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 $\varphi_{e\mu}$/$\varphi_{e\tau}$, giving rise to new degeneracies among ($\theta_{23}$, $\delta$, $\varphi$). 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 $\varphi_{e\mu}$/$\varphi_{e\tau}$. 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 $\gtrsim 0.62$ for any choices of $\delta$ 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 $\varphi_{e\mu}$/$\varphi_{e\tau}$. The typical $1\sigma$ uncertainty on $\delta$ is $10^{\circ}$ to $15^{\circ}$ and the same on $\varphi_{e\mu}$/$\varphi_{e\tau}$ is $25^{\circ}$ to $30^{\circ}$ depending on the choices of their true values.