Evolution of neutrino mass-mixing parameters in matter with non-standard interactions

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