Simultaneous precision spectroscopy of $pp$, ${}^7\mathrm{Be}$, and $pep$ solar neutrinos with Borexino Phase-II

We present the simultaneous measurement of the interaction rates $R_{pp}$, $R_{\mathrm{Be}}$, $R_{pep}$ of $pp$, ${}^7\mathrm{Be}$, and $pep$ solar neutrinos performed with a global fit to the Borexino data in an extended energy range (0.19–2.93) MeV with particular attention to details of the analysis methods. This result was obtained by analyzing 1291.51 days of Borexino Phase-II data, collected after an extensive scintillator purification campaign. Using counts per day $(\mathrm{cpd})/100\mathrm{ton}$ as unit, we find $R_{pp}=134\pm 10(\mathrm{stat}{)}_{-10}^{+6}(\mathrm{sys})$, $R_{Be}=48.3\pm 1.1(\mathrm{stat}{)}_{-0.7}^{+0.4}(\mathrm{sys})$; and $R_{pep}^{\mathrm{HZ}}=2.43\pm 0.36(\mathrm{stat}{)}_{-0.22}^{+0.15}(\mathrm{sys})$ assuming the interaction rate $R_{\mathrm{CNO}}$ of CNO-cycle (Carbon, Nitrogen, Oxigen) solar neutrinos according to the prediction of the high metallicity standard solar model, and $R_{pep}^{\mathrm{LZ}}=2.65\pm 0.36(\mathrm{stat}{)}_{-0.24}^{+0.15}(\mathrm{sys})$ according to that of the low metallicity model. An upper limit $R_{\mathrm{CNO}}<8.1\mathrm{cpd}/100\mathrm{ton}$ (95% C.L.) is obtained by setting in the fit a constraint on the ratio $R_{pp}/R_{pep}$ ($47.7\pm 0.8\mathrm{cpd}/100\mathrm{ton}$ or $47.5\pm 0.8\mathrm{cpd}/100\mathrm{ton}$ according to the high or low metallicity hypothesis).

Figure 1

Distribution of $\log ({\mathcal{L}}_{\mathrm{TFC}})$ as a function of the $N_p^{d{t}_1}$ energy estimator. The plot is built using the entire set of data surviving the selection cuts described in Sec. 2. The regions dominated by the abundant internal background of ${}^{14}\mathrm{C}$ and ${}^{210}\mathrm{Po}$ are indicated by the corresponding labels. The green-dashed horizontal line represents the ${\mathcal{L}}_{\mathrm{TFC}}$-threshold, above/below which the events are assigned to the TFC-tagged/subtracted energy spectrum. It is clearly visible that the majority of the events of the ${}^{11}\mathrm{C}$ energy decay spectrum lies above this threshold.

Figure 2

Comparison of the distributions of the $\mathrm{PS}\text{−}{\mathcal{L}}_{\mathrm{PR}}$ parameter for ${}^{214}\mathrm{Bi}$ events extracted from data (blue, continuous line) and generated using MC (black, dashed line). The MC sample of ${}^{214}\mathrm{Bi}$ was generated using the same spatial distribution of the ${}^{214}\mathrm{Bi}$ events of the data. The simulation also takes into account the proper values of the working channels $N^{\prime }(t)$.

Figure 3

Comparison of the distributions of the $\mathrm{PS}\text{−}{\mathcal{L}}_{\mathrm{PR}}$ variable for MC generated $e^{-}$ events (black, dashed line) and for $e^{+}$ events selected from the data (green, continuous line). The latter events are a high-purity ${}^{11}\mathrm{C}$ sample, obtained with the optimized TFC method, using very strict cuts on the energy and on the time correlation with the neutron and muon tracks.

Figure 4

Distribution of $\mathrm{PS}\text{−}{\mathcal{L}}_{\mathrm{PR}}$ pulse-shape discriminator as a function of $N_p^{d{t}_1}$ energy estimator. The plot is built using the entire set of data surviving the selection cuts described in Sec. 2. The comparison with Fig. 3 allows to identify the range of values belonging to the ${\beta }^{-}$-like band indicated by the arrow.

Figure 5

The figure shows the distributions of the interaction rates ($\mathrm{cpd}/100\mathrm{ton}$) of solar $\nu$ and of the background species as they result from the MC fit of pseudo-experiments simulated with the same exposure as the experimental data discussed in this paper. The fit is performed in the entire LER region and, as in the real data analysis, penalty terms are added in the likelihood to constrain the values of the ${}^{14}\mathrm{C}$ and pileup rates within the measured ones. It is interesting to note the correlation between the $pp$ and ${}^{85}\mathrm{Kr}$ rates, physically driven by the fact that a not negligible portion of the ${}^{85}\mathrm{Kr}$ spectrum lies in the energy region around about 200 keV where we are sensitive to the $pp$ $\nu \mathrm{s}$ signal. In the left plot, 6700 pseudoexperiments have been generated assuming the $R_{\mathrm{CNO}}$ according to HZ-SSM and fitted imposing a constraint on $R_{\mathrm{CNO}}$ to the same value. The same MC PDFs have been used to simulate and fit data, so these plots show only uncertainties due to statistical fluctuations and the effects of the correlations among the various components. The top right inset represents the results of the fit of 10000 pseudo-experiments fitted with the MC method while keeping the $R_{\mathrm{CNO}}$ free but constraining the $R_{pp}/R_{pep}$ ratio to ($47.7\pm 0.8$) (HZ-SSM [3, 26]). Constraining $R_{pp}/R_{pep}$ to the LZ-SSM prediction, $47.5\pm 0.8$, gives consistent results. The study included all the background and neutrino species: here we only show those components that mostly influence the sensitivity to CNO neutrinos.

Figure 6

This figure shows the results of the fit of MC simulated experiments obtained in the same conditions of Fig. 5 but, this time, removing all the constraints on $R_{\mathrm{CNO}}$ and $R_{pep}$. We only show here the correlation between $pep$, CNO, ${}^{11}\mathrm{C}$ and ${}^{210}\mathrm{Bi}$, but the study included all the spectral components. The significant correlations among these species forbid to measure at the same time $R_{\mathrm{CNO}}$ and $R_{pep}$ and to determine the ${}^{210}\mathrm{Bi}$ decay rate. As described in the text, we have constrained the CNO rate to get the $pep$ one and set a constraint on the ratio $R_{pp}/R_{pep}$ to obtain a limit on the CNO flux.

Figure 7

Multivariate fit results (an example obtained with the MC method) for the TFC-subtracted (left) and the TFC-tagged (right) energy spectra, with residuals. The sum of the individual components from the fit (black lines) is superimposed on the data (grey points). The analysis has been performed using $N_h$ as energy estimator and the transformation to keV-energy scale was performed only for the plotting purposes. The residuals are calculated in every bin as the difference between the data counts and the fit result, divided by the square root of the data counts.

Figure 8

An example of the multivariate fit showing the radial (top) and the $\mathrm{PS}\text{−}{\mathcal{L}}_{\mathrm{PR}}$ (bottom) distributions of the events (black crosses) from the TFC-subtracted spectrum, in the energy intervals $N_h>290$ and $409<N_h<645$, respectively.

Figure 9

Results of the fit for TFC-subtracted energy spectrum zoomed in to the lowest energy region (an example obtained with the analytical method) and residuals. The residual are calculated as in Fig. 7.

Figure 10

TFC-subtracted energy spectrum zoomed between 800 keV and 2700 keV after applying stringent selection cuts on the radial distribution ($\mathrm{R}<2.4\mathrm{m}$) and on the pulse-shape variable distribution (PS-${\mathcal{L}}_{\mathrm{PR}}<4.8$) to better see features due to $pep$ $\nu \mathrm{s}$ interactions. The residuals (bottom plot) are the ratio between the data and the fit model.

Figure 11

$\mathrm{\Delta }{\chi }^2$ profile for the $pep$ (top plot) and CNO (bottom plot) $\nu$ interaction rates.