Neutrino Oscillation Tomography of the Earth with the Hyper-Kamiokande Detector

Using PREM as a reference model for the Earth density distribution we investigate the sensitivity of the Hyper-Kamiokande (HK) detector to deviations of the Earth i) core average density $\bar{\rho}_C$, ii) lower mantle average density $\bar{\rho}_{lman}$) and iii) upper mantle average density $\bar{\rho}_{uman}$, from their respective PREM densities. The analysis is performed by studying the effects of the Earth matter on the oscillations of atmospheric $\nu_{\mu}$, $\nu_e$, $\bar{\nu}_\mu$ and $\bar{\nu}_e$. We implement the constraints on the variations of $\rho_C$, $\rho_{lman}$ and $\rho_{uman}$ following from the precise knowledge of the Earth mass $M_\oplus$ and moment of inertia $I_\oplus$, as well as from the requirement that the Earth be in hydrostatic equilibrium (EHE). These constraints limit in the case of the three layer Earth density structure we are considering the maximal positive deviation of $\bar{\rho}_C$ from its PREM value to $10\%$. Considering the case of normal ordering (NO) of neutrino masses, we present results which illustrate the dependence of sensitivity to the core, lower and upper mantle average densities on the energy and zenith angle resolutions and on the value of $\theta_{23}$. We show, in particular, that in the ''nominal'' case of neutrino energy resolution $E_{res} = 30\%$ and zenith angle resolution $\theta_{zres} = 20^\circ$ and for, e.g., $\sin^2\theta_{23}=0.45~(0.58)$, HK can determine the average core density $\bar{\rho}_C$ at $2\sigma$ C.L. after 6500 days of operation with an uncertainty of (-14.5\%)/+39.5\% ((-9.3\%/+31.7\%). In the ''more favorable'' case of $E_{res}= 20\%$ and $\theta_{zres} = 10^\circ$, and if $\sin^2\theta_{23}=0.58~(0.45)$, the core density would be determined at $2\sigma$ C.L. with an uncertainty of (-8.3\%)/+9.8\% ((-9.2\%)/+11.3\%).