Neutrino physics: Theory and experiment (SS2021) Solar neutrinos

Teresa Marrod´anUndagoitia Max-Planck-Institut f¨urKernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany E-mail: [email protected]

Contents

1 Lecture 3: Solar neutrinos2 1.1 Standard solar model...... 2 1.2 Neutrino production...... 3 1.3 Radiochemical experiments...... 5 1.4 Real time experiments...... 8 1.5 Reminder: Neutrino oscillations in matter...... 14 1.6 Summary...... 15 1 LECTURE 3: SOLAR NEUTRINOS

1. Lecture 3: Solar neutrinos

This lecture discusses the emission of neutrinos by the Sun and some of the measurements performed so far. Solar neutrinos help to understand better the Sun itself but they also provide an intense source of ν’s to investigate their properties. Indeed solar neutrinos have played a key role to understand neutrino oscillations.

1.1. Standard solar model Our Sun is in the most stable and long evolutionary phase of a star where hydrogen is consumed in its core (in the main sequence). A common tool to learn about the interior of the Sun is helioseismology, a methodology which employs oscillation frequencies (many modes, more than 1015) to determine the internal structure of the Sun, specifically: • density profiles • constraints on solar composition • the extension of the convective envelope ... The standard solar model (SSM) results from all these observations.

Nuclear reactions in the Sun:

Typically the reaction in the Sun are of the type:

T1 + T2 → T3 + T4 or T1 + T2 → T3 + T4 + T5. (1)

The temperature in the solar core is ∼ (10 -15)×106 eV corresponding to keV energies. The Coulomb barriers for nuclear reactions are however of ∼ MeV energies.

→ The dominant process for charged particles to undergo a reaction of the type above is quantum mechanical tunnelling.

The cross section for a nuclear reaction can be given as: S(E) Z Z e2 σ(E) = exp(−2πη) η = 1 2 (2) E ~v S(E) is a nuclear physics factor (smooth when there are no resonances) and the

exponential term is the tunnelling factor which represents the Coulomb barrier. Z1,Z2 are the charges of the reacting nuclei and v their relative velocity.

The reaction rate can then be written as: n1n2 R = < σv >12 (3) 1 + δ12

ni are the particle densities, δ12 a term to avoid double counting of particles and < σv >12 the thermally averaged cross section. For < σv >, a Maxwell-Boltzmann distribution

2 1 LECTURE 3: SOLAR NEUTRINOS for the velocity of the particles inside the Sun is assumed. Figure1 illustrates the probability for two particles to undergo a nuclear reaction by overcoming the Coulomb barrier. The interplay between the Maxwell-Boltzmann distribution of particle velocities

Figure 1. Illustration of the relative probability for two nuclear particles to undergo a nuclear reaction. and the tunnelling probability gives rise to an increased probability which is known as Gamov peak.

1.2. Neutrino production The nuclear energy generation occurs in the Sun by the fusion of hydrogen into helium being the net reaction:

4 + 4p → He + 2e + 2νe (4) where 26.7 MeV are released per reaction. There are two reaction chains that both result into the burning of equation4: the pp-cycle (makes 99% of the energy in the Sun) and the CNO-cycle (figure2). Within these cycles, there are 8 reactions producing neutrinos. Each ν is typically called as its production reaction. Consequently, there are pp-ν, pep-ν, 7Be-ν, 8B-ν ...

The reactions happen at different depths in the interior of the Sun. As general rule, the higher the nuclear charge of the ion involved in the reaction the stronger the dependence of the nuclear cross section on temperature. Accordingly, the more localized is the occurrence of reactions towards regions of higher temperature (at the Sun’s center).

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Figure 2. Burning inside the Sun: pp-chain (left) and CNO-chain (right). Figure from Borexino Collaboration, 2018 [1].

• pp-, pep- and hep-neutrinos have a broad spatial distribution (see figure3) • 7Be-, 8B, 15N-, 15O- and 17F- neutrinos are more localized

Figure 3. Normalized production profiles of solar neutrinos as a function of solar radius. Figure from Antonelli et al. 2013 [2].

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The neutrino spectrum is calculated [3] using input parameters such as: • Solar age and luminosity • the equation of state • nuclear parameters (as discussed above) • chemical abundances • opacities (due to processes like Thomson scattering ...) With all these ingredients, the solar model predicts fluxes of ∼ 1010 neutrinos·cm−2·s−1 with % precision (see figure4).

Figure 4. Predicted solar neutrino spectrum by Bahcall and Serenelli. Figure from Borexino Collaboration, 2018 [1].

• dominant flux from the pp-reaction featuring a continuous spectrum up to 0.42 MeV • A 7Be line at 0.86 MeV has the second highest rate (another 7Be line at 0.38 MeV) • At highest energies: 8B and hep-neutrinos with continuous spectra up to 14.06 MeV and 18.77 MeV, respectively.

1.3. Radiochemical experiments The search for solar neutrinos began with radiochemical experiments in the 1960s. Raymond Davis and his collaborators carried out the Homestake experiment (see figure5, left) which aim was to collect and count solar neutrinos.

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The detection reaction employed was the inverse beta decay of neutrinos on chlorine:

37 37 − νe + Cl → Ar + e (5)

37 37 − Ar → Cl + e + νe (6) • Energy threshold: 0.81 MeV • Half-life of 37Ar: 35 days

• Target volume: 615 tons of C2Cl4 (carbon tetrachloride) • 37Cl natural abundance: 24% • Detection working principle: Argon atoms produced by solar neutrinos are collected in the target over several days. Next, the argon atoms are extracted by purging the tank with helium and passing the gas through a charcoal trap. Finally, the argon decays (equation9) are counted in low noise proportional counters.

Figure 5. Chlorine Homestake experiment: picture of the tank (R. Davis, Brookhaven National Laboratory) on the left and results of the experiment. Figure from Cleveland et al., 1998 [4].

After about 20 years measuring time the rate measured by the experiment was: R = (2.56 ± 0.22) SNU (7) where SNU is a solar neutrino unit, introduced for convenience, corresponding to: 1 SNU = 1036 captures per target atom and per second. This rate is 1/3 of the expected rate constituting what was called at that time the ”solar neutrino puzzle”. The right side of figure5 shows the data acquired between 1970 and 1995. Important features of this measurement are: • No sensitivity to neutrino energy (only counting) • Energy threshold above the pp-neutrino spectrum 6 1 LECTURE 3: SOLAR NEUTRINOS

Later on, similar experiments were performed with gallium as capture element: gallium experiments. This experiments were targeted to be sensitive to the pp- neutrino flux. The detection reaction is:

71 71 − νe + Ga → Ge + e (8)

71 − 71 Ge + e → Ga + νe (9)

• Energy threshold: 0.233 MeV • Reminder: end-point of pp-ν spectrum: 0.42 MeV • Half-life of 71Ge EC-decay: 11.4 days

Two experiments of this type were performed in the 90s: • SAGE in the Baksan tunnel in Russia, 4 700 meters water equivalent (m.w.e.) under the Caucasus. • GALLEX and its successor GNO at the LNGS underground laboratory, 3 600 m.w.e. under the Apennine mountains (see figure6)

Both experiments were similar in the concept. While SAGE used a metallic gallium target (50 tons), GALLEX employed a gallium chlorine solution (30 ton of GaCl3).

Figure 6. Schematics of the GALLEX experiment. Figure from the collaboration.

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For simplicity, only details on GALLEX are given in the following. • Runs of ∼ 30 days are acquired to collect enough statistics • Afterwards, 71Ge was extracted by flushing nitrogen gas

• GeCl4 is then synthesized • Overall extraction efficiency of 95.7% derived using stable isotopes (70Ge, 72Ge ...) • 71Ge EC-decay is measured in proportional counters. Lines at 10.4 keV and 1.2 keV (Auger electrons and X-rays) appear from the K- and L-shell captures, respectively.

The results of the gallium experiments:

+3.5 +3.5 • SAGE R = 66.53.4 (stat) 3.2 (syst) • GALLEX R = 69.3 ± 4.1 (stat) ±3.6 (syst)

The combined result of GALLEX/GNO and SAGE was ∼ 50% of the prediction.

1.4. Real time experiments In real time experiments, the events are detected as they happen. This is different from the experiments described in the last section were the isotopes created during a certain time (a month for example) are collected at the end of that time period.

The first real time solar neutrino detector, Kamiokande, was built in Japan in 1982. Its successor Superkamiokande was built at the beginning of the 90s and has been taking data since then.

Some characteristics of Superkamiokande include: • 50 kton ultra-pure water Cherenkov detector (22.5 kton used for analysis) • Cylindrical stainless steel tank about 40 m in height and diameter • Light detected with about 13 000 PMTs • Energy threshold at ∼ 5.5 MeV Neutrinos are detected in Superkamiokande over the elastic scattering reaction:

− − νx + e → νx + e (10) where νx represent the neutrino in all flavours x = e, µ, τ.

The experiment uses the directionality of the Cherenkov photons to reconstruct the direction of the incoming neutrino. Figure7 shows the event rate in Superkamiokande as function of angle. The direction has to be converted to a system relative to the Sun’s position. For the energy region between 5 and 20 MeV, a clear excess of events appears for the angle corresponding to the Sun position.

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Figure 7. Angular distribution of events for (5 − 20) MeV energy range in Superkamiokande. Plot from Superkamiokande collaboration 2001, data from [5].

Also in the case of Superkamiokande, a deficit in the rate of solar neutrinos was measured being the 8B flux:

0.465 ± 0.005(stat) ± 0.0016(syst) (11) of the SSM prediction.

At the time of the measurement, the deficit could be explained as being due to ν-oscillation but there were other hypothesis for instance ν-decay.

The SNO experiment (Sudbury Neutrino Observatory) brought the answer to the solar neutrino puzzle. The experiment was located in a mine in Canada under 6 010 m.w.e (see scheme in figure8).

• Target: 1000 tons of heavy water • Inside a 12 m ∅ spherical low-radioactive vessel • Shield: 6 500 tons of pure water • Cavity of 22 m ∅ and 34 m height

The experiment used heavy water (D2O) as detection medium because this allows to compare the rates of charged-current and neutral-current interactions.

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Figure 8. Scheme of the SNO experiment. Figure from [6].

The detection of neutrinos is also via Cherenkov effect in the heavy water for changed particles produced in the reactions:

− − νx + e → νx + e (12)

− νe + d → e + p + p (13)

νx + d → νx + n + p (14)

• Reaction 12: elastic scattering (ES) of all neutrino flavours νx on deuterium. Note

that νe has a 6.5× larger cross section for this reaction than the other flavours, therefore mostly νe are measured.

• Reaction 13: charged current (CC) reaction of νe on deuterium. • Reaction 14: neutral current (NC) disintegration of deuteron by neutrinos. The

energy threshold for the reaction is Eth = 2.2 MeV which implies that the reaction is insensitive to high energy neutrinos like 8B. To identify this reaction the neutron has to be absorbed by a deuteron via: n + d → t + γ (6.25 MeV). • The electrons produced in reactions 12 and 13 have a direction correlated with the incoming neutrino. Therefore, as in Superkamiokande, the directionality of the Cherenkov effect can be used to determined that the neutrinos are from the Sun.

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The SNO results are summarized in figure9 where the ES reaction is shown in green, CC reaction on deuteron in red and the NC dissociation of deuteron in blue. The

figure shows the fluxes of electron neutrinos Φe and other flavours Φµτ . The intersection

Figure 9. Flux of 8B neutrinos deduced from the three neutrino reactions in SNO. Figure from Ahmad et al. (SNO collaboration) 2012 [7]. of the three reactions gives the values for each flux:

6 −2 −1 Φe = (1.76 ± 0.14) × 10 cm s (15)

6 −2 −1 Φµτ = (3.4 ± 0.9) × 10 cm s (16) the flux Φµτ is calculated here by subtracting the flux of neutral current (all neutrinos) and the charged current (electron neutrinos).

The SNO results showed that different neutrino flavours were arriving from the

Sun, where only νe are produced. This, together with the measurement of atmospheric neutrinos in Superkamiokande, constituted the evidence for neutrino flavour transformation!. For this discovery, Arthur McDonald and Takaaki Kajita were awarded the Nobel prize in 2015.

• The neutral current flux measured was in agreement with SSM 6 −2 −1 ΦNC (νx) = (5.09 ± 0.44 ± 0.46) × 10 cm s • KamLAND confirmed later on neutrino oscillations using reactor neutrinos (this will be discussed later in the lecture)

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The Borexino experiment is also a real time experiment using organic liquid scintillator instead of water/heavy water as detection medium. Its main goal was originally to measure the Compton-edge-like spectrum of the 7Be neutrinos using the − − detection reaction: νe + e → νe + e

• Detector located @LNGS in Italy (3 600 m.w.e. overburden) • Sphere of 14 m ∅ containing the target • 300 tons of ultra-pure liquid organic scintillator (PC solvent + PPO wavelength- shifter) • 2 200 photomultipliers to record the scintillation light • Target inside a nylon vessel (see figure 10) + outer water muon-veto

Figure 10. Scheme of the Borexino experiment from the Borexino collaboration.

In the case of Borexino, there is no directional information because scintillation light is emitted isotropically (in contrast with the directional Cherenkov light emission). This implies that the incoming direction can not be used to reject background. For this reason, extremely low backgrounds had to be achieved in the design of the experiment.

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• Goal: decreasing radioactivity levels from the outside to the inside • Use of very clean construction materials • Intrinsic contamination of the liquid scintillator O(10−18) g/g in U and Th (yellow and green curves in figure 11)

Figure 11. Distribution of events in the Boxexino detector including the fits to the neutrino and background components. Figure from [1].

Figure 11 shows how the contribution of different neutrinos were identified in the Borexino data: using the spectral shape of each background and signal component.

• 7Be-ν were measured for the first time in real-time in 2008 with a flux of Φ(7Be) = (4.48 ± 0.24) × 109 cm−2 s−1 (47.5 event per day and 100 tons) • A first evidence for pep-neutrinos (3.1 event per day and 100 tons) • 8B-neutrinos were measured in 2010 • In 2014 Borexino managed to measure pp-neutrinos, the most abundant flux [8] • Finally in 2020, Borexino measured neutrinos from the CNO-cycle [9]

Main background sources: • 14C at the lowest energies • Alpha emission from 210Po (can be reduced with pulse-shape discrimination) • 210Bi (important for CNO and pep neutrinos) • Cosmogenically produced 11C 13 1 LECTURE 3: SOLAR NEUTRINOS

1.5. Reminder: Neutrino oscillations in matter As discussed in a previous lecture, the neutrino oscillation probability changes when the medium changes from vacuum to matter. In the Sun, this is due to the additional

reaction of νe with electrons in the medium. The propagation of neutrinos in matter can be described by adding an effective potential √ A = 2 2 · GF · Ne · p (17)

where GF is the Fermi coupling constant, Ne the electron density and p is the energy of the neutrinos.

The neutrino mixing angle is modified in matter as sin 2Θ tan 2Θm = A (18) cos 2Θ − D where Θm is the angle in matter and Θ the one in vacuum. D is the mass difference in vacuum which for solar neutrinos is D = 8 · 10−5 eV2.

The minimal energy required to see matter effects in the Sun can be calculated using equations 17 and 18 and it is around 2 MeV.

Figure 12. Electron neutrino survival probability as a function of neutrino energy. Borexino collaboration 2018 [1].

Measurements - first by radiochemical experiments, later by water Cherenkov detectors and lately by the Borexino liquid scintillator detector - verified the transition from vacuum to matter-induced (MSW effect) neutrino oscillations experimentally.

Figure 12 shows the survival probability of a νe (to be detected as νe) as function of energy. 14 1 LECTURE 3: SOLAR NEUTRINOS

• Below Eν ∼ 2 MeV the probability is ∼ 0.55, neutrinos of these energies cannot see the resonant layers in the Sun • Above ∼ 2 MeV, the probability is suppressed to ∼ 0.32 which correspond to the matter dominated neutrino oscillation region • Figure 12 shows only the data of Borexino, however the curve is compatible with the integrated measurements of the radiochemical experiments and with the high energy measurements by SNO

It is important to realize that the matter resonance (denominator of equation 18 equal to zero) happens only for a positive value of D. The observation of the change in survival probability for solar neutrinos tell us the sign of D.

1.6. Summary In this lecture, we discussed the nuclear reactions in the Sun that are responsible for the emission of neutrinos. These neutrinos carry information from the inside of the Sun helping to understand it. More importantly, solar neutrinos can be employed to study neutrino oscillations.

References

[1] BOREXINO Collaboration, M. Agostini et al., “Comprehensive measurement of pp-chain solar neutrinos,” Nature 562 no. 7728, (2018) 505. [2] V. Antonelli, L. Miramonti, C. Pena Garay, and A. Serenelli, “Solar Neutrinos,” Adv. High Energy Phys. 2013 (2013) 351926, arXiv:1208.1356. [3] J. N. Bahcall, A. M. Serenelli, and S. Basu, “New solar opacities, abundances, helioseismology, and neutrino fluxes,” Astrophys. J. Lett. 621 (2005) L85, arXiv:astro-ph/0412440. [4] B. T. Cleveland, T. Daily, R. Davis, Jr., J. R. Distel, K. Lande, C. K. Lee, P. S. Wildenhain, and J. Ullman, “Measurement of the solar electron neutrino flux with the Homestake chlorine detector,” Astrophys. J. 496 (1998) 505. [5] Super-Kamiokande Collaboration, S. Fukuda et al., “Solar B-8 and hep neutrino measurements from 1258 days of Super-Kamiokande data,” Phys. Rev. Lett. 86 (2001) 5651, arXiv:hep-ex/0103032. [6] A. McDonald, “The Sudbury Neutrino Observatory:observation of flavor change for solar neutrinos,” in International Conference on History of the Neutrino: 1930-2018. 2019. [7] SNO Collaboration, Q. R. Ahmad et al., “Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory,” Phys. Rev. Lett. 89 (2002) 011301, arXiv:nucl-ex/0204008. [8] BOREXINO Collaboration, G. Bellini et al., “Neutrinos from the primary proton–proton fusion process in the Sun,” Nature 512 no. 7515, (2014) 383. [9] BOREXINO Collaboration, M. Agostini et al., “Experimental evidence of neutrinos produced in the CNO fusion cycle in the Sun,” Nature 587 (2020) 577, arXiv:2006.15115.

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