Can nonstandard interactions jeopardize the hierarchy sensitivity of DUNE ?

We study the effect of non-standard interactions (NSIs) on the propagation of neutrinos through the Earth matter and how it affects the hierarchy sensitivity of the DUNE experiment. We emphasize on the special case when the diagonal NSI parameter $\epsilon_{ee} = -1$, nullifying the standard matter effect. We show that, if in addition, CP violation is maximal then this gives rise to an exact intrinsic hierarchy degeneracy in the appearance channel, irrespective of the baseline and energy. Introduction of off-diagonal NSI parameter, $\epsilon_{e \tau}$, shifts the position of this degeneracy to a different $\epsilon_{ee}$. Moreover the unknown magnitude and phases of the off-diagonal NSI parameters can give rise to additional degeneracies. Overall, given the current model independent limits on NSI parameters, the hierarchy sensitivity of DUNE can get seriously impacted. However, a more precise knowledge on the NSI parameters, specially $\epsilon_{ee}$, can give rise to an improved sensitivity. Alternatively, if NSI exists in nature, and still DUNE shows hierarchy sensitivity, certain ranges of the NSI parameters can be excluded. Additionally, we briefly discussed the implications of $\epsilon_{ee} = -1$ (in the Earth) on MSW effect in the Sun.
Comment: 6 pages, 4 figures