Neutrino oscillations

1. Neutrino oscillations Review of particle physics, neutrino interactions and neutrino oscillations Tom Gaisser

2. Particle 1 Force carrier Particle 2 How particles interact Elementary particles are point-like (without structure) Ordinary matter is composite and is mostly empty space proton = { u u d } neutron = { u d d } nucleus = collection of protons and neutrons ~10-13 cm = 1 fermi (fm) Tom Gaisser

3. neutrino muon W boson proton Different kinds of interactions All electrically charged particles interact by exchanging photons. Photons are massless so force is long range. Protons and nuclei interact strongly via gluons. In quantum chromodynamics (QCD) the elementary constituents are quarks which are confined to a scale of 10-13 cm = 1 fermi ħc / 1 fm ~ 0.2 GeV Neutral leptons (neutrinos) interact by exchanging a very heavy W boson. Neutrinos interact very weakly because they have to exchange a very heavy W (or Z) boson. Tom Gaisser

4. Example: nm + proton  m+ n p+ nm m+ d d Example: p+ decay m+ nm W+ u u d u d Proton Neutrino interactions Particle charges ⅔ -⅓ 0 -1 Force carrier charges 0 0 0 ±1 Tom Gaisser

5. p p nm m e m+ W+ ne ne nm e+ nm p m  e Introduction to High Energy Physics D.H. Perkins 3rd edition (1987) Tom Gaisser

6. CKM Matrix ( Cabibbo, Kobayashi, Maskawa ) • Gives coupling of W± to quarks • Unitary matrix Vij • Vud ~ Vcs ~ Vtb ~ 1 > Vcd ~ Vus ~ 0.23 >> Vcb ~ Vts ~ 0.041 >> Vub , Vtd Tom Gaisser

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10. From Todor Stanev’s class February 26

11. p p m e ne nm nm Atmospheric neutrinos • Produced by cosmic-ray interactions • Last component of secondary cosmic radiation to be measured • Close genetic relation with muons • p + A  p± (K±) + other hadrons • p± (K±)  m± + nm (nm) • m±  e± + nm (nm) + ne (ne) Tom Gaisser

12. Historical context • Detection of atmospheric neutrinos • Markov (1960) suggests Cherenkov light in deep lake or ocean to • detect atmospheric n interactions for neutrino physics • Greisen (1960) suggests water Cherenkov detector in deep mine • as a neutrino telescope for extraterrestrial neutrinos • First recorded events in deep mines with electronic detectors, 1965: • CWI detector (Reines et al.); KGF detector (Menon, Miyake et al.) • Two methods for calculating atmospheric neutrinos: • From muons to parent pions infer neutrinos (Markov & Zheleznykh, 1961; Perkins) • From primaries to p, K and m to neutrinos (Cowsik, 1965 and most later calculations) • Essential features known since 1961: Markov & Zheleznykh, Zatsepin & Kuz’min • Monte Carlo calculations follow second method • Stability of matter: search for proton decay, 1980’s • IMB & Kamioka -- water Cherenkov detectors • KGF, NUSEX, Frejus, Soudan-- iron tracking calorimeters • Principal background is interactions of atmospheric neutrinos • Need to calculate flux of atmospheric neutrinos Tom Gaisser

13. Historical context (cont’d) • Atmospheric neutrino anomaly - 1986, 1988 … • IMB too few m decays (from interactions of nm) 1986 • Kamioka m-like / e-like ratio too small. • Neutrino oscillations first explicitly suggested in 1988 Kamioka paper • IMB stopping / through-going consistent with no oscillations (1992) • Hint of pathlength dependence from Kamioka, Fukuda et al., 1994 • Discovery of atmospheric neutrino oscillations by S-K • Super-K: “Evidence for neutrino oscillations” at Neutriino 98 • Subsequent increasingly detailed analyses from Super-K: nm  nt • Confirming evidence from MACRO, Soudan, K2K, MINOS • Analyses based on ratios comparing to 1D calculations • Compare up vs down • Parallel discovery of oscillations of Solar neutrinos • Homestake 1968-1995, SAGE, Gallex … chemistry counting expts. • Kamioka, Super-K, SNO … higher energy with directionality • ne ( nm, nt ) Tom Gaisser

14. p p m e nm ne nm ( ) 1.27 L(km) dm2(eV2) En(GeV) P(nmnt) = sin22q sin2 Atmospheric neutrino beam • Cosmic-ray protons produce neutrinos in atmosphere • nm/ne ~ 2 for En < GeV • Up-down symmetric • Oscillation theory: • Characteristic length (E/dm2) • related to dm2 =m12 – m22 • Mixing strength (sin22q) • Compare 2 pathlengths • Upward: 10,000 km • Downward: 10 – 20 km Tom Gaisser

15. e (or m) ne (or nm) nm Classes of atmospheric n events m Contained (any direction) n-induced m (from below) Contained events Tom Gaisser

16. Super-K atmospheric neutrino data (hep-ex/0501064) CC ne CC nm 1489day FC+PC data + 1646day upward going muon data Tom Gaisser

17. 0 0 • 0 C23 S23 • 0 -S23 C23 C13 0 S13 0 1 0 -S13 0 C13 C12 S12 0 -S12 C12 0 0 0 1 U = “atmospheric” “solar” C13 ~ 1 S13 small Atmospheric n nm nt, dm2 = 2.5 x 10-3 eV2 maximal mixing Solar neutrinos ne{nm,nt}, dm2 ~ 10-4 eV2 large mixing Yumiko Takenaga, ICRC2007 3-flavor mixing Flavor state | na ) = Si Uai | ni ), where | ni ) is a mass eigenstate

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