutrino mixing in matter
• Why Is The Neutrino Oscillation Formula Expanded In $\Delta m_{21}^2/\Delta m_{31}^2$ Still Accurate Near The Solar Resonance In Matter?
• Features of Neutrino Mixing
• Looking into Analytical Approximations for Three-flavor Neutrino Oscillation Probabilities in Matter
• Symmetric formulation of neutrino oscillations in matter and its intrinsic connection to renormalization-group equations

Cited by in corpus (12)

• Flavor structures of charged fermions and massive neutrinos
• Simple and Precise Factorization of the Jarlskog Invariant for Neutrino Oscillations in Matter
• Neutrino Oscillation in Dense Matter
• Non-standard neutrino oscillations: perspective from unitarity triangles
• On the Properties of the Effective Jarlskog Invariant for Three-flavor Neutrino Oscillations in Matter
• Sum rules and asymptotic behaviors of neutrino mixing in dense matter
• 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
• Continuous and Discrete Symmetries of Renormalization Group Equations for Neutrino Oscillations in Matter
• Analytical description of CP violation in oscillations of atmospheric neutrinos traversing the Earth
• Radiative corrections to the lepton flavor mixing in dense matter
• Matter Effects of Sterile Neutrino in Light of Renormalization-Group Equations