Looking for Lorentz invariance violation (LIV) in the latest long baseline accelerator neutrino oscillation data

In this paper, we have analysed the latest data from NO$\nu$A and T2K with the Lorentz invariance violation along with the standard oscillation hypothesis. We have found that the NO$\nu$A data cannot distinguish between the two hypotheses at $1\, \sigma$ confidence level. T2K data and the combined data analysis excluded standard oscillation at $1\, \sigma$. All three cases do not have any hierarchy sensitivity when analysed with LIV. There is a mild tension between the two experiments, when analysed with LIV, as $\theta_{23}$ at \nova best-fit is at higher octant but the same for T2K is at lower octant. NO$\nu$A has a new degeneracy over $\sin^2 \theta_{23}$ value, when analysed with LIV.