In this paper, we have presented a comprehensive study of Lorentz invariance violation (LIV) in the context of the atmospheric neutrino experiment ICAL and the long-baseline experiments T2HK and DUNE. Our study consists of the full parameter space of the LIV parameters, i.e., six $CPT$-violating LIV parameters ($a_{\alpha \beta }$) and six $CPT$-conserving LIV parameters ($c_{\alpha \beta }$). In this study, our objective is to calculate the upper bound on all the LIV parameters with respect to the individual experiments as well as their combination. Our results show that DUNE gives the best sensitivity for the parameters $a_{ee}$, $a_{e\mu }$, $a_{e\tau }$, and $a_{\mu \tau }$ in its 7 years of running, whereas ICAL gives the best sensitivity on $a_{\mu \mu }$, $a_{\mu \tau }$, $c_{ee}$, $c_{\mu \mu }$, $c_{\tau \tau }$, and $c_{\mu \tau }$ in its 10 years of running. For $a_{\tau \tau }$, the sensitivities of DUNE and ICAL are almost same. The combination of T2HK, DUNE, and ICAL gives the best sensitivity for $a_{e\mu }$ and $a_{ee}$ with respect to all the existing bounds in the literature. For the $CPT$-even diagonal parameters $c_{ee}$ and $c_{\mu \mu }$, our work provides the first-ever bounds.

• Received 10 April 2023
• Accepted 5 June 2023

DOI:https://doi.org/10.1103/PhysRevD.107.115032

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Published by the American Physical Society