Experimental evidence of neutrinos produced in the CNO fusion cycle in the Sun

In November 2020, the Borexino Collaboration publishes [Nature volume 587, 577–582 (2020)]  the first experimental evidence of neutrinos produced in the carbon-nitrogen-oxygen (CNO) fusion cycle in the Sun.

For most of their lifetime, stars are fuelled through fusion of hydrogen into helium via two processes: the pp chain and the CNO cycle. While the pp-chain is dominant in stars as massive as our Sun, the CNO is the fundamental energy-producing process in bigger stars.

In 2018 the Borexino collaboration was already able to perform a complete spectroscopy of neutrinos from the pp chain. We now report the first experimental evidence of CNO neutrinos, obtained with such an unprecedentedly radio-pure, thermally stable, large volume liquid scintillator detector as Borexino.

The Borexino collaboration was able to measure the CNO solar neutrino interaction rate to be: \mathsf{7.2^{+3.0}_{-1.7}} counts per day per 100 tonnes (t) of target at 68% C.L.

This corresponds to a flux of CNO neutrinos on Earth of \mathsf{7.0^{+3.0}_{-2.0}\;\mathrm{cm}^{-2}\,\mathrm{s}^{-1}}  assuming the Mikheyev Smirnov Wolfenstein – Large Mixing Angle conversion in matter, neutrino oscillation parameters from F. Capozzi et al. (2018) , and a density of electrons in the scintillator of \mathsf{(3.307 \pm 0.015) \times 10^{31}\;\mathrm{e}^-} per 100 t.

The absence of CNO signal is thus disfavoured at 5\sigma.

In this plot (Figure 2 of our Nature publication), we report the spectral fit of the Borexino data. The energy estimator \mathsf{N_h} represents the number of photoelectrons detected by photomultipliers, normalized to 2,000 live channels. For sake of completeness, we also report the correspondent keV energy scale.

The distribution of the electron recoil energy scattered by solar neutrinos in the Borexino detector is defined by black points (properties of the data bins available here). CNO-neutrinos, ^{210}Bi and pep-neutrinos are highlighted in solid red, dashed blue and dotted green, respectively, and all other components are in grey. The total spectral fit is depicted in magenta. The yellow band represents the region with the largest signal-to-background ratio for CNO-neutrinos.

The correlation matrix of this spectral fit is presented below and can be downloaded here.

Figure 3 of our paper  shows the spatial and temporal distribution of ^{210}Po activity.

The ^{210}Po rate in Borexino is given in cpd (counts per day) per 100 t (rainbow colour scale) as a function of time. Each small cube is of about 3 t and is ordered from the bottom (0) to the top (58) along the vertical direction.

All cubes are selected inside a sphere of radius r = 3 m. The red curve represents the average temperature in the innermost region surrounding the nylon vessel. The temperature profile can be downloaded (two separate files) here and here. The dashed vertical lines indicate the most important milestones of the temperature stabilization program: (1) the beginning of the Borexino insulation program;  (2) the turning off of the water recirculation system in the water tank; (3) the first operation of the active temperature control system; (4) the change of the active control set point; (5) the installation and commissioning of the hall temperature control system.

The white vertical bands represent different interruptions of the Borexino data acquisition.

Figure 4 of our publication report the results of the CNO counting and spectral analyses.

On the left, the counting analysis bar chart: the height represents the number of events allowed by the data for CNO-neutrinos and backgrounds in the region of interest (ROI). The less events in the ROI, the minimum the CNO signal is while backgrounds are maximum; likewise, more events in the ROI, CNO  signal is maximum and backgrounds are minimum. It is clear from this figure that the contribution of CNO neutrinos cannot be zero.

On the right, CNO-neutrino rate negative log-likelihood (\ln \mathcal{L}) profile obtained directly from the multivariate fit (dashed black line, available here) and after folding in the systematic uncertainties (black solid line, available here). The histogram in red shows the CNO-neutrino rate (bin property can be found here) obtained from the counting analysis. The blue, violet and grey vertical bands show 68% confidence intervals (CI) for the SSM-LZ (3.52 \pm 0.52 cpd per 100 t) and SSM-HZ (4.92 \pm 0.78 cpd per 100 t) predictions (according to N. Vinyoles et al. (2017), M. Agostini et al. (2020) ) and the Borexino result (corresponding to the black solid-line loglikelihood profile), respectively.

In the following plots (as in Figure Extended Data 7 of our article), we present the angular and radial uniformity of the \beta events in the optimized energy window.

The angular power spectrum as a function of the multipole moment \ell of observed \beta events (black points, bin properties available here) compared with 10 uniformly distributed events from Monte Carlo simulations at 1\sigma (dark pink) and 2\sigma (pink) confidence levels (C.L.). Data are compatible with a uniform distribution within the uncertainty of 0.59 cpd per 100 t.  The inset represents the angular distribution of the \beta events (data available here).

Here above we show the normalized radial distribution of \beta events \mathsf{r/r_0} (black points, bins properties available here), where r = 2.5 m is the radius of the sphere surrounding the analysis fiducial volume.

The linear fit of the data (red solid line) is shown along with the 1\sigma (yellow) and 2\sigma (green) confidence level bands. The data are compatible with a uniform distribution within 0.52 cpd (counts per day) per 100 t.

Figure Extended data 8 as in our publication shows the energy distributions from a multivariate fit of the Borexino data.

The full multivariate fit results for the Three Fold Coincidence (TFC)-subtracted (left) and the TFC-tagged (right) energy spectra are reported with the  corresponding residuals. Data bins content and residuals are available here: TFC-subtracted data, TFC-subtracted residuals, TFC-tagged data, TFC-tagged residualsIn both graphs the magenta lines represent the resulting fit function, the red line is the CNO neutrino electron recoil spectrum, the green dotted line is the pep neutrino electron recoil spectrum, the dashed blue line is the ^{210}Bi \beta spectrum, and in grey we report the remaining background contributions.

The radial distribution from a multivariate fit of the Borexino data is reported in Figure Extended data 9 of the Borexino publication.

In this plot, the red line is the resulting fit, the green line represents the internal uniform contribution and the blue line shows the non-uniform contribution from the external background. Bins properties of data and residuals are available for download.

Finally, we report in Figure Extended data 10 of the  Nature paper a frequentist hypothesis test for our CNO observation.

This plot shows the distribution of the test statistics q (defined in Eq. 5 of our paper), obtained from Monte Carlo pseudodatasets.

The grey distribution \mathsf{q_0} results with no CNO simulated data and includes the systematic uncertainty (bin properties available here). The black vertical line represents \mathsf{q_{data}} = 30.05. The corresponding P value of \mathsf{q_0} with respect to \mathsf{q_{data}} gives the significance of the CNO discovery (>5.0\sigma at 99% C.L.). For comparison, in blue is the \mathsf{q_0} without the systematics. The red histogram represents the expected test statistics distribution (bin properties available here) for an injected CNO rate equal to 7.2 cpd (counts per day) per 100 t that is, our best fit value.