Lecture 3 – neutrino oscillations and hadrons Review of leptons Neutrino oscillations Introduction to hadrons FK7003

The lepton family Charge (e) Mass (GeV) e- (e+) -1 (+1) 0.0005 ne,(ne) Spin 1/2 Lepton (antilepton) Charge (e) Mass (GeV) e- (e+) -1 (+1) 0.0005 ne,(ne) 0 m- (m+) 0.105 nm (nm) t- (t+) 1.8 nt (nt) 6 leptons + antileptons. Divided into 3 families/flavours/multipletes: electron,muon tau FK7003

Lepton interactions e- m- m- e- e- nm m+ W- g nm m+ Charged leptons interact via the em and weak forces. Neutrinos only interact via the weak force. Lepton number is always conserved at a vertex and in the whole process. As for all forces: Charge conservation and energy-momentum conservation for incoming and outgoing particles. Charge is conserved at a vertex though energy can appear to be violated when dealing with ”internal lines” (lecture 1). FK7003

Neutrino masses Mass (MeV) ne < 0.0003 nm <0.2 nt <18 Lepton FK7003

Neutrino oscillations m+ p+ Conserves Lm nm Conserves Lt nt t- Whole process violates: Lm, Lt FK7003

Neutrino oscillation formalism FK7003

Real(ni) Real(ni) Real(na) FK7003 nb probability L na prob. na prob.

Neutrino Interactions in Matter l I0 I(x) 103 106 109 n Neutrino interaction lengthi In water/km x  interaction 1 103 106 E  (TeV) Probability of interaction ~ 10-5 / km water at 100 TeV energy 100 billion neutrinos pass through your thumbnail each second but only 1-2 will interact in your body during your lifetime. FK7003

Neutrinos arriving at Earth – not for the exam Relevant for this lecture relics from Big Bang nuclear reactions in Sun explosions of supernova Flux/energy (cm-2s-1MeV-1) natural radioactive decay in Earth nuclear reactors remnants of supernova interactions of cosmic rays in atmosphere Active Galactic Nuclei Neutrino energy (eV) FK7003

Atmospheric neutrinos and Super Kamiokande Boat FK7003

Super-K: nm oscillations From above 15 km Super-K no oscillations P(nm nm ) (Data/Prediction for oscillations) oscillations Earth From below 13000 km FK7003

Atmospheric neutrino results E=1 GeV FK7003

Neutrinos arriving at Earth – not for the exam Relevant for this lecture relics from Big Bang nuclear reactions in Sun explosions of supernova Flux/energy (cm-2s-1MeV-1) natural radioactive decay in Earth nuclear reactors remnants of supernova interactions of cosmic rays in atmosphere Active Galactic Nuclei Neutrino energy (eV) FK7003

Neutrinos in the sun – not for the exam Fusion process leading to aa kne measured flux on earth can be predicted Solar neutrino energies FK7003

Solar neutrino problem FK7003

SNO FK7003

Results FK7003

Generalise for 3 neutrinos FK7003

Mass2 (eV2) 0.003 Flavour composition of mass state. 0.0001 FK7003

Question FK7003

Question FK7003

Question FK7003

Summary of neutrino oscillations Neutrinos produced in the weak force are flavour eigenstates but not mass eigenstates. Neutrino oscillations between flavours occur as a consequence of non-zero mixing angles and a non- zero difference between the mass states Experiments on atmospheric and solar neutrinos demonstrate neutrino oscillations. FK7003