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Discovering new neutrino interactions would represent evidence of physicsbeyond the Standard Model. We focus on new flavor-dependent long-range neutrinointeractions mediated by ultra-light mediators, with masses below $10^{-10}$eV, introduced by new lepton-number gauge symmetries $L_e-L_\mu$, $L_e-L_\tau$,and $L_\mu-L_\tau$. Because the interaction range is ultra-long, nearby anddistant matter - primarily electrons and neutrons - in the Earth, Moon, Sun,Milky Way, and the local Universe, may source a large matter potential thatmodifies neutrino oscillation probabilities. The upcoming Deep UndergroundNeutrino Experiment (DUNE) and the Tokai-to-Hyper-Kamiokande (T2HK)long-baseline neutrino experiments will provide an opportunity to search forthese interactions, thanks to their high event rates and well-characterizedneutrino beams. We forecast their probing power. Our results reveal novelperspectives. Alone, DUNE and T2HK may strongly constrain long-rangeinteractions, setting new limits on their coupling strength for mediatorslighter than $10^{-18}$ eV. However, if the new interactions are subdominant,then both DUNE and T2HK, together, will be needed to discover them, since theircombination lifts parameter degeneracies that weaken their individualsensitivity. DUNE and T2HK, especially when combined, provide a valuableopportunity to explore physics beyond the Standard Model.

Flavor-dependent long-range neutrino interactions in DUNE & T2HK: alone they constrain, together they discover