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

Abstract

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 ${\epsilon }_{\mu \tau }$ and $(\gamma -\beta )\equiv ({\epsilon }_{\tau \tau }-{\epsilon }_{\mu \mu })$ affect the running of ${\theta }_{23}$. Though all the NSI parameters influence the evolution of ${\theta }_{13}$, ${\epsilon }_{e\mu }$ and ${\epsilon }_{e\tau }$ show a stronger impact at the energies relevant for DUNE. ${\theta }_{12}$ quickly approaches to $\sim$ $90^{\circ }$ with increasing energy in both SI and SI+NSI cases. The change in $\Delta m_{21,m}^2$ is quite significant as compared to $\Delta m_{31,m}^2$ 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 ${\theta }_{23}$ and NSI parameters, b) estimating the resonance energy in presence of NSI when ${\theta }_{13}$ in matter becomes maximal, c) figuring out the required baselines and energies to have maximal matter effect in ${\nu }_{\mu }$ $\to$ ${\nu }_e$ transition in the presence of different NSI parameters, and d) studying the impact of NSI parameters ${\epsilon }_{\mu \tau }$ and $(\gamma -\beta )$ on the ${\nu }_{\mu }\to {\nu }_{\mu }$ survival probability.

37 pages, 13 figures, 2 tables. Comments are welcome

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