1. The Elementary Particles

2. e−e− e−e− γγ u u γ d d The Basic Interactions of Particles g u, d W+W+ u d Z0Z0 ν ν Z0Z0 e−e− e−e− Z0Z0 e−e− νeνe W+W+ Electromagnetic Force Strong Nuclear Force Weak Nuclear Force Charged Current Neutral Current

3. W e−e− νeνe W+W+ + u d + e−e− νeνe This diagram represent process such as: β decay: n → p + e − + ν e Inverse β decay: p + ν e → e + + n Pion decay: π + → μ + + ν μ time u d e+e+ νeνe u u d d n p u μ+μ+ νμνμ d π+π+ Processes Involving Neutrinos Charged Current u d e−e− νeνe u u d d n p

4. Processes Involving Neutrinos Neutral Current u, d, e, ν ν ν Z0Z0 particle ν ν Z0Z0 antiparticle e − e + LEP Collider e+e+ e−e− The natural width (in mass) of a short lived particle is determined in part by how many decay channels it has available to it. The Z 0 width unaccounted for in seen decay modes is consistent with exactly three neutrino states. Number of Neutrinos

5. Neutrino Sources Cosmic Rays

6. Neutrino Sources Accelerators Earth Shielding: Stops particles that are not neutrinos Decay region:  → , K→  50 m decay pipe FNAL 8 GeV Booster p Toroidal Magnet Target and toroidal focusing magnet Detector

7. Z N N=Z Typical Fission Nuclear reactors are a very intense sources of ν e coming from the  - decay of the neutron-rich fission fragments. A commercial reactor, with 3 GW thermal power, produces 6×10 20 ν e /s Neutrino Sources Know Isotopes Nuclear Reactors

8. Neutrino Sources The Sun Solar Fusion Processes The sun produces ν e as a by-product of the fusion process that fuel it.

9. Other Neutrino Sources Supernova produce a huge burst of neutrinos as all the protons in the star are converted to neutrons to form a neutron star. β-decay isotopes can be used as a source of neutrinos or antineutrinos Electron capture isotopes produce a mono-energetic beam of neutrinos Big Bang relic neutrino are as copious as photons, but they are so low in energy that no one knows how to see them

10. Important Experiments HOMESTAKE Solar Neutrinos Homestake: ν e (E>814 keV) + 37 Cl → e − + 37 Ar SAGE and Gallex: ν e (E>234 keV) + 71 Ga→ e − + 71 Ge Radiochemical solar neutrino experiments are designed to count neutrinos above the reaction threshold The resulting isotope is chemically separated and counted when they decay. Homestake saw only 33% of the expected solar neutrinos. While SAGE and Gallex found about 75% of the expected neutrinos.

11. Important Experiments Atmospheric Neutrinos Super-Kamiokande Kamiokande and later Super-Kamiokande detect neutrinos produced by cosmic rays in the atmosphere from all around the world. They see the Čerenkov rings produced by the charged leptons as they emerge inside the detector from the neutrino charged current interaction. In the atmosphere, two ν μ are produced for each ν e. This 2:1 ratio was observed for neutrinos coming from directly above the detector where the upper atmosphere is only 30 km away, but from te other side of the Earth the rate was much lower

12. Oscillations and Neutrinos Mass Remember: there are three flavors of neutrinos (ν e, ν μ and ν τ ), so we might expect three different masses (m 1, m 2 and m 3 ) But neutrinos are quantum mechanical particles → They behave in strange ways For example: the masses and flavors don’t have to be aligned. In fact, the masses form a second basis In quantum mechanics this happens a lot. We use the linear algebra for the rotation of vectors to handle this. Now and νμνμ ν2ν2 ν1ν1 νeνe θ

13. Follow the prescription of quantum mechanics: The ν’s are “Wave Functions” The ν’s are “Wave Functions” Their evolution in time is given by the Schrödinger Equation… Their evolution in time is given by the Schrödinger Equation… This is the “Oscillation Probability” This is the “Oscillation Probability” It has constant amplitude piece: sin 2 2θ It has constant amplitude piece: sin 2 2θ And an oscillatory piece: And an oscillatory piece: Δm 2 12 = m 1 2 -m 2 2 (Not only need mass, but different masses!) Δm 2 12 = m 1 2 -m 2 2 (Not only need mass, but different masses!) How Does Neutrino Mass Lead to Oscillations? Schrödinger's Equation ν ν ν ν ν ν

14. Generalizing for Three Neutrinos For three neutrinos just add another dimension to the mixing matrix It can be parameterized in terms of three rotation (mixing) angles: θ 12, θ 13 and θ 23 There are three corresponding mass squared differences: Δm 12 2, Δm 13 2 and Δm 23 2

15. Important Experiments More Solar Neutrinos SNO used a heavy water (D 2 O) target to measure the solar flux with neutral current (NC), charges current (CC) and elastic scattering (mixed NC and CC) CC: ν e + d → e − + p + p NC: ν + d → ν + p + n ES: ν + e − → ν + e − They definitively showed that some of the solar neutrinos, which began life as ν e, where interacting in the SNO detector as ν μ and ν τ.

16. ν-e Elastic Scattering νeνe νeνe e−e− e−e− W−W− ν Z0Z0 ν e−e− e−e− For electron neutrinos elastic scattering is part charged current and part neutral current, while for ν μ and ν τ it is pure neutral current. This results in a 6 times larger probability of elastic scattering for ν e. Elastic scattering with a very low momentum transfer (forward scattering) has a very high probability. This causes a “drag” on neutrinos as they pass through matter. This drag is greater on ν e causing accelerated mixing which is a function of electron density. This is know as the matter effect (or MSW effect) and it is the dominant oscillation effect in the dense solar core.

17. Important Experiments More “Solar” Neutrinos The KamLAND experiment used neutrinos from all of the nuclear reactors in Japan and Korea (flux averaged baseline of 180 km and average energy of 3 MeV) to study oscillations at the solar neutrino Δm 2. Neutrinos were detected with inverse β-decay in scintillator.

18. Neutrino Oscillation Data sin 2 2θ Δm 2 (eV 2 ) Atmospheric (θ 23 ) Solar (θ 12 ) Two of the three mixing angles are known. Only θ 13 is unknown. ν3ν3 ν2ν2 ν1ν1  m 23 2  m 12 2  m 13 2 ≈ Δm 12 2 + Δm 23 2

19. ν3ν3 ν2ν2 ν1ν1 m22m22 m12m12 mass 2 Other Unknowns and Big Questions The absolute mass scale: Oscillation experiment are sensitive to the differences between mass 2, but not the actual masses

20. ν3ν3 m22m22 ν2ν2 ν1ν1 m12m12 mass 2 Other Unknowns and Big Questions The mass hierarchy: Not knowing the absolute mass of the mass eigenstates means that we don’t know which is heaviest ν3ν3 m22m22 ν2ν2 ν1ν1 m12m12 mass 2 ν3ν3 m22m22 ν2ν2 ν1ν1 m12m12 Normal Hierarchy Inverted Hierarchy