Correlated and integrated directionality for sub-MeV solar neutrinos in Borexino

Liquid scintillator detectors play a central role in the detection of neutrinos from various sources. In particular, it is the only technique used so far for the precision spectroscopy of sub-MeV solar neutrinos, as demonstrated by the Borexino experiment at the Gran Sasso National Laboratory in Italy. The benefit of a high light yield, and thus a low energy threshold and a good energy resolution, comes at the cost of the directional information featured by water Cherenkov detectors, measuring ${}^8\mathrm{B}$ solar neutrinos above a few MeV. In this paper we provide the first directionality measurement of sub-MeV solar neutrinos which exploits the correlation between the first few detected photons in each event and the known position of the Sun for each event. This is also the first signature of directionality in neutrinos elastically scattering off electrons in a liquid scintillator target. This measurement exploits the subdominant, fast Cherenkov light emission that precedes the dominant yet slower scintillation light signal. Through this measurement, we have also been able to extract the rate of ${}^7\mathrm{Be}$ solar neutrinos in Borexino. The demonstration of directional sensitivity in a traditional liquid scintillator target paves the way for the possible exploitation of the Cherenkov light signal in future kton-scale experiments using liquid scintillator targets. Directionality is important for background suppression as well as the disentanglement of signals from various sources.

Figure 1

Schematic representation of the Borexino detector.

Figure 2

The spectral fit of the energy spectrum performed in phase I [20]. The PDFs of the different solar neutrino components and backgrounds are also shown along with the fitted data. The energy region of interest (ROI) used for the directional analysis of phase I is shown as a shaded yellow area.

Figure 3

Schematic representation of the angular correlation, expressed by the angle $\alpha$ between the direction of emitted photons, given by the reconstructed vertex, and the position of the Sun with respect to Borexino for different event types. (a) Electron recoiling off a solar neutrino at the center of the detector produces a Cherenkov cone (red arrows) pointing forward in the direction of the Sun and isotropic scintillation photons (blue arrows). ${\alpha }_1$ and ${\alpha }_2$ are the directional angles of the first and second detected photons of the event, respectively. The Cherenkov photons and, in turn, the PMT hits they trigger are correlated to the incoming direction of the solar neutrinos. (b) It is possible that the first detected photon in an event is a scintillation photon, therefore not correlated to the direction of the solar neutrino, and the second detected photon is a Cherenkov photon. Compared to (a), this event results in a flatter angular distribution. In addition, this event happens off-center. (c) An electron from the intrinsic radioactive background also produces a Cherenkov light cone (green arrows) and isotropic scintillation photons (blue arrows). As before, ${\alpha }_1$ and ${\alpha }_2$ are the directional angles of the first and second photons of the background event, respectively. These are Cherenkov photons, but have no correlation to the Sun’s direction. (d) Background event similar to (c), but this is an off-center event where the first photon is a scintillation photon and the second detected photon is a Cherenkov photon.

Figure 4

The energy distributions of the data events passing the selection cuts described in Sec. 5 in phase I (blue), phase II (red), and phase III (green).

Figure 5

The $\cos \alpha$ distribution of the selected data events for phase $\mathrm{I}+\mathrm{II}+\mathrm{III}$. The very first hit (red) of all the events after time-of-flight correction is compared to all the hits detected later than the $>5$th time ordered hit of the events (blue). The histograms are normalized to the same statistics.

Figure 6

(a) Borexino Monte-Carlo wavelength spectra as detected by the PMTs. (b) Monte-Carlo distributions of the hit times corrected with their time-of-flight for ${}^7\mathrm{Be}$ solar neutrino recoil electrons (0.54 MeV to 0.74 MeV). In both figures, the left y-axis shows the scintillation (blue), where the area is normalized to 1 and the right y-axis corresponds to Cherenkov light (red), normalized to the number of Cherenkov hits relative to scintillation ($\sim 0.4\%$). Both scintillation profiles also include those photons that have been produced in the Cherenkov process, but have been absorbed and reemitted by the LS.

Figure 7

(a) Time-of-flight corrected hit times for phase I data (black) and MC (red) in the ROI, where the MC is normalized to data statistics. Both ${}^7\mathrm{Be}$ and ${}^{210}\mathrm{Bi}$ MC are comparable within their statistics and only ${}^7\mathrm{Be}$ is shown. (b) Ratio of detected Cherenkov-to-scintillation hits as a function of the time-of-flight sorted hits for all events of ${}^7\mathrm{Be}$ MC.

Figure 8

Distributions of the $\cos \alpha$ directional angle. The first hits are shown as solid lines and the second hits are shown as dotted lines. (a) $\cos \alpha$ distribution of data events from Borexino phase I, i.e., $19904\beta$-events consisting of solar neutrinos $+\beta$-backgrounds (black) chosen using the selection cuts as in Sec. 5 and 1.8 million ${}^{210}\mathrm{Po}$ ($\alpha$) background events (blue) in phase I. The histograms are normalized to have 19904 entries. A clear peak at positive $\cos \alpha$ values can be observed only for the solar neutrino-rich sample. (b) $\cos \alpha$ distributions for MC events of ${}^7\mathrm{Be}$ solar neutrinos (red) and ${}^{210}\mathrm{Bi}$ background (blue). The histograms are normalized to have the same area. The first hit (solid line) of ${}^7\mathrm{Be}$ MC carries more directional information than the second hit (dotted line).

Figure 9

(a) Effect of the biased position reconstruction $\mathrm{\Delta }{r}_{\mathrm{dir}}$ observed in MC where the $e^{-}$ position is reconstructed slightly toward the direction of the $e^{-}$. This bias of $\sim 2\mathrm{cm}$ is not visible on an event-by-event basis due to the position reconstruction resolution of 12 in the ROI. (b) The effect of this parameter, where the normal ${}^7\mathrm{Be}$ MC has $\mathrm{\Delta }{r}_{\mathrm{dir}}=1.89\mathrm{cm}$ (black). For comparison, a larger $\mathrm{\Delta }{r}_{\mathrm{dir}}=2.35\mathrm{cm}$ (blue) increases the slope at $\cos \alpha =-1$.

Figure 10

Schematic representation of the $\cos \delta$ angle used for the Cherenkov calibration with gamma sources. A $\gamma$ (red dashed line) is emitted from the calibration source position ${\overrightarrow{r}}_{\text{source}}$ (red filled circle). The Compton-scattered $e^{-}\mathrm{s}$ (red solid line) in turn emit Cherenkov light (orange cone) in correlation to the direction of the incident $\gamma$. The direction of scintillation photons (blue) are uncorrelated to the $\gamma$ direction. The directional angle $\delta$ used for the calibration of the Cherenkov light in this analysis is the angle between the reconstructed gamma direction (based on the reconstructed position ${\overrightarrow{r}}_{\mathrm{rec}}$ (green circle)) and the photon direction of the hit (based on the known source position and the PMT position ${\overrightarrow{r}}^{\mathrm{PMT}}$), as defined in Eq. (5).

Figure 11

(a) Time-of-flight corrected hit times for PMT hits of all events in data (black) and MC (red) of the ${}^{54}\mathrm{Mn}$ gamma calibration source. The distributions are normalized to have the same area. (b) The difference between the data and MC time distributions in (a).

Figure 12

Example of the effect of using separate, modified direction reconstruction PDFs, for data and MC $\gamma$ sources for two different values of $g{v}_{\mathrm{ch}}^{\mathrm{corr}}$: $0.08\mathrm{ns}{\mathrm{m}}^{-1}$ (red), $0.16\mathrm{ns}{\mathrm{m}}^{-1}$ (blue). (a) $\cos \delta$ distributions of the ${}^{54}\mathrm{Mn}$ source where the direction of data (black) and MC (red, blue) are reconstructed with the same unmodified direction reconstruction PDF. (b) $\cos \delta$ distributions of the same ${}^{54}\mathrm{Mn}$ source for one scenario where the direction is reconstructed with different, modified PDFs for data and both $g{v}_{\mathrm{ch}}^{\mathrm{corr}}$ MC simulations. The PDFs are selected to give a good agreement for the $\cos \delta$ distributions. (c) $\cos \delta$ distributions of the ${}^{40}\mathrm{K}$ source with the same combination of direction reconstruction PDFs that are used for ${}^{54}\mathrm{Mn}$ in (b). (d) Position reconstruction of data (black) and MC (red, blue) with the modified position reconstruction PDFs that are also used for (b), (c). Both the modification of the PDFs and the Cherenkov group velocity correction $g{v}_{\mathrm{ch}}^{\mathrm{corr}}$ do not impact the position reconstruction performance, as shown for ${}^{40}\mathrm{K}$.

Figure 13

The $g{v}_{\mathrm{ch}}^{\mathrm{corr}}$ fit results of the gamma Cherenkov calibration as a function of ${\chi }^2/\mathrm{ndf}$ of the ${}^{40}\mathrm{K}$ $\cos \delta$ histograms [Eq. (8)]. The red data points are the $g{v}_{\mathrm{ch}}^{\mathrm{corr}}$ estimated from the fit between data and MC, for which the best estimate $0.108\mathrm{ns}{\mathrm{m}}^{-1}$ is given by the red dotted line. The blue squares represent the extracted $g{v}_{\mathrm{ch}}^{\mathrm{corr}}$ from MC studies, falling in the same ${\chi }^2/\mathrm{ndf}$ space, for an injected $g{v}_{\mathrm{ch}}^{\mathrm{corr}}=0.10\mathrm{ns}{\mathrm{m}}^{-1}$ represented by the blue dotted line.

Figure 14

The $\cos \alpha$ distributions of the first (a) and second (b) hits of all the selected events (black points) compared with the best fit curve (red) for the resulting number of solar neutrinos $N_{\text{solar}-\nu }$ plus background, as reported in Sec. 10. All histograms are normalized to the data statistics. It can be seen that the data points cannot be explained by the background-only hypothesis (blue). (c) $\mathrm{\Delta }{\chi }^2$ profiles of the first and second hits from the fit as a function of $N_{\text{solar}-\nu }$ with (blue solid curve) and without (blue dotted curve) the systematic uncertainty. The no-neutrino signal hypothesis (pure background, $N_{\text{solar}-\nu }=0$) can be rejected with $\mathrm{\Delta }{\chi }^2>25$, $>5\sigma$. The 68% CI from the $\mathrm{\Delta }{\chi }^2$ profile gives $N_{\text{solar}-\nu }={10887}_{-2103}^{+2386}(\mathrm{stat})\pm 947(\mathrm{syst})$, with a ${\chi }^2/ndf=124.6/117$. This is represented by the blue shaded band and the best fit value is shown as a vertical blue dotted line. The 68% CI of the solar neutrino signal expected based on the standard solar model (SSM) predictions [29] is shown as an orange band.

Figure 15

The $\cos \alpha$ distribution of phase $\mathrm{I}+\text{phase}\mathrm{II}+\text{phase}\mathrm{III}\text{data events}$, compared with the $\beta$ background MC PDF normalized to the statistics of data. It can be seen that the data cannot be explained with a background-only hypothesis.