Scanning the Earth with solar neutrinos and DUNE

We explore oscillations of the solar ${}^8\mathrm{B}$ neutrinos in the Earth in detail. The relative excess of night ${\nu }_e$ events (the day-night asymmetry) is computed as function of the neutrino energy and the nadir angle $\eta$ of its trajectory. The finite energy resolution of the detector causes an important attenuation effect, while the layer-like structure of the Earth density leads to an interesting parametric suppression of the oscillations. Different features of the $\eta -$ dependence encode information about the structure (such as density jumps) of the Earth density profile; thus measuring the $\eta$ distribution allows the scanning of the interior of the Earth. We estimate the sensitivity of the DUNE experiment to such measurements. About 75 neutrino events are expected per day in 40 kt. For high values of $\mathrm{\Delta }{m}_{21}^2$ and $E_{\nu }>11\mathrm{MeV}$, the corresponding D-N asymmetry is about 4% and can be measured with 15% accuracy after 5 years of data taking. The difference of the D-N asymmetry between high and low values of $\mathrm{\Delta }{m}_{21}^2$ can be measured at the $4\sigma$ level. The relative excess of the ${\nu }_e$ signal varies with the nadir angle up to 50%. DUNE may establish the existence of the dip in the $\eta -$ distribution at the $(2–3)\sigma$ level.

Figure 1

The attenuation factor $F$ as function of distance from a detector, $d$, for $E=11\mathrm{MeV}$ and different values of the energy resolution ${\sigma }_E$: 0.5 MeV (blue line), 1 MeV (green line), 2 MeV (red line). We take $\mathrm{\Delta }{m}_{21}^2=7.5\times {10}^{-5}{\mathrm{eV}}^2$.

Figure 2

The relative excess of the night events produced by boron neutrinos as function of the nadir angle and reconstructed neutrino energy for different energy resolutions: ${\sigma }_E=0.5\mathrm{MeV}$ (upper panel), 1 MeV (middle panel) and 2 MeV (bottom panel). The Gaussian form of the reconstruction function is used.

Figure 3

The relative excess of night events as function of the nadir angle for different values of the reconstructed energy: $E_r=11\mathrm{MeV}$ (violet solid line), 13 MeV (green dash line), and 15 MeV (red long-dash line). The upper (lower) panel corresponds to the energy resolution ${\sigma }_E=0.5\mathrm{MeV}$ (${\sigma }_E=2\mathrm{MeV}$).

Figure 4

The relative excess of the night events integrated over $E_r>11\mathrm{MeV}$ as function of the nadir angle of the neutrino trajectory for different density profiles: PREM profile (red solid line); profile without density jumps at 400 and 660 km (black dot line) and with density jumps at outer and inner cores only (blue dash line).

Figure 5

Graphic representation of the neutrino oscillations in the Earth. Shown are the positions of neutrino polarization vector ${\mathbf{P}}_i$ at the borders of different layers. ${\mathbf{A}}_i$ is the precession axis in the layer $i$. The upper panel: the parametric suppression of oscillations for $\eta =1.489$; the bottom panel: formation of the dip. See further details in the text.

Figure 6

The relative excess of night events integrated over $E_r>11\mathrm{MeV}$ as function of the nadir angle of the neutrino trajectory for changed parameters for the density jumps. The red line is the conventional one with jumps at 15 km and 25 km; blue-dotted line is for jumps at $h_1=20.5\mathrm{km}$ and $h_2=30\mathrm{km}$; green-dashed line is for jumps at $h_1=15$, $h_2=30$. Parametric enhancement of oscillations is seen in the 3rd and 4th periods.

Figure 7

The energy ($E_R$) distribution of the annually detected events at DUNE for different energy resolutions ${\sigma }_E$. The solid (black) line represents perfect resolution, ${\sigma }_E=0$, the other lines correspond to ${\sigma }_E=0.5\mathrm{MeV}$—dash-dotted (blue) line, ${\sigma }_E=1\mathrm{MeV}$ dashed (green) line, ${\sigma }_E=2\mathrm{MeV}$ dotted (red) line. The distributions are normalized to annual number of events 27000 at $E_r>11\mathrm{MeV}$.

Figure 8

Scanning of the Earth density profile. The crosses denote the average values of the relative night event excess over the $\eta$-interval given by the horizontal line; the vertical lines give the expected accuracy after 5 years of data taking.

Figure 9

Annual exposure time as function of nadir angle for different positions of a detector: Homestake mine (red solid line), tropics (dotted blue line), equator (dashed green line).