Neutrino Oscillations

Transcription

1 Neutrino Oscillations Heidi Schellman June 6, 2000 Lots of help from Janet Conrad

2 Charge mass,mev tandard Model of Elementary Particles 3 Generations of Fermions Force Carriers Q u a r k s u d 2/3 2/3 2/3 c s t ~5 ~ /3-1/3-1/3 b ~9 ~175 ~4500 g Strong Interactions Electromagnetism L e p t o n s n e e n ν 0? m 0? t 0? Z 0 m t W ± Weak Interactions ± Masses are in MeV July 1997

3 Fermions in the Weak Interactions Leptons ψ L = Quarks ( νi l i ) = ( νe e ) ψ R = l = e +,µ +,τ + ψ L = ( ui d i ) = ( ) u d ψ R = q i = u, c, d,, ( νµ µ ( ) c s ),, ( ντ τ ( ) t No weak interactions for right handed ν or Left handed anti-ν b )

4 Two types of neutrino interactions, One transforms neutrino to lepton Other doesn t ν k k µ W + charged current (W exchange) ν ν k k Z 0 neutral current (Z 0 exchange)

5 Weak Interactions Mass Eigenstates d s b = V us V us V ub V cs V cs V cb V ts V ts V tb d s b Weak quarks are not mass eigenstates V = The quark sector shows significant mixing between generations what about leptons?

6 Mixing in the Lepton Sector If neutrinos are massless, there may be mixing but it is durned hard to see. If neutrinos have different masses then, in principle, their weak flavor should evolve as they travel through space.

7 Two flavor mixing Assume that the weak eigenstates ν e and ν µ are mixtures of the mass eigenstates ν 1 and ν 2 ν e ν µ = cos θ sin θ sin θ cos θ ν 1 ν 2 Then the time evolution of a ν µ is ν µ ν e ν 1 ν 2 ν(0) >= ν µ >= sin θ ν 1 > + cos θ ν 2 > ν(t) >= sin θe ie 1t ν 1 > + cos θe ie 2t ν 2 >

8 The probability of seeing an electron neutrino at time t is: P (t) = <ν e ν(t) > 2 = 1 2 sin2 2θ[1 cos(e 2 E 1 )t] Because the two mass states have different wavelengths. If E >> m then: So: E p + m2 2p t p L E P (L) = <ν e ν(t) > 2 = sin 2 2θ sin 2 [ (m2 2 m2 1 )L ] 4E P (L) = <ν e ν(t) > 2 = sin 2 2θ sin 2 [ 1.27 m2 L ] 4E Where L is in km, E is in GeV, m is in ev

9 Experiments can be described by their E/L coverage P(ν α -> ν β ) ~ sin 2 2θ sin 2 [1.27 m 2 L/E] m in ev, L in km, E in GeV ev ev 2 Oscillation Probability ev 2 E/L 0.02 GeV/km If E/L << m 2, P(ν α -> ν β ) ~½ sin 2 2θ If E/L >> m 2, P(ν α -> ν β ) ~ 0 If E/L ~ m 2, can measure both m 2 and sin 2 2θ

10 Sun Earth Primary neutrino source p + p D + e + + ν e Solar core ~10 8 kilometers Underground ν e detector Other sources of neutrinos: e + 7 Be 7 Li + ν e 8 B 2 4 He + e + + ν e Flux at 1 AU (cm 2 s 1 MeV 1 ) [for lines, cm 2 s 1 ] N 15 O 17 F pp Ga 7 Be Cl pep 8 B hep Kamiokande Neutrino energy (MeV)

11 Solar neutrino detectors ν e + 37 Cl 37 Ar + e ν e + 71 Ga 71 Ge + e Homestake, Sage, Gallex extract Argon and Ge from large samples of Cl and Ga

12 SuperKamiokande 50kTons Water, 11, cm γ-tubes

13 Cerenkov Detectors short track, no multiple scattering From side Ring Sharp Ring electrons: short track, mult. scat., brems. Fuzzy Ring muons: long track, slows down Sharp Outer Ring with Fuzzy Inner Region neutral pions: 2 electron-like tracks Two Fuzzy Rings

14 Solar models Use integro-differential equations to extrapolate from surface to core Need to know composition of sun Use nuclear cross sections for processes at the core. Some go as T 10 Need to know about diffusive, convective zones Make predictions for ratios of different processes Can now be checked by helioseismology!

15 Results of solar neutrino experiments All energy ranges are consistent with lower numbers of neutrinos. This is hard to explain with a multi-process solar model but easy to explain with a loss of neutrinos between sun and earth.

16 ν e Z ν e νe, νµ, ντ ν e W only νe e ν Solar neutrinos appear via ν e interactions E ~ 7 MeV

17 Oscillations on the 1 astronomical unit scale are still possible but seasonal variation due to earth s orbit can rule out some m 2 10 Cl+Ga+SK spectrum SK seasonal Cl+Ga+SK spectrum +SK seasonal δm 2 (10 10 ev 2 ) excluded sin 2 (2θ) sin 2 (2θ)

18 all ν can interact with matter Other oscillation lengths are consistent with solar data! electron ν have additional interactions As neutrinos pass through the sun, their E = T + U changes. Resonant conversion m 2 ~ 10-5 ev 2 ν e ν µ Energy ν µ ν e

19 νe ->??? m 2 (ev 2 ) Three additional solutions are possible! solar LMA projected KamLAND day-night asymmetry in 7 Be solar SMA SuperK exclusion day-night asymmetry solar LOW Projected KamLAND seasonal variation in 7 Be solar VAC sin 2 2θ

20 Summary so far Solar neutrino experiments indicate a deficit in electron neutrinos once they get to the earth Solar models cannot accommodate this deficit. There could be oscillations on the scale of the earths orbit ( m 2 ~ ) Or resonant oscillations in the sun with solutions δm 2 21 (ev 2 ) sin 2 2θ solar But no experiment has seen conclusive variations with E/L

21 Reactor Experiments Nuclear reactors produce very low energy anti-electron neutrinos. Current experiments have baselines of 1km or less but still set stringent limits. Future experiment: KAMLAND 2002 Large Liquid Scintillation detectors Measure interaction rates as nuclear reactors in Japan go on and off Effective baseline of 200 km Sensitivity to ν e ->? with M 2 > 10-6 ev 2 Can test the Solar Large Mixing Angle solution Can also do solar neutrinos

22 Bugey m 2 (ev 2 ) KamLAND reactor neutrino Palo Verde CHOOZ SuperK exclusion day-night asymmetry 1 SuperK νe ->??? sin 2 2θ

23 Atmospheric Neutrinos Cosmic-ray shower π + π 0 ~30 kilometers µ + e + ν e ν µ ν µ Atmospheric neutrino source π + µ + + ν µ e + + ν e + ν µ π µ + ν µ Underground ν e, ν e, ν µ, ν µ detector e + ν e + ν µ Cosmic-ray shower π + νµ νµ π 0 µ + e + νe Other side of earth > km way ~30 kilometers

24 Super Kamiokande Sees ν µ >ν τ? Electron ν Muon ν

25 e + µ + π + νe π 0 νe e + νµ νµ e + µ + ν µ ν µ π + Cosθ=1 π 0 ν µ ν µ e + ν e π 0 π + µ + ν µ ν µ ν e e + ν µ ν µ µ + π + π 0 SuperK sees baselines from 20km to 14000km ν e νµ νµ ν e e + µ + π + π 0 µ + π + π 0 Cosθ=-1 Consistent with ν µ ->ν τ or ν µ ->?

26 Atmospheric results Consistent with oscillations with M 2 ~ ev 2 Sin 2 2θ ~ 0.8-1

27 This is can be seen with accelerators with longbaselines K2K Running Now! Aim a ~ 1-2GeV beam from KEK to Super-K, about 200 km Running Sees 3 events where expected 12? CERN to Gran Sasso About 700 km Opera Emulsions to see νµ >ντ Icanoe Liquid Argon to see νµ >νe Fermilab to Soudan 2003 About 700 km MINOS Iron Fe for high rate, νµ >νe

28 Steel-Scintillator MINOS

29 View From Above: MN WI IA MO IL IN Side View: θ 55 mrad 20 km not shown: other 9996 lakes

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31 K2K, Minos and Cern experiments are very likely to measure parameters quite accurately

32 Liquid Argon with drift readout 720 ν e event drift time (µs) 0 0 Z-coordinate (Wire #) 900

33 Situation so far Solar neutrinos consistent with mixing angles for electron neutrinos below 10-4 ev 2 Atmospheric neutrinos consistent with mixing angles for muon neutrinos ~ ev 2 and no electron mixing at that scale. These can be accommodated in a 3-flavor scheme which is what we have anyways for quarks

34 KARMEN 2 BooNE expected CCFR 96 LSND 10-1 m 2 (ev 2 ) K2K ν µ ν e expected MINOS ν µ ν e expected SuperK ν µ ->??? SuperK exclusion day-night asymmetry sin 2 2θ

35 KARMEN 2 CCFR 96 Bugey 95 1 BooNE expected LSND m 2 (ev 2 ) solar SMA K2K ν µ ν e expected MINOS ν µ ν e expected KamLAND reactor neutrino Palo Verde CHOOZ solar LMA SuperK exclusion day-night asymmetry 1 SuperK KamLAND day-night asymmetry in 7 Be solar LOW KamLAND seasonal variation in 7 Be solar VAC sin 2 2θ

36 Charge mass,mev tandard Model of Elementary Particles 3 Generations of Fermions Force Carriers Q u a r k s u d 2/3 2/3 2/3 c s t ~5 ~ /3-1/3-1/3 b ~9 ~175 ~4500 g Strong Interactions Electromagnetism L e p t o n s ν 0? 0? 3 0? n 1 n 2 e Z 0 m t W ± Weak Interactions ± Masses are in MeV July 1997