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

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