Solar Neutrino Problem where astrophysics and fundamental physics meet

Neutrinos  Neutron  neutrino Weakly interacting light particles Produced by nuclear interaction when weak force is involved

CNO not important

Photons vs. Neutrinos   Photons mean free path 1cm at core nuclear reactions cannot be observed directly with EM radiation Diffuse to surface >105 year  mean free path 1010R* leaves the star freely  

Why Important? Direct evidence of nuclear reaction “Real time” energy production in the Sun Compare with photon flux, thermodynamic equilibrium > 105yr Test the Standard Solar Model

CNO not important

Solar Neutrinos Interaction Energy (MeV) Flux at Earth (m-2s-1) 𝑝+𝑝⟶ 2 D + 𝑒 + +𝜈 ≤0.42 6.0×1014 7 B e+ 𝑒 − ⟶ 7 L i+𝜈 0.86 (90%) 0.38 (10%) 4.9×1013 7 B ⟶ 7 B e+ 𝑒 + +𝜈 ≤15 5.7×1010 billion of photons passing us every s

Solar Neutrinos

How to detect ?

Neutrino Detection 1 event per day needs 1030 atoms ktons of targets Interaction cross-section 10-46cm2  solar  flux 1010cm-2s-1 1 event per day needs 1030 atoms ktons of targets Common detectors: Water, chlorine, gallium, scintillation

Neutrino Detection scintillator gallium chlorine water

Radiochemical Chlorine 𝜈+ 37 C l⟶ 𝑒 − + 37 A r Gallium 𝜈+ 71 G a⟶ 𝑒 − + 71 G e

Chlorine 𝜈+ 37 C l⟶ 𝑒 − + 37 A r (=35days) Energy threshold: 0.8MeV e.g. Homestake (1960s) 600 tons C2Cl4 (dry clean liquid)

Homestake Experiment Raymond Davis, Jr. & John N. Bahcall in late 1960s Homestake Gold Mine in South Dakota, USA 1,500m deep (why underground?) 𝜈+ 37 CL ⟶ 𝑒 − +37Ar energy threshold 0.8MeV Half-life of 37Ar = 35 days 400,000L = 600 tons C2Cl4 ∼2× 10 30 Cl atoms (Perchloroethylene C2Cl4 -- dry clean liquid) Only tens of 37Ar atoms are found by a Geiger counter ⅓  ½ of prediction!

Gallium 𝜈+ 71 G a⟶ 𝑒 − + 71 G e 𝜏=11.4d 71 G a+𝛾 0.23MeV, can detect p-p  e.g. GALLEX (1990-2006) 30 tons of Ga SAGE (1999-2007) 60 tons of metallic Ga (> annual world production!).

GALLEX and SAGE Neutrino-electron scattering: 𝜈+ 71 Ga ⟶ 𝑒 − +71Ge Ge  Ga+ , half-life 11.4day Much lower detection threshold energy: 0.23MeV, can detect major reaction in the p-p chain 1990-2006: GALLEX experiment in Russia by T. Kirsten, 30 tons of Ga in aqueous solution. SAGE experiment in Italy by V. Garvin, 60 tons of metallic Ga (more than annual world production!).  flux only 60% of prediction

Water Cerenkov Electron scattering 𝜈+ 𝑒 − ⟶𝜈+ 𝑒 − Superluminal e- ⟶ Cerenkov radiation 5MeV threshold, only sensitive to 8B e.g. Super-Kamiokande, Sudbury Neutrino Observatory (SNO) SNO: Heavy water

Kamiokande Experiments Kamioka Mozumi Mine in Japan, >1000m deep Neutrino-electron scattering: 𝜈+ 𝑒 − ⟶ 𝑣 ′ + 𝑒 − ′ Kamiokande II: M. Koshiba & Y. Totsuka in 1980s Super-Kamiokande: Y. Totsuka & Y. Suzuki in 2000s Huge water tank: 40m diameter x 40m height = 50,000m3 pure water 11,000 light detectors to detect Cherenkov (radiation from particles faster than speed of light)  >7MeV, fewer than 20 events per day!

Solar Neutrino Problem Solar model wrong? But all other observations match theory, e.g., sound speed from helioseismology agrees with prediction. Measurement error? But similar results from different experiments. Standard model wrong? New physics is needed.

Sudbury Neutrino Observatory SNO: Creighton Mine in Ontario, Canada, 2,000m underground Led by A. McDonald in the 2000s 1,000 tons of salt heavy water 10,000 PMT to detect Cherenkov radiation Sensitive to all flavors of neutrinos: e, , 

Electron scattering channel: 𝜈 𝑒 + 𝑒 − ⟶ 𝜈 𝑒 ′ + 𝑒 − ′ Charged Current channel: 𝜈 𝑒 +𝑑⟶𝑝+𝑝+ 𝑒 − Neutral Current channel: 𝜈+𝑑⟶𝑛+𝑝+𝜈

Sudbury Neutrino Observatory SNO: Creighton Mine in Ontario, Canada, 2,000m underground Led by A. McDonald in the 2000s 1,000 tons of salt heavy water 10,000 PMT to detect Cherenkov radiation Sensitive to all flavors of neutrinos: e, ,  Total  flux consistent with theory!

What was wrong before? Neutrino oscillation, only e were detected in previous experiments except SNO. 100% e produced in the Sun, but some converted to other spices (, ) on the way to the Earth. Only 35%  arrived on Earth are e. (This is energy dependent)

Neutrino Oscillation Why? Because flavour eigenstates  mass (i.e. energy) eigenstates

Nature, 512, 383 (2014)

Solar Neutrinos 86%

Liquid Scintillator Elastic scattering 𝜈+ 𝑒 − ⟶𝜈+ 𝑒 − More photons than Cherenkov can detect single event Real-time, good energy resolution threshold limited by background No directional information e.g., KamLAND, Borexino

Neutrino Detection scintillator gallium chlorine water

Borexino Borex: Boron Solar Neutrino Experiment 2000t TMB i.e. B(OCH3)3 BOREX  Borexino (cf. neutron neutrino) 2000t300t Main goal: detect neutrinos from 7Be

Borexino Gran Sasso in Italy, 2007- 280 tons liquid scintillator, 2200 PMTs 1,2,4-Trimethyl-benzene C6H3(CH3)3 from crude oil to reduce 14C Real-time detection Single event down to 150keV, good energy spectrum by photon counting

18m

Background

Results 144±13/day/100t

Results

Results 144±13(stat)±10(sys) cts/day/100t Accounted for oscillation: (6.6±0.7) x1010cm-2s-1 Predicted flux 5.98x(1±0.006) x1010cm-2s-1 (high metallicity) 6.03x(1±0.006) x1010cm-2s-1 (low metallicity)

Survival Probability 𝑃 𝜈 𝑒 → 𝜈 𝑒 =0.64±0.12

Summary Solar p-p neutrinos first time directly detected: (6.6±0.7) x1010cm-2s-1 P 𝜈 𝑒 → 𝜈 𝑒 = 0.61±0.12 Agree with Standard Solar Model Thermodynamic equilibrium > 100,000yr Precise test of solar model and oscillation need 1% level measurements

Neutrino Oscillation

Neutrino Oscillation Flavour eigenstates  mass (i.e. energy) eigenstates Simple example: two-flavour oscillation 𝜈 𝑒 𝜈 𝜇 = cos 𝜃 sin 𝜃 − sin 𝜃 cos 𝜃 𝜈 1 𝜈 2 , 𝜈 1 , 𝜈 2 are mass (energy) eigenstates,  is called the mixing angle

Time Evolution of 𝜈 𝑒 𝜈 𝑒 𝑡 = cos 𝜃 𝑒 −𝑖 𝑝 2 + 𝑚 1 2 | 𝜈 1 ⟩ +sin 𝜃 𝑒 −𝑖 𝑝 2 + 𝑚 2 2 | ν 2 ⟩ ≈ 𝑒 −𝑖𝑧 𝑐𝑜𝑠 𝜃 | 𝜈 1 ⟩+ sin 𝜃 𝑒 𝑖𝛥 𝑚 2 𝑥/𝑝 | 𝜈 2 ⟩ , where 𝑐=1, 𝑧= 𝑝+ 𝑚 1 2 2𝑝 𝑡 and 𝛥 𝑚 2 = 𝑚 1 2 − 𝑚 2 2 .

Neutrino Mixing in Vacuum 𝑃 𝜈 𝑒 → 𝜈 𝜇 = 𝜈 𝜇 𝜈 𝑒 𝑡 2 = 𝑒 −𝑖𝑧 −sin𝜃 cos 𝜃 + sin 𝜃 cos 𝜃 𝑒 𝑖𝛥 𝑚 2 𝑥/𝑝 2 = sin 2 2𝜃 sin 2 Δ 𝑚 2 𝐿 4 𝐸 𝜈 = sin 2 2𝜃 sin 2 1.27Δ 𝑚 2 𝐿 km 𝐸 𝜈 GeV  is called the mixing angle, if neutrinos are massless, then m2=0 and there will be no oscillation.

Solar Neutrinos Put in E and L = 1AU? Not that simple! Enhanced oscillation due to the matter effect (MSW effect) Three-flavor neutrino mixing

Oscillation in Matter Mikheyev–Smirnov–Wolfenstein (MSW) effect: enhanced oscillation in matter 𝑒 − in matter change  energy levels, enhanced oscillation and mixing angle becomes tan 2 𝜃 𝑚 = 𝑡𝑎𝑛 2𝜃 1− 2𝑝 2 𝐺 𝐹 𝑛 𝑒 /Δ 𝑚 2 cos 2𝜃 >5MeV 𝜈 𝑒 ⟶ 𝜈 𝜇 inside the Sun No effect on p-p , but affects 8B 

Solar Neutrinos Put in E and L = 1AU? Not that simple! Enhanced oscillation due to the matter effect (MSW effect) Taking these into account, the survival probability of e arrive on Earth is 57%, consistent with the experiments Best-measured  =34

Three-Flavour  Oscillation Since there are 3 flavours of , the actual scenario is more complicated. where 𝑠 𝑖𝑗 ≡ sin 𝜃 𝑖𝑗 and 𝑐 𝑖𝑗 ≡ cos 𝜃 𝑖𝑗 .  are usually neglected in solar neutrino oscillation, i.e. 13 is assumed to be 0, since Δ 𝑚 31 2 ≈ Δ 𝑚 32 2 ≈30× Δ 𝑚 12 However, in March 2012, Daya Bay Experiment found 𝜃 13 =0.092±0.017, i.e. non-zero at 5.2 level. May need to consider ? 𝜈 𝑒 𝜈 𝜇 𝜈 𝜏 = 1 0 0 0 𝑐 23 𝑠 23 0 − 𝑠 23 𝑐 23 𝑐 13 0 𝑠 13 𝑒 −𝑖𝛿 0 1 0 − 𝑠 13 𝑒 −𝑖𝛿 0 𝑐 13 𝑐 12 𝑠 12 0 − 𝑠 12 𝑐 12 0 0 0 1 𝑒 𝑖 𝛼 1 /2 0 0 0 𝑒 𝑖 𝛼 2 /2 0 0 0 1 𝜈 1 𝜈 2 𝜈 3 ,

PRL (2012) 107, 171803

Unsolved Problems Absolute neutrino mass scales? Nuclear beta decay, neutrinoless double beta decay Mass hierarchy?

Unsolved Problems Absolute neutrino mass scales? Nuclear beta decay, neutrinoless double beta decay Mass hierarchy?

Unsolved Problems Absolute neutrino mass scales? Nuclear beta decay, neutrinoless double beta decay Mass hierarchy? Dirac or Majorana statistics? i.e. 𝜈= 𝜈 ? Neutrinoless double beta decay

Unsolved Problems Absolute neutrino mass scales? Nuclear beta decay, neutrinoless double beta decay Mass hierarchy? Dirac or Majorana statistics? i.e. 𝜈= 𝜈 ? Neutrinoless double beta decay 4th flavor?

Neutrino Astronomy

Neutrino Astronomy Sources: Neutrino Observatories: Sun, supernova, AGN, GRB, neutron star merger, etc Neutrino Observatories: IceCube, Super-Kamiokande

Science, 342, 1242856 (2013) 28 events >30TeV from beyond solar system

KM3NeT