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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 $θ_{23}$ and CP phases in the context of the Deep Underground Neutrino Experiment (DUNE). We consider the CPT-violating LIV parameters involving $e - μ$ ($a_{eμ}$) and $e - τ$ ($a_{eτ}$) flavors, which induce an additional interference term in neutrino and antineutrino appearance probabilities. This new interference term depends on both the standard CP phase $δ$ and the new dynamical CP phase $φ_{eμ}$/$φ_{eτ}$, giving rise to new degeneracies among ($θ_{23}$, $δ$, $φ$). Taking one LIV parameter at-a-time and considering a small value of $|a_{eμ}| = |a_{eτ}| = 5 \times 10^{-24}$ GeV, we find that the octant discovery potential of DUNE gets substantially deteriorated for unfavorable combinations of $δ$ and $φ_{eμ}$/$φ_{eτ}$. The octant of $θ_{23}$ can only be resolved at $3σ$ if the true value of $\sin^2θ_{23} \lesssim 0.42$ or $\gtrsim 0.62$ for any choices of $δ$ and $φ$. Interestingly, we also observe that when both the LIV parameters $a_{eμ}$ and $a_{eτ}$ 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 $δ$ and $φ_{eμ}$/$φ_{eτ}$. The typical $1σ$ uncertainty on $δ$ is $10^{\circ}$ to $15^{\circ}$ and the same on $φ_{eμ}$/$φ_{eτ}$ is $25^{\circ}$ to $30^{\circ}$ depending on the choices of their true values.