Future leptonic $CP$ phase determination in the presence of NSI

The precise determination of the leptonic $CP$-phase is one of the major goals for future generation long Baseline experiments. On the other hand, if new physics beyond the Standard Model exists, a robust determination of such a $CP$-phase may be a challenge. Moreover, it has been pointed out that, in this scenario, an apparent discrepancy in the $CP$-phase measurement at different experiments may arise. In this work, we investigate the determination of the Dirac $CP$-phase and the atmospheric mixing angle $\theta_{23}$ at several long-baseline configurations: ESSnuSB, T2HKK, and a DUNE-like experiment. We use the nonstandard neutrino interactions (NSI) formalism as a framework. We found that complementary between ESSnuSB and a DUNE-like experiment will be favorable to obtain a reliable value of the $CP$-phase, within the aforementioned scenario. Moreover, the T2HKK proposal can help to constrain the matter NSI parameters.