Interplay of CPT-Violating and CPT-Conserving Lorentz Invariance Violation at DUNE

We present a study of Lorentz invariance violation (LIV) in neutrino oscillations, with primary emphasis on the interplay between CPT-violating and CPT-conserving Standard Model Extension (SME) coefficients. We find that $a_{ee}$ and $a_{\tau\tau}$ dominate among the diagonal LIV coefficients, whereas $a_{e\mu}$ and $a_{e\tau}$ provide the most significant off-diagonal contributions. In contrast, the corresponding $c_{\alpha\beta}$ coefficients have comparatively sub-leading effects. Taking DUNE as a representative long-baseline experiment, we show that the sensitivity to CP violation is modified by LIV in a parameter-specific manner. We find correlations between off-diagonal LIV parameters, and non-trivial dependence on the new phases. In absence of LIV, DUNE is expected to establish CP violation at $5\sigma$ for a limited fraction of $\delta_{CP}$ values. We find that the presence of $a_{ee}$, $a_{\tau\tau}$, $a_{e\mu}$ and $a_{e\tau}$ weakens the CP discovery potential, reducing the achievable significance to below $3\sigma$ over a substantial fraction of $\delta_{\rm CP}$. The independent impact of $c_{\alpha\beta}$ terms also results in suppression, but in combination with $a_{\alpha\beta}$, they introduce degeneracies, complicating the extraction of $\delta_{CP}$. This generally results in a deterioration of CP violation sensitivities below $5\sigma$. These findings emphasize the importance of incorporating LIV effects in precision oscillation studies at upcoming long-baseline experiments.