This paper studies how tiny departures from two fundamental symmetries could change what the planned Deep Underground Neutrino Experiment (DUNE) will see. The symmetries are Lorentz invariance (the idea that the laws of physics look the same to all observers) and CPT symmetry (a combined symmetry of charge, parity and time reversal). The authors ask how both CPT‑violating and CPT‑conserving forms of Lorentz‑invariance violation (LIV) would alter neutrino oscillations and, in particular, DUNE’s projected sensitivity to charge‑parity (CP) violation in the neutrino sector.

The team works inside a common effective framework called the minimal Standard Model Extension (SME). In that framework the new effects show up as two sets of coefficients. One set, called aαβ, violates CPT and does not grow with neutrino energy. The other set, called cαβ, conserves CPT but scales with energy. The authors focus on the isotropic limit (only the time‑like components are kept) and derive analytic formulas for how these coefficients change the neutrino oscillation probabilities. They then use DUNE — a long‑baseline experiment with a 1300 km path and a broad energy beam — as a concrete case to explore consequences for measurements.

Their main findings identify which coefficients matter most and how they affect CP studies. Among diagonal LIV terms, aee and aττ give the largest effects. Among off‑diagonal terms, aeµ and aeτ are most important. The cαβ coefficients are generally smaller in impact for the scenarios considered, although their energy dependence makes them relevant at higher energies. The authors find that the presence of certain aαβ terms can weaken DUNE’s ability to claim CP violation. In the standard case without LIV, DUNE would reach a 5σ level of discovery for CP violation for only some values of the unknown CP phase δCP. Adding aee, aττ, aeµ or aeτ can drop that significance below 3σ for a substantial range of δCP. Including cαβ terms tends to suppress sensitivity further and, when both aαβ and cαβ are present, new degeneracies appear that make it harder to extract the true δCP.