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One of the main goals of the Deep Underground Neutrino Experiment (DUNE) isto look for new sources of CP-invariance violation. Another is to significantlytest the three-massive-neutrinos paradigm. Here, we show that there areCP-invariant new physics scenarios which, as far as DUNE data are concerned,cannot be distinguished from the three-massive-neutrinos paradigm with verylarge CP-invariance violating effects. We discuss examples with non-standardneutrino interactions and with a fourth neutrino mass eigenstate. We brieflydiscuss how ambiguities can be resolved by combining DUNE data with data fromother long-baseline experiments, including Hyper-Kamiokande.

False Signals of CP-Invariance Violation at DUNE