Neutrinos: the dark side of the light fermions missing energy: neutrino discovered • missing particles: neutrino oscillations • missing people: from Majorana to Gamow, to Pontecorvo • missing mass: dark matter • missing symmetries and leptogenesis • missing fundamental theory • concentrate on the dark side: singlet (right-handed) neutrinos Missing energy in β-decays A A + e− 1 ! 2 Why is the electron energy not equal the mass difference between the two nuclei? Is the energy conserved? Missing energy in β-decays A A + e− 1 ! 2 Why is the electron energy not equal the mass difference between the two nuclei? Is the energy conserved? A A + e−+ new particle 1 ! 2 Pauli's letter (December 4, 1930) Dear Radioactive Ladies and Gentlemen, As the bearer of these lines, to whom I graciously ask you to listen, will explain to you in more detail, how because of the "wrong" statistics of the N and Li6 nuclei and the continuous beta spectrum, I have hit upon a deseperate remedy to save the "exchange theorem" of statistics and the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin 1/2 and obey the exclusion principle and which further differ from light quanta in that they do not travel with the velocity of light. The mass of the neutrons should be of the same order of magnitude as the electron mass and in any event not larger than 0.01 proton masses. The continuous beta spectrum would then become understandable by the assumption that in beta decay a neutron is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant... Your humble servant W. Pauli Pauli's letter (December 4, 1930) Dear Radioactive Ladies and Gentlemen, As the bearer of these lines, to whom I graciously ask you to listen, will explain to you in more detail, how because of the "wrong" statistics of the N and Li6 nuclei and the continuous beta spectrum, I have hit upon a deseperate remedy to save the "exchange theorem" of statistics and the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin 1/2 and obey the exclusion principle and which further differ from light quanta in that they do not travel with the velocity of light. The mass of the neutrons should be of the same order of magnitude as the electron mass and in any event not larger than 0.01 proton masses. The continuous beta spectrum would then become understandable by the assumption that in beta decay a neutron is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant... Your humble servant W. Pauli In 1932 Chadwick discovered the neutron. In 1933 Enrico Fermi develops a theory of beta decay, including neutrino, and gives it the name. Thee families of fermions Astrophysical neutrinos are flying at us! Neutrinos from stars, including Sun • Neutrinos from supernovae, including 1987A • Relic neutrinos from Big Bang (have not seen) • Ultrahigh-energy neutrinos (ANITA, Ice Cube, etc.) • Neutrinos available: natural (blue) and man-made (red) GZK 1010 109 8 10 end 107 Cosmic ν rays? 106 of visible 105 GeV 4 oscill in 10 oscill atmos atm 3 universe 10 solar NuTeV pheric 100 ν factory? Energy 10 Minos, CNGS 1 beams supernova K2K 0.1 0.01 LSND,Karmen solar − reactors 10 3 − 10 4 − 10 4 0.01 1 100 104 106 108 1010 1012 1014 1016 1018 1020 1022 1024 Path−length in km Solar neutrinos Neutrinos in the Sun are produced by nuclear reactions (which also power the Sun). [Bethe, Fowler, Bahcall, Ulrich] Solar neutrinos 2p → d e+ νe (pp) 2p e → d νe (pep) 99.75% 0.25% d p → 3He γ 86% 0.00002% 14% (hep) 3 → α 3 α → 7 γ 3 2 He 2p He Be He p → α e+ νe 99.9% 0.01% 7 7 7 8 Be e → Li νe (Be) Be p → B γ 7 8 Li p → 2α B → 2α e+ νe (B) Solar neutrinos 1014 100 % 1 - Gallium 1012 pp Chlorine 80 % MeV 1 Water - 1010 Be pep sec 60 % 2 - 8 CNO 10 probability cm night 40 % in 6 ν 10 B day dE Survival / 4 20 % ν 10 Φ d hep 102 0 % 0.1 1 10 Energy of solar neutrinos in MeV Solar neutrinos discovered Missing neutrinos The deficit of solar neutrinos indicated new physics, most likely, neutrino oscillations Atmospheric neutrinos p... ϑ SK 2 nm 2 GeV 10 1 ν - _ sr _ 1 ne ne nm - sec 2 - m in 10 n dE earth / n F d 3 n p... E π − ϑ 1 10-1 1 10 102 103 104 Neutrino energy En in GeV Neutrino oscillations If neutrinos have masses, their mass eigenstates need not be the same as their weak eigenstates: ν = cos θ ν sin θ ν j 1i j ei − j µi (1) ν = sin θ ν + cos θ ν j 2i j ei j µi In general, for three neutrinos, (mass) (weak) νi = Uiα να ˛ E ˛ E ˛ ˛ ˛ ˛ Oscillations in vacuum Weak eigenstates are produced in the electroweak interactions, ν (α = e; µ, τ). j αi What propagates through space is mass eigenstates (irreps of the Poincar´e group), ν j ii (i = 1; 2; 3). In a two-neutrino case, if νe is produced at some point x, ν(x) = eip1x cos θ ν + eip2x sin θ ν : j i j 1i j 2i The probability of ν appearance at distance x L is µ ≈ P (ν ν ) = ν ν(L) 2 = e ! µ jh µj ij 2 (p2 p1)L ∆m L sin2 2θ sin2 − sin2 2θ sin2 12 : 2 ' 4E Neutrino oscillations imply neutrino masses Two possibilities: \normal" or \inverted" hierarchy νµ ντ ν3 νe νµ ντ ν2 sun νe ν1 atm ν νµ ντ ν2 e atm sun νe ν1 νµ ντ ν3 ∆m2 L Neutrion oscillations probability, e.g., P (ν ν ) sin2 2θ sin2 12 is not e ! µ ' 4E sensitive to the sign of ∆m2. Neutrino oscillations in matter The interactions with matter are described by GF µ H = ν¯eγ (1 γ5)νe eγ¯ µ(1 γ5)e p2 − − For the electrons at rest, only γ = γ contributes, and eγ¯ (1 γ )e is the number µ 0 0 − 5 density. Matter introduces an effective interaction: H = p2GF ne p2 m2 = (E V )2 E2 2EV − − ≈ − Thus, the matter adds to the mass squared the equivalent of 2 m = 2EV = 2p2GF ne 2008 J. J. Sakurai Prize for Theoretical Particle Physics Alexei Smirnov Stanislav Mikheyev "For pioneering and influential work on the enhancement of neutrino oscillations in matter, which is essential to a quantitative understanding of the solar neutrino flux.” Neutrino oscillations in matter: MSW resonance When m2 m2 = 2E, 1 − 2 m2 m2 1− 2 or 2E = V , level crossing ) The resonance condition is 2 2 mi mj cos 2θij + V (νi) = cos 2θij + V (νj) (2) 2k 2k Here V is the forward scattering amplitude. Neutrino oscillations change the flavor composition of the detected neutrino signal • indicate that the mass eigenstates are not the same as the weak eigenstates • have a typical length scale • 4πE E eV2 λ = = 2:48 km ∆m2 GeV ∆m2 „ « ij ! . for a resonance to occur, need (i) adiabaticity, (ii) weak damping. • Need a theory of the neutrino masses! Neutrino masses: Majorana, Dirac one Weyl spinor ν enough need two Weyl spinors, ν ; ν , • L • L R ν¯c ν (ν¯ ν + ν¯ ν ) L L L R R L SU(2) triplet in SM SU(2) doublet in SM • • Majorana or Dirac? µ– ν A gedanken experiment. A neutrino, initially at rest, µ at rest accelerated to a high energy in the upward direction Dirac would always produce a µ−. However, if accelerated Majorana downward, it would produce either µ+ or nothing at all µ+ in CC interactions. Neutrinoless double-beta decay p p n n e e ν ν ∆L = 2 ν mass ν e e n n p p Neutrinoless double-beta decay p p n n e e ν ν ∆ L = 2 counts ν mass 2ν2β 0ν2β ν e e n n p p 0 Q Total energy in electrons Neutrinoless double-beta decay 1 disfavoured by 0n2b 10-1 2 Dm23 < 0 eV disfavoured in -2 | 10 If inverted hierarchy, can measure in the near ee m | future Dm2 > 0 23 by 10-3 cosmology 99% CL (1 dof) 10-4 10-4 10-3 10-2 10-1 1 lightest neutrino mass in eV Neutrino masses Discovery of neutrino masses implies a plausible existence of right-handed (sterile) neutrinos. Most models of neutrino masses introduce sterile states ν ; ν ; ν ;ν ; ν ; :::; ν f e µ τ s;1 s;2 s;N g The number of dark-side neutrinos is unknown: minimum two These states may have some additional gauge interactions that can be discovered at LHC. [PQ Hung] Sterile neutrinos The name "sterile" was coined by Bruno Pontecorvo in a paper [JETP, 53, 1717 (1967)], which also discussed lepton number violation • neutrinoless double beta decay • rare processes (e.g. µ eγ) • ! vacuum neutrino oscillations • detection of neutrino oscillations • astrophysical neutrino oscillations • Pontecorvo: neutrino oscillations can "convert potentially active particles into particles that are, from the point of view of ordinary weak interactions, sterile, i.e.