Nonstandard interactions (NSI) of neutrinos with matter has received renewed interest in recent years. In particular, it has been shown that NSI can reconcile the $3+1$ solution with IceCube atmospheric data with $E_{\nu }>500\mathrm{GeV}$, provided that the effective coupling of NSI is large, e.g., $\sim 6G_F$. The main goal of the present paper is to show that contrary to intuition, it is possible to build viable models with large NSI by invoking a new $U(1)$ gauge symmetry with gauge boson of mass $\sim 10\mathrm{eV}$. We refer to these new constructions as $3+1+U(1)$ models. In the framework of a $3+1$ solution to LSND and MiniBooNE anomalies, we show that this novel NSI can help to solve the tension with cosmological bounds and constraints from IceCube atmospheric data with $E_{\nu }>500\mathrm{GeV}$. We then discuss the implications of the MINOS and MINOS+ results for the $3+1+U(1)$ scenario.

• Received 13 November 2018

DOI:https://doi.org/10.1103/PhysRevD.99.035003

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Published by the American Physical Society