Probing Lorentz Invariance Violation with Atmospheric Neutrinos at INO-ICAL

The possibility of Lorentz Invariance Violation (LIV) may appear in unified theories, such as string theory, which allow the existence of a new space-time structure at the Planck scale ($M_p \sim 10^{19}$ GeV). This effect can be observed at low energies with a strength of $\sim 1/M_p$ using the perturbative approach. In the minimal Standard Model extension (SME) framework, the neutrino mass-induced flavor oscillation gets modified in the presence of LIV. The Iron Calorimeter (ICAL) detector at the proposed India-based Neutrino Observatory (INO) offers a unique window to probe these LIV parameters by observing atmospheric neutrinos and antineutrinos separately over a wide range of baselines in the multi-GeV energy range. In this paper, for the first time, we study in detail how the CPT-violating LIV parameters $(a_{\mu\tau}, a_{e\mu}, a_{e\tau})$ can alter muon survival probabilities and expected $\mu^-$ and $\mu^+$ event rates at ICAL. Using 500 kt$\cdot$yr exposure of ICAL, we place stringent bounds on these CPT-violating LIV parameters at 95\% C.L., which are slightly better than the present Super-Kamiokande limits. We demonstrate the advantage of incorporating hadron energy information and charge identification capability at ICAL while constraining these LIV parameters. Further, the impact of the marginalization over the oscillation parameters and choice of true values of $\sin^2\theta_{23}$ on LIV constraints is described. We also study the impact of these LIV parameters on mass ordering determination and precision measurement of atmospheric oscillation parameters.