Evolution of Neutrino Mass-Mixing Parameters in Matter with Non-Standard Interactions

We explore the role of matter effect in the evolution of neutrino oscillation parameters in the presence of lepton-flavor-conserving and lepton-flavor-violating neutral-current non-standard interactions (NSI) of the neutrino. We derive simple approximate analytical expressions showing the evolution/running of mass-mixing parameters in matter with energy in the presence of standard interactions (SI) and SI+NSI (considering both positive and negative values of real NSI parameters). We observe that only the NSI parameters in the (2,3) block, namely $\varepsilon_{μτ}$ and $(γ- β) \equiv (\varepsilon_{ττ} - \varepsilon_{μμ})$ affect the running of $θ_{23}$. Though all the NSI parameters influence the evolution of $θ_{13}$, $\varepsilon_{eμ}$ and $\varepsilon_{eτ}$ show a stronger impact at the energies relevant for DUNE. $θ_{12}$ quickly approaches to $\sim$ $90^{\circ}$ with increasing energy in both SI and SI+NSI cases. The change in $Δm^2_{21,m}$ is quite significant as compared to $Δm^2_{31,m}$ both in SI and SI+NSI frameworks. Flipping the signs of the NSI parameters alters the way in which mass-mixing parameters run with energy. We demonstrate the utility of our approach in addressing several important features related to neutrino oscillation such as: a) unraveling interesting degeneracies between $θ_{23}$ and NSI parameters, b) estimating the resonance energy in presence of NSI when $θ_{13}$ in matter becomes maximal, c) figuring out the required baselines and energies to have maximal matter effect in $ν_μ$ $\rightarrow$ $ν_{e}$ transition in the presence of different NSI parameters, and d) studying the impact of NSI parameters $\varepsilon_{μτ}$ and $(γ- β)$ on the $ν_μ \to ν_μ$ survival probability.