Running of Oscillation Parameters in Matter with Flavor-Diagonal Non-Standard Interactions of the Neutrino

In this article we unravel the role of matter effect in neutrino oscillation in the presence of lepton-flavor-conserving, non-universal non-standard interactions (NSI's) of the neutrino. Employing the Jacobi method, we derive approximate analytical expressions for the effective mass-squared differences and mixing angles in matter. It is shown that, within the effective mixing matrix, the Standard Model (SM) W-exchange interaction only affects $θ_{12}$ and $θ_{13}$, while the flavor-diagonal NSI's only affect $θ_{23}$. The CP-violating phase $δ$ remains unaffected. Using our simple and compact analytical approximation, we study the impact of the flavor-diagonal NSI's on the neutrino oscillation probabilities for various appearance and disappearance channels. At higher energies and longer baselines, it is found that the impact of the NSI's can be significant in the numu to numu channel, which can probed in future atmospheric neutrino experiments, if the NSI's are of the order of their current upper bounds. Our analysis also enables us to explore the possible degeneracy between the octant of $θ_{23}$ and the sign of the NSI parameter for a given choice of mass hierarchy in a simple manner.

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