Neutrino Basics CDHSW m 2 [ev 2 ] 10 0 10 3 10 6 10 9 KARMEN2 Cl 95% NOMAD MiniBooNE Ga 95% Bugey CHOOZ ν X ν µ ν τ ν τ NOMAD all solar 95% SNO 95% CHORUS NOMAD CHORUS LSND 90/99% SuperK 90/99% MINOS K2K KamLAND 95% Super-K 95% Neutrinos as a Probe Electroweak Interactions of Neutrinos Mass, Mixing, and Intrinsic Properties Neutrino Oscillations Models Outstanding Issues 10 12 ν µ All limits are at 90%CL unless otherwise noted 10 4 10 2 10 0 tan 2 θ 10 2 Reference: The Standard Model and Beyond, CRC Press http://hitoshi.berkeley.edu/neutrino
Neutrino Counting Invisible Z width: N ν = 3 + N ν N ν = 0.015(9) (also counts light ν (1/2), triplet Majoron + scalar (2), etc.) Cosmology: big bang nucleosynthesis, large scale structure
Dirac or Majorana ββ 0ν nn ppe e (m ββ i U 2 ei m i) Magnetic or electric dipole moments Dirac: may have diagonal ( νσ αβ νf αβ ) or transition ( ν i σ αβ ν j F αβ, i j) moments Majorana: only transition moments (diagonal Dirac from off-diagonal Majorana) One loop (Dirac): µ i 3eG F m i 8 3.2 10 ( 19 m i 2π 2 (much larger in some models) Laboratory, astrophysical limits: µ < 10 10 10 12 µ B 1 ev) µb p e e p n m ee ev 10 0 10 1 10 2 10 3 10 4 W m ββ W General theory prediction Disfavored by 0ΝΒΒ decay m 2 31 0 IO m 2 31 0 NO Disfavored by cosmology 10 4 10 3 10 2 10 1 10 0 m ev Winter, 1004.4160 n
Tritium β spectrum (KATRIN) m ( i U 2 ei m2 i Absolute Mass Scale ) 1/2 2 ev 0.2 ev Large scale structure: Σ i m i (0.5 1) ev O(0.05) ev If ββ 0ν observed (m ββ 0.01 ev) inverted or degenerate
Neutrino Oscillations and Propagation The two flavor case: }{{} weak = ν 1 cos θ + ν 2 sin θ, ν }{{} µ = ν 1 sin θ + ν 2 cos θ mass t = 0: ν(0) = ν µ (from π + µ + ν µ ) t > 0: ν(t) = ν 1 sin θe ie1t + ν 2 cos θe ie 2t [ ] ν 1 sin θe im2 1 t 2E + ν2 cos θe im2 2 t 2E e iet
Probability of oscillating to (appearance experiment) P νµ (L) = ν(t) 2 = sin 2 θ cos 2 θ ( m = sin 2 2θ sin 2 2 ) L 4E e im m 2 L/4E large 2 1 t 2E t + e im2 2 t 2 2E t 1 2 sin2 2θ µ+ π + ν µ L e ν e p m 2 = m 2 2 m2 1, Oscillation length: L osc = 4πE m 2 L t Survival probability (disappearance experiment): P νµ ν µ (L) = 1 P νµ (L)
Three or More Families ν(0) = ν a }{{} weak = i U ai ν i }{{} mass ν(t) i U ai ν i e im2 i t 2E P νa ν b (L) = ν b ν(t) 2 =δ ab 4 Re ( ( ) U ai U biu aj U ) bj sin 2 ij L 4E i<j + 2 Im ( ( ) U ai U biu aj U ) ij L bj sin }{{} 2E i<j CP violating ij m 2 i m2 j Rephasing invariant
Antineutrinos P νal ν bl (L) =δ ab 4 Re ( ( ) U ai U biu aj U ) bj sin 2 ij L 4E i<j +2 Im ( ( ) U ai U biu aj U ) ij L bj sin }{{} 2E i<j CP violating P νal ν bl (L) U U P νbl ν al (L) P ν c ar ν c br (L) = P ν bl ν al (L) (by CP T ) =δ ab 4 i<j Re ( U ai U biu aj U bj 2 i<j Im ( U ai U biu aj U bj ( ) ) sin 2 ij L 4E ( ) ) ij L sin 2E
Propagation in Matter Coherent forward scattering in matter potential (cf optics) Two flavor oscillations in vacuum: ν(t) = a c a(t) ν a i d dt ( ca (t) c b (t) ) = m2 4E ( ) ( cos 2θ sin 2θ ca (t) sin 2θ cos 2θ c b (t) ) In matter (different interactions of ν a and ν b ): ν µ e e e Z W Z ν µ e e e
i d dt ( ca (t) c b (t) ) = n = m2 4E cos 2θ + G F 2 n m 2 4E sin 2θ m 2 4E m 2 4E sin 2θ cos 2θ G F n e for L ν µl, ν τ L 0 for ν µl ν τ L n e 2 1n n for 1 2 n n for L νl c ν µl, ν τ L νl c 2 n ( ca (t) c b (t) ) Signs reversed for ν c R, ν R Solar (MSW), atmospheric (not sterile; (hierarchy), supernovae also WNC), long baseline MINOS vs νr c : new flavor-dependent matter interaction? (to mimic CP T violation)
Long Baseline (LBL) Oscillation Experiments 3 ν oscillations, small s 13 and m 2 (Akhmedov et al, JHEP 04, 078): P ν µ νe = α 2 sin 2 2θ 12 c 2 sin 2 A 23 + 4 s 2 sin 2 (A 1) A 2 13 s2 23 (A 1) 2 where α = + 2 α s 13 sin 2θ 12 sin 2θ 23 cos( + δ) m2 m 2 Atm 0.03, δ δ and A A for P νµ, A > 0 (normal),, A < 0 (inverted) sin A A sin(a 1) A 1 = m2 Atm L 4E, A = 2 2EGF n e m }{{ 2 Atm } matter In principle, determine s 13, δ, hierarchy (easier if s 13 from reactor)
Sterile Neutrinos CDHSW 10 0 KARMEN2 NOMAD MiniBooNE Bugey NOMAD CHORUS NOMAD CHORUS LSND 90/99% 1 st class oscillations: ν a ν b, both active m 2 [ev 2 ] 10 3 10 6 10 9 10 12 Cl 95% Ga 95% CHOOZ all solar 95% SNO 95% ν X ν µ ν τ ν τ ν µ All limits are at 90%CL unless otherwise noted SuperK 90/99% MINOS 10 4 10 2 10 0 tan 2 θ http://hitoshi.berkeley.edu/neutrino K2K KamLAND 95% Super-K 95% 10 2 2 nd class: active sterile LSND: third ij sterile ν s LSND + MiniBooNE: sterile ν s and CP violation (but reactor, accelerator disappearance; other appearance; cosmology?) ν c L appearance (need new interactions) Non-orthogonal light neutrinos (from mixing with heavy)
m2 atm m 2 LSND m 2 LSND m 2 m 2 atm m 2
Models No unbroken gauge symmetry forbids Majorana mass for active ν s Seesaw leptogenesis (heavy ν 2M decay in Type I) But New TeV physics or string constraints may forbid seesaw Appropriate masses not automatic (e.g., SO(10) Higgs 126 or HDO) so that Majorana may be negligible Alternative baryogenesis (e.g., electroweak) Other plausible mechanisms for both Majorana and Dirac (especially in strings) Type, mechanism, scale is open question
Small Dirac masses Usually forbid bare mass (string? U(1)?) Higher dimensional operator (m D ν ϕ S /M P ) Large extra dimension (wave function overlap) String instanton Non-holomorphic soft h ν ν R φ 0 ν R φ S φ 0 φ S
Small Majorana masses The Standard Electroweak Theory Higgs triplet (spontaneous L excluded) Stringy Weinberg operator h T νl φ 0 T φ 0 φ 0 φ 0 φ 0 Heavy ν R (Type I seesaw) Heavy Higgs triplet (Type II seesaw) φ S ν R ν R h S h T φ 0 T κ Loops (new scalars) TeV (extended) seesaws φ 0 φ 0 φ 0 φ 0 φ 0 φ 0 R P violation φ 0 Typeset by FoilTEX ν µl e e L h φ φ 0
Outstanding Issues (intrinsic properties) Scale of underlying physics? (string, GUT, TeV?) Mechanism? (seesaw, LED, HDO, stringy instanton?) Hierarchy, U e3, leptonic CP violation? (mechanism, leptogenesis) Absolute mass scale? (cosmology) Dirac or Majorana? (mechanism, scale, leptogenesis) Baryon asymmetry? (leptogenesis, electroweak baryogenesis, other?)
Outstanding Issues (intrinsic properties) Scale of underlying physics? (string, GUT, TeV?) (LHC, flavor) Mechanism? (seesaw, LED, HDO, stringy instanton?)(indirect: LHC) Hierarchy, U e3, leptonic CP violation? (mechanism, leptogenesis) (long baseline, reactor, ββ 0ν, supernova) Absolute mass scale? (cosmology) (β decay, cosmology, ββ 0ν, supernova) Dirac or Majorana? (mechanism, scale, leptogenesis) (ββ 0ν ) Baryon asymmetry? (leptogenesis, electroweak baryogenesis, other?) (indirect: LHC)
Other Topics Puzzles/anomalies (LSND, NuTeV, MiniBooNE, GSI, MINOS) Quantum subtleties Sterile ν models/constraints ν decay Decoherence Non-standard interactions Heavy ν s CP T, Lorentz, equivalence violation FCNC (associated ν, l) R P violation Mass-varying ν s Time-varying ν s Correlated LHC physics Model approaches (GUTs, family symmetries, string instantons/hdos, textures, anarchy, bimaximal, tri-bimaximal, discrete S4/A4)
Neutrino Spectra ν Oscillations P νa ν b = sin 2 2θ sin 2 ( m 2 L 4E ) 10 0 KARMEN2 NOMAD MiniBooNE Bugey NOMAD CDHSW CHORUS NOMAD CHORUS LSND 90/99% 3 ν Patterns Solar: LMA (SNO, KamLAND, Borexino) m 2 8 10 5 ev 2, mixing large but nonmaximal Atmospheric + K2K + MINOS: m 2 Atm 2.4 10 3 ev 2, near-maximal mixing Reactor: U e3 small (U V l ) m 2 [ev 2 ] 10 3 10 6 10 9 10 12 Cl 95% Ga 95% CHOOZ all solar 95% SNO 95% ν X ν µ ν τ ν τ ν µ All limits are at 90%CL unless otherwise noted SuperK 90/99% MINOS 10 4 10 2 10 0 tan 2 θ http://hitoshi.berkeley.edu/neutrino K2K KamLAND 95% Super-K 95% 10 2
Mixings: let ν ± 1 2 (ν µ ± ν τ ): ν 3 ν + ν 2 cos θ ν sin θ ν 1 sin θ ν + cos θ 3 2 m 2 m 2 atm 1 m 2 atm Normal hierarchy 2 1 m2 3 Inverted hierarchy Analogous to quarks, charged leptons ββ 0ν rate very small ββ 0ν if Majorana Degenerate pattern for m m 2
Conclusions Neutrino physics is extremely interesting
Conclusions Neutrino physics is extremely interesting Neutrino physics is extremely difficult