1. PHYS 564 – Fall 2007 SOLAR NEUTRINOS & NEUTRINO OSCILLATIONS 12/03/2007* Ozgur UNAL

2. Solar Neutrinos & Neutrino Oscillations • Standard Solar Model • Neutrino Oscillations • Solar Neutrino Experiments • Homestake • SAGE • GALLEX/GNO • SNO

3. Standard Solar Model (SSM) SSM: • The best physical model of the Sun • Describes the nuclear reactions taking place in the Sun (p-p chain and CNO cycle) • Most of the neutrinos come from p-p chain

4. Standard Solar Model (SSM) SSM: • Neutrino fluxes and energy spectrum can be predicted by SSM • First experiment (Homestake) to detect the solar neutrinos found much less than predicted Solar Neutrino Problem SSM? Neutrino Oscillations?

5. Neutrino Oscillations • The flavor change of neutrinos suggests that they are not massless • Eigenstates of the weak interaction, , are linear superpositions of mass eigenstates, , where, U is a unitary matrix • For simplicity, consider a two mass eigenstates and two corresponding flavor eigenstates, • Time evolution of an electron neutrino with momentum p is, where E1and E2are the energies of the mass eigenstates,

6. Neutrino Oscillations • The probability of an electron neutrino remains an electron neutrino after travelling a distance L is, and the probability to observe a muon neutrino is, • The transition probability depends on the mixing angle, θ, mass square difference, Δm2, the energy and the distance traveled for vacuum oscillations • In medium with constant density, neutrinos interact with matter through electroweak interaction: • This interaction changes the mixing angle and the effective mass of the neutrino eigenstates:

7. Neutrino Oscillations • The transition probability is maximum for a certain energy of the neutrino and the electron density of matter • Resonance condition: • If the density is not constant, the mixing angle and the effective masses and the eigenstates change continuously • Adiabatic conversion: If density is assumed to change very slowly, some approximations can be made • There are three effects for solar neutrinos on their way to Earth: • Adiabatic conversion inside the Sun • Loss of coherence of the neutrino state • Oscillation of the neutrino mass states in the matter of the Earth

8. Solar Neutrino Experiments Homestake Experiment: • First SN experiment started in the mid 1960s by Ray Davis • Used 615 tons of dry-cleaning fluid, C2Cl4 • The detection of neutrinos was achieved through the reaction, with 0.814 MeV energy threshold • Announced the first results in 1968: One quarter of the predicted amount of SN • Took data between 1970-1995 and found, ФCl = 2.56 ± 0.16 ± 0.16 SNU whereas SSM prediction is, ФCl (SSM) = 8.1 ± 1.3 SNU 1 SNU is equal to captures per target atom per second.

9. Solar Neutrino Experiments SAGE: • Russian-American Experiment started in 1990 at Baksan Laboratory in Russia • Used 50 tons of liquid gallium metal • Based on the reaction, with 0.233 MeV threshold energy • Data collected between the years 1990 and 2003 yielded, ФGa = 66.9 ± 3.9 ± 3.6 SNU whereas SSM prediction is, ФGa (SSM) = 126 ± 10 SNU

10. Solar Neutrino Experiments GALLEX: • Another gallium based experiment started in 1991 at LNGS • Used 30 tons of Ga in an aqueous acid solution (GaCl3-HCl) • Obtained the following capture rate between 1991 and 1997, ФGa = 77.5 ± 6.2 ± 4.5 SNU GNO: • Successor of GALLEX • Took data between 1998 and 2003, ФGa = 62.9 ± 5.4 ± 2.5 SNU SAGE/GALLEX/GNO: • An overall analysis yields, ФGa = 68.1 ± 3.75 SNU

11. Solar Neutrino Experiments Sudbury Neutrino Observatory (SNO): • Located in 2 km underground in Creighton mine in Canada • Used 1,000 tons of heavy water (D2O) in a 12 m diamater acrylic vessel • Consists of 3 phases: • Phase 1: Only D2O • Phase 2: D2O + NaCl (2 tons) • Phase 3: D2O + NCDs

12. Solar Neutrino Experiments SNO: • Thanks to D2O, three types of interactions take place in the vessel, νe + d → p + p + e- (CC) νx + d → p + n + νx (NC) νx + e- → νx + e- (ES) • CC is only sensitive to electron neutrinos, → ФCC = øe • NC is equally sensitive to all types of neutrinos, → ФNC = øe + øμτ • ES is mainly sensitive to the electron neutrinos, σ(νe) = 6.5*σ(νμτ) → ФES = øe + 0.15*øμτ

13. Solar Neutrino Experiments SNO Phase 1: SNO Phase 2: Total 8B flux predicted by SSM: (5.69 ± 0.91)*10-6cm-2s-1

14. Concluding Remarks • SSM seems to be the best solar model • Success of the theory of neutrino oscillations in explaining the Solar Neutrino Problem • Neutrinos are not massless • A global (Radiochemical + SNO + KamLAND experiments) 2-flavor neutrino oscillation analysis has the best fit values:

15. References • http://www.columbia.edu/~ah297/unesa/sun/sun-chapter4.html • http://www.sno.phy.queensu.ca/ • http://www.physics.purdue.edu/Zope/courses/phys570E/posting/lecture/Files/lec21.ppt • Bellerive, A. “Review of Solar Neutrino Experiments” hep-ex/0312045, 2003 • Bahcall, J. “New Solar Opacities, Abundances, Helioseismology, and Neutrino Fluxes” The Astrophysical Journal, 621:L85-L88, 2005 • Nakamura, K. “Solar Neutrinos Review”, 2005 • Maneira, J. “SNO & Solar Neutrino Results” Nuclear Physics B (Proc. Suppl.), 168 84-89, 2007 • Cleveland, B. T. et al “Measurement of the Solar Electron Neutrino Flux with the Homestake Chlorine Detector” The Astrophysical Journal, 496:505-526, 1998 • Cattadori, C. et al “Results from Radiachemical Experiments with Main Emphasis on the Gallium Ones” Nuclear Physics B (Proc. Suppl.), 143 3-12, 2005 • SNO Collaboration “Electron Energy Spectra, Fluxes, and Day-Night Asymmetries of 8B Solar Neutrinos from the 391-Day Salt Phase SNO Data Set” • Ahmad, Q. R. et al “Direct Evidence for Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory” Physical Review Letters 89, 011301, 2002 • Smirnov, A. “Recent Developments in Neutrino Phenomenology” hep-ph/0702061v1, 2006