| The total analytic probability $P_{\mu e}$ (orange) along with its other dominant terms in the top panel and the absolute differences $|P_{\mu e}-P_{\mu e}^\mathrm{num}|$ (red) and $|P_{\mu e}-P_{\mu e}^\mathrm{GL}|$ (cyan) in the bottom panel at 1300 km(left), and 7000 km(right) baselines. |
| The total analytic probability $P_{\mu e}$ (orange) along with its other dominant terms in the top panel and the absolute differences $|P_{\mu e}-P_{\mu e}^\mathrm{num}|$ (red) and $|P_{\mu e}-P_{\mu e}^\mathrm{GL}|$ (cyan) in the bottom panel at 1300 km(left), and 7000 km(right) baselines. |
| The total analytic probability $P_{\mu e}$ (orange) along with its other dominant terms in the top panel and the absolute differences $|P_{\mu e}-P_{\mu e}^\mathrm{num}|$ (red) and $|P_{\mu e}-P_{\mu e}^\mathrm{GL}|$ (cyan) in the bottom panel at 1300 km(left), and 7000 km(right) baselines. |
| The total analytic probability $P_{\mu e}$ (orange) along with its other dominant terms in the top panel and the absolute differences $|P_{\mu e}-P_{\mu e}^\mathrm{num}|$ (red) and $|P_{\mu e}-P_{\mu e}^\mathrm{GL}|$ (cyan) in the bottom panel at 1300 km(left), and 7000 km(right) baselines. |
| The total analytic probability $P_{\mu \mu}$ (orange) along with its other dominant terms in the top panel and the absolute differences $|P_{\mu\mu}-P_{\mu\mu}^\mathrm{num}|$ (red) and $|P_{\mu\mu}-P_{\mu\mu}^\mathrm{GL}|$ (cyan) in the bottom panel at 1300 km(left), and 7000 km(right). |
| The total analytic probability $P_{\mu \mu}$ (orange) along with its other dominant terms in the top panel and the absolute differences $|P_{\mu\mu}-P_{\mu\mu}^\mathrm{num}|$ (red) and $|P_{\mu\mu}-P_{\mu\mu}^\mathrm{GL}|$ (cyan) in the bottom panel at 1300 km(left), and 7000 km(right). |
| The total analytic probability $P_{\mu \mu}$ (orange) along with its other dominant terms in the top panel and the absolute differences $|P_{\mu\mu}-P_{\mu\mu}^\mathrm{num}|$ (red) and $|P_{\mu\mu}-P_{\mu\mu}^\mathrm{GL}|$ (cyan) in the bottom panel at 1300 km(left), and 7000 km(right). |
| The total analytic probability $P_{\mu \mu}$ (orange) along with its other dominant terms in the top panel and the absolute differences $|P_{\mu\mu}-P_{\mu\mu}^\mathrm{num}|$ (red) and $|P_{\mu\mu}-P_{\mu\mu}^\mathrm{GL}|$ (cyan) in the bottom panel at 1300 km(left), and 7000 km(right). |
| $\Delta P_{\mu e}$(left), $\Delta P_{\mu\mu} $(right), i.e, the absolute differences in probabilities for $\theta_{23}$ values from opposite octant with fixed value of $\delta_{13},\delta_{14}$ in $\cos\theta_\nu -E_\nu$ plane. |
| $P_{\mu e}$ as a function of energy at 1300 km (left), and 7000 km (right). Blue and red bands are due to variation of $\delta_{13},\delta_{14}$ for $\theta_{23}=49^\circ$, $41^\circ$ using $\theta_{14}=\theta_{24}=4^\circ$. The regions between blue, and red dotted curves are for $49^\circ$, $41^\circ$ respectively, considering $\theta_{14}=\theta_{24}=7^\circ$. |
| $ P_{\mu e}$ (left), and $P_{\bar{\mu}\bar{e}}$ (right) as a function of $\delta_{13}$ (top), $\delta_{14}$ (bottom) for variation of the respective another phase at neutrino energy 2.5 GeV at 1300 km baseline for NH. |
| $ P_{\mu e}$ (left), and $P_{\bar{\mu}\bar{e}}$ (right) as a function of $\delta_{13}$ (top), $\delta_{14}$ (bottom) for variation of the respective another phase at neutrino energy 2.5 GeV at 1300 km baseline for NH. |
| $ P_{\mu e}$ (left), and $P_{\bar{\mu}\bar{e}}$ (right) as a function of $\delta_{13}$ for variation of the phase $\delta_{14}$ at neutrino energy 2.5 GeV at 1300 km baseline for NH. |
| $ P_{\mu \mu}$ (left), and $P_{\bar{\mu}\bar{\mu}}$ (right) vs $\delta_{13}$ (top), $\delta_{14}$ (bottom) for variation of the respective another phase at neutrino energy 2.5 GeV at 1300 km baseline for NH. |
| $ P_{\mu \mu}$ (left), and $P_{\bar{\mu}\bar{\mu}}$ (right) vs $\delta_{13}$ (top), $\delta_{14}$ (bottom) for variation of the respective another phase at neutrino energy 2.5 GeV at 1300 km baseline for NH. |
| $ P_{\mu e}$ vs $\delta_{13}$(left), and $\delta_{14}$(right) for variation of the respective another phase at neutrino energy 6.5 GeV at 7000 km baseline for NH. |
| $ P_{\mu \mu}$ vs $\delta_{13}$(left), and $\delta_{14}$(right) for variation of the respective another phase at energy 7 GeV at 7000 km baseline for NH. |
| Electron (left) and muon neutrino (right) event spectrum for neutrinos (top) and anti-neutrinos (bottom) as a function of energy for true $\theta_{23}=41^\circ$(green) with true phases $\delta_{13}=-90^\circ,\delta_{14}=90^\circ$ at 1300 km for test values of $\theta_{23}=46^\circ$(blue) and $\theta_{23}=50^\circ$(orange) for NH. |
| Bi-events plot in $\nu_e-\bar{\nu}_e$ plane for $\theta_{23}=41^\circ$(red, green), $49^\circ$(blue, yellow) at 1300 km with variation of phases $ \delta_{13},\delta_{14}$ corresponding to $\theta_{14},\theta_{24}=7^\circ$ (left), $4^\circ$ (right) for NH. |
| The difference of atmospheric events between HO and LO has been plotted in $E_\nu-\cos\theta_\nu$ plane for $e^+ + e^-$(left), and $\mu^+ +\mu^-$(right) events. |
| Sensitivity to the octant of $\theta_{23}$ with beam only analysis as a function of $\delta_{13}^{true}$ due to $\theta_{23}^{true}=41^\circ$ in LO(blue), and $49^\circ$in HO(red) for $\delta_{14}^{true}=0^\circ$ (left), $90^\circ$ (right). |
| Sensitivity to the octant of $\theta_{23}$ as a function of $\delta_{13}^{\rm{true}}$ at $\delta_{14}^{\rm{true}}=0^\circ$ for $\theta_{23}^{\rm{true}}=41^\circ$ (left) and $49^\circ$ (right). The representative plots are shown for simulated data from beam only(red), atmospheric only w/o charge-id (blue), atmospheric only with charge-id (violet), beam+atmospheric w/o charge-id(green), and beam+atmospheric with charge-id(yellow) analysis with 280 kt-yr exposure. |
| Sensitivity to the octant of $\theta_{23}$ with beam only (dotted) and beam+atmospheric with charge-id (dashed) analysis as a function of $\delta_{13}^{true}$ for true values of $\delta_{14}=0^\circ$ (left), $90^\circ$ (right). The representative plots are shown for true values of $\theta_{23}$ in HO (red), LO (blue), and $\theta_{14},\theta_{24}=4^\circ$. |
| Octant sensitivity as a function of $\theta_{23}^{\rm{test}}$ from beam (left), and atmospheric (right) neutrinos using 280 kt-yr exposure of LArTPC detector with $\theta_{23}^{tr} = 41^{\circ},\delta_{13}^{tr}=-90^\circ, \delta_{14}^{tr}=90^\circ$. |
| $3\sigma$ contour plot of sensitivity to the octant of $\theta_{23}$ in test $\delta_{13}-\delta_{14}$ plane with 7 years of data for $\delta_{14}^{true}=0^\circ$ and $\delta_{13}^{true}=-90^\circ,0^\circ,90^\circ,150^\circ$ in panels a,b,c,d respectively. The representative plots are shown for the true value of $\theta_{23}=41^\circ$ in LO (blue and violet) and $49^\circ$ in HO (yellow and red) for right octant solutions(solid) and wrong octant solutions(dashed) for simulated beam only (B) and beam+atmospheric (B+A) data. |
| $3\sigma$ contour plot of sensitivity to the octant of $\theta_{23}$ in test $\delta_{13}-\delta_{14}$ plane with 7 years of beam only simulated data for $\delta_{14}^{true}=90^\circ$ and $\delta_{13}^{true}=-90^\circ,0^\circ,90^\circ,150^\circ$ in panels a,b,c,d respectively. The representative plots are shown for true value of $\theta_{23}=41^\circ$ in LO (blue) and $49^\circ$(yellow) in HO for right octant solutions(solid) and wrong octant solutions(dashed). |
| Contour plot in test $\delta_{13}-\delta_{14}$ plane showing the difference in probability $\Delta P_{\mu e}$ with $\theta_{23}$ being fixed at one octant while $\theta_{23}$ varies in the opposite octant for WO solutions (right) and in the same octant for RO solutions (left) at true values of $\delta_{13}=-90^\circ,\delta_{14}=0^\circ,\theta_{23}=49^\circ$(top), $41^\circ$(bottom). Black and dark red show the least differences, while blue and white show the highest. |
| Comparison of the probabilities using GLoBES $P_{\mu e}^{GL}$ (red), the Cayley Hamilton method $ P_{\mu e}^{CH}$ (green), and TMSD approx. $P_{\mu e}$ (blue) at 1300 km(left), 7000 km(right) baseline. |
| Comparison of the probabilities using GLoBES $P_{\mu e}^{GL}$ (red), the Cayley Hamilton method $ P_{\mu e}^{CH}$ (green), and TMSD approx. $P_{\mu e}$ (blue) at 1300 km(left), 7000 km(right) baseline. |