Exploring Earth's Matter Effect in High-Precision Long-Baseline Experiments

The Earth's matter effect is going to play a crucial role in measuring the unknown three-flavor neutrino oscillation parameters at high confidence level in future high-precision long-baseline experiments. We observe that owing to the new degeneracies among the most uncertain oscillation parameters ($\delta_{CP}, \theta_{23}$) and the average Earth's matter density ($\rho_{avg}$) for the 1300 km baseline, the sensitivity of the upcoming Deep Underground Neutrino Experiment (DUNE) to establish Earth's matter effect reaches only about 2$\sigma$ C.L. for all possible choices of oscillation parameters. We notice that the current uncertainty in $\delta_{CP}$ degrades the measurement of $\rho_{avg}$ more as compared to $\theta_{23}$. To lift these degeneracies, we explore the possible complementarity between DUNE and Tokai to Hyper-Kamiokande (T2HK/JD) facility with a second detector in Korea, popularly known as T2HKK or JD+KD setup. While DUNE uses wide-band beam with on-axis detector, T2HKK setup plans to use narrow-band beam with two off-axis detectors: one in Japan and other in Korea. We exhibit how the high-precision measurement of $\delta_{CP}$ in JD+KD setup and the information on $\rho_{avg}$ coming from DUNE can reduce the impact of these degeneracies in both ($\rho_{avg}-\delta_{CP}$) and ($\rho_{avg}-\theta_{23}$) planes. We show that the combined data from DUNE and JD+KD setups can establish Earth's matter effect at more than 6$\sigma$ C.L. irrespective of both the choices of mass hierarchy: normal (NH) and inverted (IH), $\delta_{CP}$, and $\theta_{23}$. With the help of this combined data set, we can measure the average matter density ($\rho_{avg}$) with a relative 1$\sigma$ precision of around 11.2% (9.4%) assuming true NH (IH) and $\delta_{CP} = -90^{\circ}/90^{\circ}$.