Comprehensive study of Lorentz invariance violation in atmospheric and long-baseline experiments

In this paper, we have presented a comprehensive study of Lorentz Invariance Violation (LIV) in the context of atmospheric neutrino experiment ICAL and long-baseline experiments T2HK and DUNE. Our study consists of the full parameter space of the LIV parameters (isotropic), 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 and 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 sensitivity of DUNE and ICAL is similar. 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 (isotropic) $c_{ee}$ and $c_{\mu\mu}$, our work provides the first ever bounds.