The Scalar MSW Effect: Compact analytical formulas for neutrino oscillations with large matter effects, including $μ-μ$ and $τ-τ$ dominant matter potentials

Abstract

Deriving simple and accurate three-flavor neutrino oscillation probability formulas in matter is critical for understanding the phenomenology of upcoming experiments. In this article, we extend the Jacobi diagonalization method for deriving effective parameter mappings for neutrino oscillations in matter. The key insight behind the extension is to purposefully parameterize the mixing matrix, $U_{\text{PMNS}}$, using particular arrangements of Euler rotations. This novel extension allows for deriving simple and accurate effective mixing parameter mappings for exotic types of matter potentials. First, we revisit the Jacobi diagonalization method for neutrino oscillations with standard matter effects and use this to demonstrate our generalization. Subsequently, we apply the Jacobi diagonalization method to scalar non-standard interactions (SNSI) and derive effective parameter mappings for all three single diagonal coupling cases. The resulting formulas reveal that all diagonal SNSI couplings could give rise to a scalar MSW (SMSW) effect, that is an energy independent resonant enhancement analogous to the MSW effect. Finally, we study the accuracy of the derived SNSI formulas for various contemporary and upcoming experiments. For $δm_{ee}$, the accuracy is excellent for all considered experiments. For $δm_{μμ}$ and $δm_{ττ}$ the accuracy is worse since $A_{CC}$ must be neglected, and first order perturbative corrections are applied to amend this.