Effects of matter density profiles on neutrino oscillations for T2HK and T2HKK

This paper explores the effects of changes in matter density profiles on neutrino oscillation probabilities, and whether these could potentially be seen by the future Hyper-Kamiokande long-baseline oscillation experiment (T2HK). The analysis is extended to include the possibility of having an additional detector in Korea (T2HKK). In both cases, we find that these effects will be immeasurable, as the magnitudes of the changes in the oscillation probabilities induced in all density profile scenarios considered here remain smaller than the estimated experimental sensitivity to the oscillation probabilities of each experiment, for both appearance and disappearance channels. Therefore, we conclude that using a constant density profile is sufficient for both the T2HK and T2HKK experiments.

Figure 1

Simplified map showing the geographical features present between Japan and Korea, the positions of J-PARC and Kamioka (the approximate location of the Super-K and Hyper-K detectors) and five potential placements for a Korean detector, from Ref. [6].

Figure 2

Cross section view of the matter density profile (in $\mathrm{g}/{\mathrm{cm}}^3$) from Tokai, with approximate neutrino beamlines for T2HK and five possible sites for a Korean detector, from Ref. [6].

Figure 3

Oscillation probability as a function of energy (top) or $E/L$ (bottom) for all five baseline profiles of T2HKK, taken from Fig. 2 and increasing in length from left to right (1000, 1050, 1100, 1150, and 1200 km). Left and right panels correspond to the appearance and disappearance channels, respectively.

Figure 4

Sensitivity estimates for T2HK (above) and T2HKK (below). The continuous black curves depict the results using the globes method, which uses information from both detectors to determine an uncertainty on oscillation probability. The naive method, shown in the gray energy bins, assumes that—at a given energy—only the events in the same energy bin contribute to the sensitivity. The vertical error bars then correspond to the range of values for the estimated uncertainty as the energy is varied across the bin. The dashed line is obtained by using the total number of events across all energies, rather than from each specific bin. The left and right panels show appearance and disappearance channels, respectively.

Figure 5

Changes in oscillation probability due to parameter variation at T2HK (above) and T2HKK (below). Left panel shows the parameters measured by the appearance channel (${\delta }_{\mathrm{CP}}$ and ${\theta }_{13}$), and the right panel shows the parameters associated with the disappearance channel ($\mathrm{\Delta }{m}_{32}$ and ${\theta }_{23}$). The corresponding globes sensitivity estimates from Fig. 4 are overlaid in gray.

Figure 6

Changes in oscillation probability from variations in the density profile with respect to average density of T2HK. To obtain the solid (dashed) blue curve, the average density is varied by $\pm 1\%$ ($\pm 6\%$), and the difference between the two extremes is taken at each point. The red curve is produced by taking the difference at each point between the probability calculated using the changing (real) matter density profile and the probability computed using its average density value as a constant. For comparison purposes, the sensitivity estimate obtained using GLoBES for T2HK in Fig. 4 is overlaid in gray.

Figure 7

Density profile changes with respect to average density corresponding to the two most likely candidate sites for the Korean detector, Mount Bisul (above) and Mount Bohyun (below). The blue ($\mathrm{solid}+\text{dashed}$) and red curves are the same as in Fig. 6, and the sensitivity estimate shown here in gray corresponds to that of T2HKK in Fig. 4 (globes method).

Figure 8

Changes in oscillation probability from variations in the density profile corresponding to the two most likely candidate sites for the Korean detector, Mount Bisul (above) and Mount Bohyun (below). The four curves correspond to changes in probability when comparing the four scenarios described in Sec. 6 to a representative basic profile with no high-density region at all, taking the difference between the two at each energy point. As before, the sensitivity estimate obtained for T2HKK in Fig. 4 is shown in gray for comparison. The appearance channel is shown on the left, and the disappearance channel is on the right.

Figure 9

Sensitivity of T2HK (left) and T2HKK (right) to the matter density scale ${\rho }^{\prime }/\rho$ with ${\delta }_{CP}$, for true values of $\delta =0$, $\pi /2$, $\pi$, and $3\pi /2$ (from top to bottom). Contours correspond to 68.3% (red), 95% (green), and 99% (blue) confidence regions with no prior constraint (solid) and a 6% Gaussian prior constraint (dashed) on ${\rho }^{\prime }/\rho$.

Figure 10

Sensitivity of T2HK (left) and T2HKK (right) to the matter density scale ${\rho }^{\prime }/\rho$ with ${\theta }_{23}$ (top), ${\theta }_{13}$ (middle), and $\mathrm{\Delta }{m}_{31}^2$ (bottom). Contours correspond to 68.3% (red), 95% (green), and 99% (blue) confidence regions with no prior constraint (solid) and a 6% Gaussian prior constraint (dashed) on ${\rho }^{\prime }/\rho$.

Figure 11

Sensitivity to the matter density scale for T2HK (${\rho }_{\mathrm{HK}}^{\prime }/{\rho }_{\mathrm{HK}}$) vs T2HKK (${\rho }_{\mathrm{HKK}}^{\prime }/{\rho }_{\mathrm{HKK}}$). The sensitivity is shown for different true values of $\delta$: 0, $\pi /2$, $\pi$, and $3\pi /2$. Contours correspond to 68.3% (red), 95% (green), and 99% (blue) confidence regions (no prior constraint).

Figure 12

Summary of the main results obtained for T2HK. Results are grouped into sensitivity estimate, oscillation parameter variation, and matter density profile studies. The left and right panels show the appearance (app.) and disappearance (disapp.) channels, respectively.

Figure 13

Summary of the main results obtained for Mount Bisul (above) and Mount Bohyun (below). Results shown are for all energies and are grouped into sensitivity estimate, oscillation parameter variation, and matter density profile studies. The left and right panels show the appearance and disappearance channels, respectively.

Figure 14

Density profile changes with respect to average density corresponding to the five potential candidate sites for the Korean detector, with baselines ranging from 1000 to 1200 km. The solid (dashed) blue curve is obtained by varying the average density by $\pm 1\%$ ($\pm 6\%$) and taking the difference between the two extremes at each point. The red curve is produced by taking the difference at each point between the probability calculated using the changing (real) matter density profile and the probability computed using its average density value as a constant. The left and right panels correspond to the appearance and disappearance channels, respectively.

Figure 15

Changes in oscillation probability as a function of energy (top) and $E/L$ (bottom) for the five different potential baselines with respect to average density of T2HKK.

Figure 16

Changes in oscillation probability as a function of energy (top) and $E/L$ (bottom) arising from varying the average density of the five different potential baselines of T2HKK by $\pm 1\%$.

Figure 17

Changes in oscillation probability as a function of energy (top) and $E/L$ (bottom) arising from varying the average density of the five different potential baselines of T2HKK by $\pm 6\%$.