Neutrino oscillations and masses 1. Neutrino oscillations 2. Atmospheric neutrinos 3. Solar neutrinos, MSW effect 4. Reactor neutrinos 5. Accelerator neutrinos 6. Neutrino masses, double beta decay
1. Neutrino Oscillations For massive neutrinos, one can introduce in analogy to the quark mixing a mixing matrix describing the relation between mass and flavor states:
e U e1 U e2 U e3 1 e=U e1 1U e2 2U e3 3 = U 1 U 3 U 3 2 Constant for massless ν: U 1 U 2 U 3 3 mixing is question of convention
Massive neutrinos develop differently in time. m 2 i p i for masses m < iE t iE t t = U e i 0= U U * e i i i i i i i , Two-Flavor mixing (for simplicity) cos sin = 1 sin cos Definite momentum p; same for 2 all mass eigenstate components Time development for an initially pure | να> beam: 2 2 2 m i iE t iE t E i= p mi = p 1 2 2p t =cos e 1 sin e 2 2 2 2 m1m2 m iE t iE t E E = = [ cos 2 e 1 sin 2 e 2 ] 2 1 2p 2 E assuming p is the same iE t iE t i 1 2 t =L/ w/ 1 : [ cos sin e e ] m2 E E t= L 2 1 2E Mixing probability: E E P , t = t 2=2cos sin 2 1cos 2 2 1 t [ 2 ] m2 1. 27 m2[ eV ] P , t =sin 2 2 sin 2 L =sin 2 2 sin 2 L [ km ] 4 E 4 E [ GeV ] Search for Neutrino Oscillations (PDG 1996) m2 Exclusion plots P , t =sin 2 2 sin 2 L 4 E • Disappearance: reactor experiments. Nuclear reactors are most intensive More ν– statistics sources of e on Eearth. (I) With known neutrino flux: measure flux at distance L. excluded ν– Only e flux is measured via ν– + + + e p e n (II) Measure neutrino flux at position 1 and verify flux after distance L. More sensitive to small ∆m2 , as longer L can be used due to high flux Baseline longer • Appearance: (–) Use neutrino beam of type A ( νµ) and (–ν) search at distance L for neutrinos of type B ( e). More sensitive to small sin θ due to appearance Observation of Neutrino Oscillations Neutrino source Experiment Comments Solar neutrinos Radio-chemical exp.: First observation of “neutrino Homestake Cl exp., disappearance” dates more GALLEX, SAGE than 20 years ago: “Solar neutrino problem” Water experiments: Confirm disappearance of (Super)Kamiokande, IMB solar neutrinos Heavy water: SNO Ultimate “solar neutrino experiment”: proves the oscillation of solar ν Atmospheric neutrinos (Super)Kamiokande Oscillation signal Accelerator LSND much disputed Oscillation signal KARMEN and MiniBooNE refuted K2K Clear disappearance signal MINOS Clear disappearance signal Reactor KamLAND, CHOOZ Clear disappearance signal 2 Atmospheric neutrino problem Cosmic radiation: Air shower pN ± ,K ± ± ± ± ,K ± ± e e e R= =2 e e Exact calculation: R=2.1 (E ν<1GeV) (For larger energies R>2.1) Neutrino detection with water detectors [ Eν~O(GeV)] Water = “active target” x x Cherenkov Z Light Elastic scattering e e X X Charged current W Kinematical limit for νµ: E ν>m µ e e Detection of Cherenkov photons: photomultiplier Experiments: (Super)-Kamiokande in Kamioka Mining and Smelting Co.'s Mine in Japanese Alpes, IMB (Irvine-Michigan-Brookhaven) in salt mine on the shore of lake Erie (USA) Primary goal of both experiments: discover proton decay. KamiokaNDE = Kamioka Nucleon Decay Experiment. Super-Kamiokande located 1 km underground • Largest artificial water detector (50 kt), 41 m height and 39 m diameter • Until the 2001 accident: 11000 PMTs (50 cm tubes!): 40% of surface covered with photo-cathode • Back in operation since 2003, fully restored 2006 Cherenkov cone: 1 cos = n =42 o =1 Stopped Muon Experiment can distinguish electron and muon events, and can measure energy Electrons suffer multiple interactions – fuzzy ring. Muons fly straight through – sharp edge ring. Ratio of muon to electron neutrinos Prediction with oscillation • Too few muon neutrinos observed • Can be explained by oscillations Oscillation pattern of atmospheric neutrinos 1.27 m2 (eV) 2 Survival probability: P =1sin 2 2 sin 2 L (km) E(GeV) Oscillation pattern of atmospheric neutrinos ν ↔ ν mixing of atmos. neutrinos allowed µ τ m2=2.4±0. 4×10 3 eV sin 2 20.92 @ 90% CL 3 Solar neutrino problem Neutrino production Neutrino energy spectrum Sage, Gallex Homestake 2-body decays Neutrino experiments: ν 37 → 37 37 → 37 Cl 2 detectors e + Cl Ar + e, Ar Cl (EC) Eν>0.8 MeV ν 71 → 71 Ga detectors e + Ga Ge + e Eν>0.2 MeV ν → ν H2O detectors Elastic scattering: e + e e + e Eν>5 MeV (detection) Scintillator (Borexino started 2007, SNO+ under construction) Eν > 0.25 MeV Radio-chemical experiments: Homestake, SAGE, GALLEX • Homestake mine, 1400 m underground Homestake Cl 2 experiment • 615 t of C 2Cl 4 (perchloroethilene) = (Homestake gold mine, South Dakota) 2.2x10 30 atoms of 37 Cl • Use He and 36 Ar and 38 Ar to carry-out the few atoms of 37 Ar (~ 1 atom/day) • Count radioactive 37 Ar decays SSM prediction The Nobel Prize in Physics 2002 Raymond Davis Jr. Masatoshi Koshiba Riccardo Giaconi "for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos" "for pioneering contributions to astrophysics, which have led to the discovery of cosmic X-ray sources" Solar Neutrino Problem: Experimental summary Eν>0.8 MeV Eν> 5 MeV Eν> 5 MeV Eν>0.2 MeV Neutrino disappearance Can one measure the oscillated neutrinos? CCES CC ES Sudbury Neutrino Observatory in Vale Inco's Creighton Mine in Sudbury, Ontario, Canada, located 2 km underground • 6 m radius transparent acrylic vessel • 1000 t of heavy water (D 2O) • 9456 inward looking photo multipliers • Add 2 t of NaCl to improve detection of neutrons (salt phase) • Surrounded by normal water (H 20) shielding external radiation Neutrino detection with SNO Cherenkov Charged current e e light Eν < m µ,τ W = =0 = n p measure Eν e E = E + 1.442 MeV ν e x x Elastic scattering Z = 0.154 e e e = e e Cherenkov light = /6 e W lower rate, strong forward peak e e Neutral current x x = = Z e Neutron 2 3 35 36 = e n n H n , H or Cl n , Cl γ− ray 6.25 MeV or 8.5 MeV Signals are determined not event-by-event but on statistical basis softer γ-ray in NC makes than CC Compton scattering or e +e- pair and Cerenkov light is observed. 6.25 MeV resembles line within resolution 8B ν spectrum NC only on Energy deuterons in heavy water decreases due CC only on also in to long thermal deuterons water diffusion of n. within heavy In normal water water vessel E = 2.2 MeV – RAV = acrylic vessel radius γ below analysis threshold strong forward peak no correlation direction from the Sun SNO Evidence for Neutrino Oscillation Electron neutrino flux is too low: Pe e = 35 ±2 % Total flux of neutrinos is correct. Interpreted as ν ↔ ν ν e µ or τ oscillation 1 2 But in case of simple “vacuum oscillation”: P 1 sin 2=50% e e 2 ? Neutrino oscillations in matter: MSW-effect Mikheyev, Smirnov (1986), Wolfenstein (1976) Neutrino oscillation in vacuum: 2 d 1 m1 0 time development of i 1 = 1 dt 2p 2 mass eigenstates 2 0 m2 2 M With unitary transformation U cos sin U = one obtains for the flavor oscillation sin cos in vacuum: d 1 2 i e = UMU T e T m cos2 sin 2 dt 2p UMU = 2 sin 2 cos 2 M 2 = e 2p Neutrinos in matter: e x x e Z W e e e e Electron neutrinos suffer an additional potential Ve affecting the forward ν scattering amplitude which leads to change in the effective mass for e: N = electron density V e=G F 2 N e e 2 2 2 2 2 2 m =E p EV e p m 2 EV e 2 m M=2 2 G F N e E Neutrino oscillation in matter: 2 m M=2 2 G F N e E 2 2 2 2 m cos2 sin 2 m 0 M M = M M 2 sin 2 cos 2 2 0 mM Go the opposite direction… Define the matter mass eigenstates which one obtains by diagonalizing M M 1m T e =U m 2m x T 2 1 2 2 m 0 U M U = m1m1 m m 2 0 m 2 2 2 m=m acos2 sin 2 2 a=2 2 EG F N e / m cos sin 2 2 m m with sin 2 =410 U = 2 2 m sin m cos m sin 2 =110 sin 2 2=410 3 sin 2 2 sin 2 2 = m cos 2a 2sin 2 2 Matter mixing angle can go through a resonance: 2 cos2 cos 2 a=0 i .e. N e= m 2 2 2 EG F a=2 2 EG F N e / m As in the core of the sun, N e is larger than the critical density, the resonance condition will always be fulfilled: oscillation is largely modified by matter. ExplainsP = 35 ±2% observed with SNO e e