Solar Neutrinos: Fluxes pp chain Sun shines by : 4 p 4 He + e + + ν e + γ Solar Standard Model Fluxes CNO cycle e + N 13 <E >=0.707MeV He 4 C 1 C 13 p p p p N 15 N 14 He 4 O 15 O 16 e + <E >=0.997MeV O17 p F 17 p e + <E >=0.999MeV
Neutrinos in The Sun : MSW Effect
Neutrinos in The Sun : MSW Effect Solar neutrinos are ν e produced in the core (R 0.3R ) of the Sun
Neutrinos in The Sun : MSW Effect Solar neutrinos are ν e produced in the core (R 0.3R ) of the Sun The solar atter density V CC = G F N e 10 14 N e N A ev At core: V CC,0 10 14 10 1 ev
Neutrinos in The Sun : MSW Effect Solar neutrinos are ν e produced in the core (R 0.3R ) of the Sun The solar atter density The energy spectru of solar ν es V CC = G F N e 10 14 N e N A ev At core: V CC,0 10 14 10 1 ev E ν 0.1 10 MeV
Neutrinos in The Sun : MSW Effect Solar neutrinos are ν e produced in the core (R 0.3R ) of the Sun The solar atter density The energy spectru of solar ν es V CC = G F N e 10 14 N e N A ev At core: V CC,0 10 14 10 1 ev E ν 0.1 10 MeV For ν e ν µ(τ), in vacuu ν e = cos θ ν 1 + sinθ ν For 10 9 ev 10 4 ev E ν V CC,0 > cos θ
Neutrinos in The Sun : MSW Effect Solar neutrinos are ν e produced in the core (R 0.3R ) of the Sun The solar atter density The energy spectru of solar ν es V CC = G F N e 10 14 N e N A ev At core: V CC,0 10 14 10 1 ev E ν 0.1 10 MeV For ν e ν µ(τ), in vacuu ν e = cos θ ν 1 + sinθ ν For 10 9 ev 10 4 ev E ν V CC,0 > cos θ ν can cross resonance condition in its way out of the Sun
For θ π 4 : In vacuu ν e = cosθ ν 1 + sinθ ν is ostly ν 1 In Sun core ν e = cosθ,0 ν 1 + sinθ,0 ν is ostly ν
For θ π 4 : In vacuu ν e = cosθ ν 1 + sinθ ν is ostly ν 1 In Sun core ν e = cosθ,0 ν 1 + sinθ,0 ν is ostly ν If ( /ev ) sin θ (E/MeV)cos θ 3 10 9 Adiabatic transition ν is ostly ν before and after resonance θ draatically at resonance ν e coponent P ee This is the MSW effect µ ν e ν 1 ν µ ν e ν µ ν 1 A R A P ee = 1 [1 + cosθ,0 cos θ]
For θ π 4 : In vacuu ν e = cosθ ν 1 + sinθ ν is ostly ν 1 In Sun core ν e = cosθ,0 ν 1 + sinθ,0 ν is ostly ν If ( /ev ) sin θ (E/MeV)cos θ 3 10 9 Adiabatic transition ν is ostly ν before and after resonance θ draatically at resonance ν e coponent P ee This is the MSW effect µ ν e ν If ( /ev ) sin θ (E/MeV)cosθ 3 10 9 Non-Adiabatic transition ν is ostly ν till the resonance At resonance the state can jup into ν 1 (with probability P LZ ) ν e coponent P ee µ ν e ν 1 ν µ ν e ν µ ν 1 1 ν µ ν e ν µ ν 1 A R A A R A P ee = 1 [1 + cosθ,0 cos θ] P ee = 1 [1 + (1 P LZ)cosθ,0 cos θ]
Neutrinos in The Sun : MSW Effect
Neutrinos in The Sun : MSW Effect ν does not cross resonance: P ee = 1 1 sin θ > 1
Neutrinos in The Sun : MSW Effect ν does not cross resonance: P ee = 1 1 sin θ > 1 ν crosses resonance MSW effect
Neutrinos in The Sun : MSW Effect ν does not cross resonance: P ee = 1 1 sin θ > 1 ν crosses resonance MSW effect Adiabatic MSW transition P ee = sin θ < 1
Neutrinos in The Sun : MSW Effect ν does not cross resonance: P ee = 1 1 sin θ > 1 Adiabacity breaking Effect of P LZ ν crosses resonance MSW effect Adiabatic MSW transition P ee = sin θ < 1
Solar Neutrinos: Data radiocheical Experient Detection Flavour E th (MeV) Data BS05 Hoestake 37 Cl(ν, e ) 37 Ar ν e E ν > 0.81 0.30 ± 0.03 Sage + 71 Ga(ν, e ) 71 Ge ν e E ν > 0.3 0.5 ± 0.03 Gallex+GNO real tie ν e, ν Ka SK ES ν µ/τ x e ν x e σµτ E e > 5 0.41 ± 0.01 1 σ e 6 SNO CC ν e d ppe ν e T e > 5 0.9 ± 0.0 NC ν x d ν x p n ν e, ν µ/τ T γ > 5 0.87 ± 0.07 ES ν x e ν x e ν e, ν µ/τ T e > 5 0.41 ± 0.05 Borexino ν x e ν x e ν e, ν µ/τ E ν = 0.86 0.66 ± 0.07 All experients easuring ostly ν e observed a deficit Deficit is energy dependent Deficit disappears in NC
Solar Neutrinos: Oscillation Solutions RATES ONLY SK and SNO E and t dependence GLOBAL 10-3 5 LMA 10-4 LMA 10-6 0 [10 ev ] 10-5 SMA -7-5 10 15 LOW 10-8 -9 10 10-10 10 5 VAC 10-11 SMA, LOW, VAC at > 5σ -1 10 10-4 10-3 10-10-1 1 10. 0 0. 0.3 0.5 0.6 0.7 0.4 tan θ Best fit = 6.8 10 5 ev tan θ = 0.43 0.9
5 0 10 8 Solar ν e ν active [10-5 ev ] 15 10 + KaLAND ν e / ν e [10-5 ev ] 6 4 5 0 0. 0.3 0.4 0.5 0.6 0.7 0.9 tan θ 0 0.5 0.5 1 4 tan θ
5 0 10 8 Solar ν e ν active [10-5 ev ] 15 10 + KaLAND ν e / ν e [10-5 ev ] 6 4 5 0 0. 0.3 0.4 0.5 0.6 0.7 0.9 tan θ 0 0.5 0.5 1 4 tan θ ν e oscillation paraeters copatible with ν e : Sensible to assue CPT: P ee = Pēē 9 [10-5 ev ] 8.5 8 7.5 = 7.7 10 5 ev tan θ = 0.43 7 6.5 0.3 0.4 0.5 0.6 0.7 0.8 tan θ
Solar+Atospheric+Reactor+LBL 3ν Oscillations U: 3 angles, 1 CP-phase + ( Majorana phases) 0 @ 1 0 1 0 0 0 c 3 s 3 A @ 0 s 3 c 3 c 13 0 s 13 e iδ 0 1 0 s 13 e iδ 0 c 13 1 0 A @ c 1 s 1 1 0 s 1 c 1 0 A 0 0 1 Two ass schees NORMAL 3 atos 1 INVERTED M solar solar 1 3 ν oscillation analysis 1 = M at ± 3 ± 31
Solar+Atospheric+Reactor+LBL 3ν Oscillations U: 3 angles, 1 CP-phase + ( Majorana phases) 0 @ 1 0 1 0 0 0 c 3 s 3 A @ 0 s 3 c 3 c 13 0 s 13 e iδ 0 1 0 s 13 e iδ 0 c 13 1 0 A @ c 1 s 1 1 0 s 1 c 1 0 A 0 0 1 Two ass schees NORMAL 3 atos 1 INVERTED M solar solar 1 3 ν oscillation analysis 1 = M at ± 3 ± 31 Generic 3ν ixing effects: Effects due to θ 13 Difference between Inverted and Noral Interference of two wavelength oscillations CP violation due to phase δ
w/o KaLand Global Analysis: Three Neutrino Oscillations 9 15 8.5 1 [10-5 ev ] 8 7.5 χ 10 5 7 6.5 0.3 0.4 0.5 0.6 0.7 0 0.01 0.0 0.03 0.04 0.05 0.06 0 0 5 10 15 0.3 0.4 0.5 0.6 0.7 0.8 3 tan θ 1 sin θ 13 15 1 [10-5 ev ] tan θ 1 31 [10-3 ev ] - χ 10 5 w/o LBL -3 δ CP 0.3 0.5 1 3 tan θ 3 360 300 40 180 10 60 Noral 0 0 0.01 0.0 0.03 0.04 0.05 sin θ 13 0 0.01 0.0 0.03 0.04 0.05 0.06 sin θ 13 Inverted 0 0.01 0.0 0.03 0.04 0.05 0.06 sin θ 13 χ 0 15 10 5-4 - 0 4 31 [10-3 ev ] sin θ 13 = 0.050 sin θ 13 = 0.035 sin θ 13 = 0.00 0 0 60 10 180 40 300 δ CP 0.3 0.5 1 3 tan θ 3 w/o LBL w/o Chooz 0 0.0 0.04 0.06 sin θ 13
The derived ranges for the six paraeters at 1σ (3σ) are: 1 = 7.7 +0. ( +0.67 0.1 0.61) 10 5 ev 31 =.37 ± 0.17 (0.46) 10 3 ev θ 1 = 34.5 ± 1.4 ( ) +4.8 4.0 θ 3 = 4.3 +5.1 ( +11.3 ) 3.3 7.7 θ 13 = 0 +7.9 ( +1.9 ) 0.0 0.0 δ CP [0, 360] U 3σ = 0.77 0.86 0.50 0.63 0.00 0. 0. 0.56 0.44 0.73 0.57 0.80 0.1 0.55 0.40 0.71 0.59 0.8
The derived ranges for the six paraeters at 1σ (3σ) are: 1 = 7.7 +0. ( +0.67 0.1 0.61) 10 5 ev 31 =.37 ± 0.17 (0.46) 10 3 ev θ 1 = 34.5 ± 1.4 ( ) +4.8 4.0 θ 3 = 4.3 +5.1 ( +11.3 ) 3.3 7.7 θ 13 = 0 +7.9 ( +1.9 ) 0.0 0.0 δ CP [0, 360] U 3σ = 0.77 0.86 0.50 0.63 0.00 0. 0. 0.56 0.44 0.73 0.57 0.80 0.1 0.55 0.40 0.71 0.59 0.8 with structure U LEP 1 (1 + O(λ)) 1 (1 O(λ)) 1 (1 O(λ) + ǫ) 1 (1 + O(λ) ǫ) 1 1 (1 O(λ) ǫ) 1 (1 + O(λ) ǫ) 1 ǫ λ 0. ǫ 0.
The derived ranges for the six paraeters at 1σ (3σ) are: 1 = 7.7 +0. ( +0.67 0.1 0.61) 10 5 ev 31 =.37 ± 0.17 (0.46) 10 3 ev θ 1 = 34.5 ± 1.4 ( ) +4.8 4.0 θ 3 = 4.3 +5.1 ( +11.3 ) 3.3 7.7 θ 13 = 0 +7.9 ( +1.9 ) 0.0 0.0 δ CP [0, 360] U 3σ = 0.77 0.86 0.50 0.63 0.00 0. 0. 0.56 0.44 0.73 0.57 0.80 0.1 0.55 0.40 0.71 0.59 0.8 with structure U LEP 1 (1 + O(λ)) 1 (1 O(λ)) 1 (1 O(λ) + ǫ) 1 (1 + O(λ) ǫ) 1 1 (1 O(λ) ǫ) 1 (1 + O(λ) ǫ) 1 ǫ λ 0. ǫ 0. very different fro quark s U CKM 1 O(λ) O(λ 3 ) O(λ) 1 O(λ ) λ 0. O(λ 3 ) O(λ ) 1
We still ignore: { (1) Open Questions Is θ13 0? How sall? () Is θ 3 = π 4? If not, is it > or <? (3) Is there CP violation in the leptons (is δ 0, π)? (4) What is the ordering of the neutrino states? (5) Are neutrino asses: hierarchical: i j i + j? degenerated: i j i + j? (6) Dirac or Majorana?