Tag Archives: 2020

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.

Constraints on flavor-diagonal non-standard neutrino interactions from Borexino Phase-II

In February 2020, the Borexino Collaboration in collaboration with Tatsu Takeuchi, Sanjib Kumar Agarwalla and Chen Sun published [Journal of High Energy Physics 2 (2020) 038] the analysis of flavor-diagonal non-standard neutrino interactions (NSI) based on the Phase-II data.  

Within the last few decades, solar neutrino physics has evolved into a field of relevance not only for probing our understanding of the Sun but also for investigating and determining intrinsic neutrino properties. Solar neutrinos can be utilized as a probe for new physics beyond the Standard Model that affect neutrino interactions with the charged leptons and quarks. 

Monochromatic nature of the ^7Be solar neutrinos results in an electron recoil spectrum whose shape is more sensitive to the \nu_e couplings than that from a continuous neutrino energy spectrum. It gives an advantage in using the Sun as a neutrino source for the study of NSI’s.

In this paper, the neutrino-flavor-diagonal NSI’s that affect \nu_e-e and \nu_{\tau}-e interactions were investigated since Borexino is particularly sensitive to this set of parameters. The obtained bounds showed remarkable improvement, regardless of the choice of metallicity in the Standard Solar Model (SSM). The bounds are comparable to the global ones. In particular, the best constraint to-date on \varepsilon ^L_e was obtained.

The same dataset, but without any NSI’s assumed, was used to measure \sin^2\theta_W, resulting in the value of 0.229 \pm 0.026 (stat+syst). The precision is comparable to that measured by reactor antineutrino experiments.


This first sequence of plots (left panels of Figure 5 in our paper) shows the  Log-likelihood profiles for the NSI parameters \varepsilon^R_e (red line) and \varepsilon^L_e (blue line) assuming HZ and LZ SSM’s.  

The correspondent \chi^2 profiles are available here: \varepsilon^R_e-HZ profile, \varepsilon^L_e-HZ profile, \varepsilon^R_e-LZ profile, \varepsilon^L_e-LZ profile.

This sequence of plots (right panels of Figure 5 in our paper) shows the  Log-likelihood profiles for the NSI parameters \varepsilon^R_{\tau} (red line) and \varepsilon^L_{\tau} (blue line) assuming HZ and LZ SSM’s.

The correspondent \chi^2 profiles are available here: \varepsilon^R_{\tau}-HZ profile, \varepsilon^L_{\tau}-HZ profile, \varepsilon^R_{\tau}-LZ profile, \varepsilon^L_{\tau}-LZ profile.

The one-dimensional \chi^2 profiles were obtained considering one NSI parameter at-a-time, while remaining NSI parameters were fixed to zero.  

In this plot (Figure 6 of the paper),  we report the allowed region for NSI parameters in \varepsilon^{R/L}_e plane. The bounds from LSND and TEXONO are provided for comparison. The contour obtained from the global analysis of solar neutrino experiments is presented by a dashed black line. Each contribution can be downloaded at the following links: TEXONO_top contour and TEXONO_bottom contour; LSND contour; Solar-KamLand contour; \varepsilon_e-HZ_Borexino contour; \varepsilon_e-LZ_Borexino contour.

The plot above (Figure 7 of our paper) shows the allowed region for NSI parameters in \varepsilon^{R/L}_{\tau} plane obtained in the present work. The contour from LEP is provided for comparison. Each contribution can be downloaded at the following links: \varepsilon_{\tau}-HZ_Borexino contour, \varepsilon_{\tau}-LZ_Borexino_right contour, \varepsilon_{\tau}-LZ_Borexino_left contourLEP contour.

Comprehensive geoneutrino analysis with Borexino


The Borexino collaboration published a paper [Physical Review D 101, (2020) 012009] on an updated geoneutrino measurement in January 2020 using the data obtained from Dec 2007 to Apr 2019. The updated statistics and the improved analysis techniques, such as an increased fiducial volume, improved veto for cosmogenic backgrounds, extended energy and coincidence time windows, as well as a more efficient \alpha/\beta particle discrimination, led to more than a factor two increase in exposure and an improvement in the precision from 26.2% to 17.5%, when compared to the previous measurement in 2015.

The measured geoneutrino signal at Gran Sasso was 47.0^{+8.4}_{-7.7} (stat) ^{+2.4}_{-1.9} (sys) TNU.

The paper also provides the geological interpretations of the obtained results, namely, the estimation of the mantle signal by exploiting the relatively well-known lithospheric contribution, the calculation of the radiogenic heat, as well as the comparison of these results to the various predictions. The null-hypothesis of the mantle signal was rejected at 99% C.L. for the first time. Even though the results were compatible with all the Earth models, a 2.4\sigma tension was observed with those models that predict the lowest concentration of heat-producing elements inside the mantle. Additionally, the upper limits for a hypothetical georeactor that might be present at different locations inside the Earth were obtained. Particular attention was given to the details of the analysis techniques which might be useful for next generation liquid scintillator detectors.

Here below we provide some important figures and their respective data categorized into: theoretical spectra, spectral fit inputs, spectral fit results, and geological inputs.

Theoretical Spectra


    In this plot (Fig. 14a of our paper) we show the energy spectra for ^{238}U, ^{235}U, ^{232}Th and ^{40}K geoneutrinos normalized to one decay from the head element of the chain. Input data can be found here.


       This plot (Fig. 14b of our paper) shows geoneutrino fluxes from ^{238}U, ^{232}Th and ^{40}K and their sum at LNGS as a function of geoneutrino energies calculated adopting geophysical and geochemical inputs. Inputs are available here.

Figure 19 of our paper shows the energy spectra for reactor antineutrinos with and without excess at 5 MeV expected at Gran Sasso calculated using PRIS database and the correction factor from Daya Bay for the excess.  Data available here.

Spectral fit inputs

The final unbinned likelihood spectral fit is done using the charge of the 154 golden candidates and the Monte-Carlo PDFs of signal and backgrounds. The contribution of the three main backgrounds namely accidentals, cosmogenic ^9Li and (\alpha,\,n) are constrained. Geoneutrino and reactor antineutrino contributions are usually left free.

The fit is done in the following configurations:

  • Figure 48a: U/Th fixed to chondritic ratio (The fit is also done after constraining the atmoshperic neutrino background contribution and after constraining the reactor antineutrino contribution).

  • Figure 48b: U and Th contributions as free parameters.

  • Figure 52a: Extraction of mantle geoneutrino signal after constraining the contribution from bulk lithosphere.

  • Extraction of upper limits on georeactor placed at different positions after constraining the contribution of reactor antineutrinos.

Charge (available here) of the 154 golden candidates used for the unbinned likelihood spectral fit.

Monte-Carlo charge PDFs of geoneutrinos (U/Th fixed) , reactor antineutrinos , ^{238}U geoneutrinos , ^{232}Th geoneutrinos as in Figure 32 of our paper are available here.

Monte-Carlo charge PDFs of cosmogenic ^{9}Li, (\alpha,\,n) interactions, atmospheric neutrinos, and accidental background data as in Figure 33 and 37 of the paper are available here.  

Monte-Carlo charge PDFs of georeactor placed at different positions as in Figure 34 of the paper are available here.

Spectral fit results

Confidence contours:

Figure 48c: Reactor vs geoneutrino confidence contours for U/Th fixed to chondritic ratio in the fit.  Inputs can be found here.


Figure 48d: ^{238}U vs ^{232}Th geoneutrino confidence contours when their contributions are left free in the fit. Inputs can be found here.

Likelihood profiles

Figure 49a: Likelihood profile of geoneutrinos from the spectral fit after fixing U/Th to the chondritic ratio. Input can be found here.Figure 49b: Likelihood profile of reactor neutrinos from the spectral fit after fixing U/Th to the chondritic ratio. Input is available here.Figure 49c: Likelihood profile of ^{238}U geoneutrinos from the spectral fit after leaving U and Th as free parameters in the spectral fit. Input can be found here.Figure 49d: Likelihood profile of ^{232}Th geoneutrinos from the spectral fit after leaving U and Th as free parameters in the spectral fit. Input is available here.Figure 52b: Likelihood profile of mantle geoneutrinos after constraining the contribution from bulklithosphere. Input can be found here.Figure 57: Likelihood profile of georeactor at different positions after constraining the contribution from reactor-antineutrinos. Input is available here.

Geological interpretations

Figure 50: Comparison of the geoneutrino signal obtained from Borexino with different theoretical models. Inputs can be downloaded here.


Figure 54: Signal of mantle geoneutrinos vs Radiogenic heat for cosmochemical, geochemical, geodynamical, and fully radiogenic models along with Borexino results. Input can be found here.


Figure 55: Radiogenic heat obtained with Borexino results compared with different theoretical models along with the total surface heat flux. Data can be downloaded here.


Figure 56: Convective Urey Ratio obtained with Borexino results compared with different theoretical models. Input are available here.