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 flavor-conserving and flavor-violating non-standard interactions (NSIs) of the neutrino. We derive simple approximate analytical expressions showing the evolution/running of the mass-mixing parameters in matter with energy and in presence of NSIs. We observe that only the NSIs in (2,3) block ($\varepsilon_{\mu\mu}$, $\varepsilon_{\tau\tau}$, and $\varepsilon_{\mu\tau}$) affect the running of $\theta_{23}$. Though all the NSIs influence the evolution of $\theta_{13}$, $\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$ show a stronger impact. $\theta^m_{12}$ saturates to $\pi/2$ at smaller energy. We demonstrate the utility of our approach in addressing several important features related to neutrino oscillation such as: a) unraveling interesting degeneracies between $\theta_{23}$ and NSI parameters, b) estimating the resonance energy in presence of NSIs when $\theta_{13}$ in matter becomes maximal, c) figuring out the required baseline length and neutrino energies to have maximal matter effect in $\nu_{\mu}$ $\rightarrow$ $\nu_{e}$ transition with NSIs, and d) studying the impact of NSIs in (2,3) block on the $\nu_{\mu}$ survival probability.