Generalized mass ordering degeneracy in neutrino oscillation experiments

We consider the impact of neutral-current (NC) non-standard neutrino interactions (NSI) on the determination of the neutrino mass ordering. We show that in presence of NSI there is an exact degeneracy which makes it impossible to determine the neutrino mass ordering and the octant of the solar mixing angle $\theta_{12}$ at oscillation experiments. The degeneracy holds at the probability level and for arbitrary matter density profiles, and hence, solar, atmospheric, reactor, and accelerator neutrino experiments are affected simultaneously. The degeneracy requires order-one corrections from NSI to the NC neutrino--quark interaction and can be tested in neutrino--nucleus NC scattering experiments.