Can Lorentz Invariance Violation affect the Sensitivity of Deep Underground Neutrino Experiment?

We examine the impact of Lorentz Invariance Violation (LIV) in measuring the octant of ${\theta }_{23}$ and CP phases in the context of the Deep Underground Neutrino Experiment (DUNE). We consider the CPT-violating LIV parameters involving $e-\mu$ ($a_{e\mu }$) and $e-\tau$ ($a_{e\tau }$) flavors, which induce an additional interference term in neutrino and antineutrino appearance probabilities. This new interference term depends on both the standard CP phase $\delta$ and the new dynamical CP phase ${\phi }_{e\mu }$/${\phi }_{e\tau }$, giving rise to new degeneracies among (${\theta }_{23}$, $\delta$, $\phi$). Taking one LIV parameter at-a-time and considering a small value of $|a_{e\mu}| = |a_{e\tau}| = 5 \times 10^{-24}$ GeV, we find that the octant discovery potential of DUNE gets substantially deteriorated for unfavorable combinations of $\delta$ and ${\phi }_{e\mu }$/${\phi }_{e\tau }$. The octant of ${\theta }_{23}$ can only be resolved at $3\sigma$ if the true value of $\sin^2\theta_{23} \lesssim 0.42$or$\gtrsim 0.62$foranychoicesof$\delta$and$\varphi$. Interestingly, we also observe that when both the LIV parameters $a_{e\mu }$ and $a_{e\tau }$ are present together, they cancel out the impact of each other to a significant extent, allowing DUNE to largely regain its octant resolution capability. We also reconstruct the CP phases $\delta$ and ${\phi }_{e\mu }$/${\phi }_{e\tau }$. The typical $1\sigma$ uncertainty on $\delta$ is ${10}^{\circ }$ to ${15}^{\circ }$ and the same on ${\phi }_{e\mu }$/${\phi }_{e\tau }$ is ${25}^{\circ }$ to ${30}^{\circ }$ depending on the choices of their true values.