The Elementary Particles

1. The Elementary Particles

2. The Basic Interactions of Particles e− u d γ γ γ e− u d u, d d e− g W+ W+ u, d u νe e− ν u, d Z0 Z0 Z0 e− ν u, d Weak Nuclear Force Electromagnetic Force Charged Current Strong Nuclear Force Neutral Current

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

4. Processes Involving Neutrinos Number of Neutrinos u, d, e, ν ν Z0 e+ e− u, d, e, ν ν Neutral Current ν ν Z0 antiparticle particle e− e+ LEP Collider 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 Z0 width unaccounted for in seen decay modes is consistent with exactly three neutrino states.

5. Neutrino Sources Cosmic Rays

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

7. Neutrino Sources Typical Fission Nuclear Reactors Nuclear reactors are a very intense sources of νe coming from the b-decay of the neutron-rich fission fragments. Know Isotopes Z N=Z A commercial reactor, with 3 GW thermal power, produces 6×1020νe/s N

8. Neutrino Sources The Sun Solar Fusion Processes The sun produces νe 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 Solar Neutrinos Radiochemical solar neutrino experiments are designed to count neutrinos above the reaction threshold Homestake: νe (E>814 keV)+ 37Cl → e− + 37Ar SAGE and Gallex: νe (E>234 keV) + 71Ga→ e− + 71Ge 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. HOMESTAKE

11. Important Experiments Atmospheric Neutrinos 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 νμ are produced for each νe. 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 Super-Kamiokande

12. Oscillations and Neutrinos Mass νμ ν2 ν1 θ νe Remember: there are three flavors of neutrinos (νe, νμ and ντ), so we might expect three different masses (m1, m2 and m3) 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

13. How Does Neutrino Mass Lead to Oscillations? ν Schrödinger's Equation ν ν ν ν ν • Follow the prescription of quantum mechanics: • The ν’s are“Wave Functions” • Their evolution in time is given by the Schrödinger Equation… • This is the“Oscillation Probability” • It has constant amplitude piece:sin22θ • And an oscillatory piece: • Δm212 = m12-m22(Not only need mass, but different masses!)

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: θ12, θ13 and θ23 There are three corresponding mass squared differences: Δm122, Δm132 and Δm232

15. Important Experiments More Solar Neutrinos SNO used a heavy water (D2O) target to measure the solar flux with neutral current (NC), charges current (CC) and elastic scattering (mixed NC and CC) CC: νe + 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 νe, where interacting in the SNO detector as νμ and ντ.

16. ν-e Elastic Scattering νe e− W− νe e− ν e− Z0 ν e− For electron neutrinos elastic scattering is part charged current and part neutral current, while for νμ and ντ it is pure neutral current. This results in a 6 times larger probability of elastic scattering for νe. 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 νe 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 Δm2. Neutrinos were detected with inverse β-decay in scintillator.

18. Neutrino Oscillation Data ν3 Dm232 ν2 ν1 Dm122 Δm2 (eV2) Atmospheric (θ23) Solar (θ12) sin22θ Dm132≈ Δm122 + Δm232 Two of the three mixing angles are known. Only θ13 is unknown.

19. Other Unknowns and Big Questions • The absolute mass scale: • Oscillation experiment are sensitive to the differences between mass2, but not the actual masses ν3 Dm22 mass2 ν2 Dm12 ν1

20. Other Unknowns and Big Questions ν3 ν3 ν3 Dm22 Dm22 mass2 mass2 ν2 ν2 ν2 Dm12 Dm12 Dm12 ν1 ν1 ν1 • The mass hierarchy: • Not knowing the absolute mass of the mass eigenstates means that we don’t know which is heaviest Dm22 mass2 Inverted Hierarchy Normal Hierarchy