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The Solution to the Solar n Problem

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Jordan A. Goodman

University of Maryland

January 2003

- Solar Neutrinos
- MSW Oscillations
- Super-K Results
- SNO Results
- Kamland Results
- Overall Results

- P is uud
- N is udd
- p+ is ud
- k+ is us
- and so on…

}Baryons

(nucleons)

}Mesons

The Standard Model

Neutrinos are only weakly interacting

40 billion neutrinos continuously hit every cm2 on earth from the Sun (24hrs/day)

Interaction length is ~1 light-year of steel

1 out of 100 billion interact going through the Earth

1931 – Pauli predicts a neutral particle to explain energy and momentum non-conservation in Beta decay.

1934 - Enrico Fermi develops a comprehensive theory of radioactive decays, including Pauli's particle, Fermi calls it the neutrino (Italian: "little neutral one").

1959 - Discovery of the neutrino is announced by Clyde Cowan and Fred Reines

Neutrinos

They only interact weakly

If they have mass at all – it is very small

- They may be small, but there sure are a lot of them!
- 300 million per cubic meter left over from the Big Bang
- with even a small mass they could be most of the mass in the Universe!

- Homestake - Radiochemical
- Huge tank of Cleaning Fluid
- ne + 37Cl e- + 37Ar
- Mostly 8B neutrinos + some 7Be
- 35 years at <0.5 ev/day
- ~1/3 SSM
- (Davis - 2002 Nobel Prize)

- Sage/Gallex - Radiochemical
- “All” neutrinos
- ne + 71Ga e- + 71Ge
- 4 years at ~0.75 ev /day
- ~2/3 SSM

- Kamiokande-II and -III
- 8B neutrinos only
- ne Elastic Scattering
- 10 years at 0.44 ev /day
- ~1/2 SSM
- (Koshiba 2002 Nobel Prize)

- All of these experiments (except SNO) are sensitive mostly to ne
- The energies are too low to produce m or t so they can only see neutral current interactions from other flavors

- If neutrinos could transform from electron type to muon or tau type the data might be understood
- Neutrinos can only “oscillate” if they have different masses
- This implies that they have mass!
- This would have significant cosmological importance
- A neutrino mass of ~20ev would close the Universe

- It would also imply violation of lepton flavor conservation

- If neutrinos of one type transform to another type they must have mass:
- The rate at which they oscillate will tell us the mass difference between the neutrinos and their mixing

=Electron n

=Muon n

n1n2

n1n2

Muonn

Electronn

- Could Neutrino Oscillations solve the solar neutrino problem?
- Simple oscillations would require a cosmic conspiracy
- The earth/sun distance would have to be just right to get rid of Be neutrinos

- Another solution was proposed –
Resonant Matter Oscillations in the sun (MSW- Mikheev, Smirnov, Wolfenstein)

- Because electron neutrinos “feel” the effect of electrons in matter they acquire a larger effective mass
- This is like an index of refraction

(Mikheev, Smirnov, Wolfenstein)

LMA

SMA

LOW

VAC

- The ratio of NC/CC cross section is ~1/6.5

Aircraft moves through

air faster than speed of

sound.

Sonic Boom

Sonic boom

When a charged particle moves through

transparent media faster

than speed of light in that

media.

Cone of

light

Cherenkov radiation

Cherenkov ring on the wall

Electron or muon track

The pattern tells us the energy and type of particle

We can easily tell muons from electrons

- 1496 day sample (22.5 kiloton fiducial volume)
- Super-K measures:
- The flux of 8B solar neutrinos
- Energy spectrum and direction of recoil electron
- Energy spectrum is flat from 0 to Tmax

- The zenith angle distribution
- Day / Night rates
- Seasonal variations

SK+Gallium+Cholrine - flux only allowed 95% C.L.

95% excluded by SK flux-independent zenith angle energy spectrum

95% C.L allowed. - SK flux constrained w/ zenith angle energy spectrum

SK+Gallium+Cholrine - flux only allowed 95% C.L.

95% excluded by SK flux-independent zenith angle energy spectrum

95% C.L allowed. - SK flux constrained w/ zenith angle energy spectrum

(Like SK)

Fne= (35 ± 3 )% Fssm

- SNO measures Fne= (35 ± 3 )% Fssm
- SK Measures Fes= (47 ± .5 ± 1.6)% Fssm
- No Oscillation to active neutrinos:
- ~3s difference

- If Oscillation to active neutrinos:
- SNO Measures just Fne
- This implies that Fnm,t= ~65% Fssm (~2/3 have oscillated)

- SK measures Fes =(Fne + (Fnm,t)/6.5)

- SNO Measures just Fne
- Assuming osc. SNO predicts that SK will see Fes ~ (35%+ 65%/6.5) Fssm = 45% ± 3% Fssm

- SNO Results

The Winner

- It looks like the Solar Neutrino problem has been solved!
- All Data (except LSND) is now consistent with the large angle MSW solution
- We have ruled out SMA and Low solutions
- Disfavor Sterile Neutrino solutions

- Neutrinos have mass!
- This confirms the atmospheric neutrino results
- Neutrinos contribute approximately as much mass as all of the visible stars

- Future Experiments –
- MiniBoone – LSND effect