Beta and double beta decay

Transcription

1 Fakultät Mathematik und Naturwissenschaften, Institut für Kern- und Teilchenphysik Beta and double beta decay Kai Zuber Institut für Kern- und Teilchenphysik , SNOLAB

2 Contents Lecture 1 History, neutrino masses, beta decay Lecture 2 beta decay (ctd) Lecture 3 Double beta decay Lecture 4 double beta (ctd), cosmological mass bounds Kai Zuber 2

3 History - Radioactivity Three kinds of radioactivity? Kai Zuber 3

4 Back in time beta decay Another problem Understanding of atomic nucleus; Contains protons and electrons Example : - Isotope 14 C contains 6 protons (atomic number) and 8 electron proton pairs (atomic mass) - Isotope 14 N contains 7 protons and 7 electrons pair 14 C( 0 + ) 14 N 1 + How to do that? 2 ( ) + e Kai Zuber

5 Why neutrinos? Why do beta decays show a continuous energy spectrum of electrons? Bohr: At the present stage of atomic theory, however, we may say that we have no argument, either empirical or theoretical, for upholding the energy principle in the case of β-ray disintegrations Kai Zuber 5

6 The solution? Kai Zuber 6

7 The discovery C. Cowan, F. Reines 1953,1956 ν e + p e + + n Project Poltergeist Herr Auge Kai Zuber 7

8 Texting Pauli... Kai Zuber 8

9 The Standard Model Neutrinos in the Standard Model are massless particles LEP Major progress of last 15 years: Neutrinos have a non-vanishing rest mass Kai Zuber 9

10 The Standard Model SU(3) SU(2) U(1) QCD Weak isospin Hypercharge Q = I 3 + Y 2 All particles are massless W-exchange Singlet states because there are no right handed weak charged currents Kai Zuber 10

11 Higgs Mechanism Origin of masses In general: Masses via spontaneous symmetry breaking Higgs Mechanism Doublet of complex scalar fields Vacuum expectation value (VEV) Particle masses via coupling to Higgs VEV (for fermions = Yukawa- couplings) m e Kai Zuber 11

12 Neutrino masses in the SM Easiest way: Include right-handed neutrino singlets in SM = c ν v2 ν ν Why is neutrino so much lighter? ν er ;ν µr ;ν τr More symmetric solution You have to explain why c v is so much smaller than the other couplings Neutrinos would be Dirac particles (4-state objects like the other fermions) Is there a chance to generate neutrino masses without adding neutrino states? Kai Zuber 12

13 Further mass terms Lorentz-scalars: Option: Couple neutrino to its charge conjugate, consequence lepton number violation Majorana neutrinos Ψ Ψ,Ψ C Ψ C,Ψ C Ψ,Ψ Ψ C Lorentz Lorentz ν D CPT Dirac CPT CPT Majorana

14 Fermi theory of weak interaction I : Neutron was discoverd 1932 by Chadwick Kai Zuber 14

15 Fermi theory of weak interaction II : Finally: Parity violation, absence of Fierz-terms, angular correlation in beta decay V-A structure is right structure Kai Zuber 15

16 Fermi theory of weak interaction III : E. Fermi (1934) Kai Zuber 16

17 Within a few years... + Racah (1936) and Majorana (1937) Kai Zuber 17

18 Beta decay Allowed transitions (no angular momentum involved), energy spectrum can be reasonably well calculated Kai Zuber 18

19 Isotopes and mass parabola Beta+/EC region Beta- region Kai Zuber 19

20 Beta decay and neutrino mass measurement Basic idea: Study the endpoint region of the electron spectrum (Fermi 1934) Starting point: Fermi s golden rule Transition rate of beta decay producing an electron with energy in intervall E to E+dE For allowed transitions this is independent of E Neutrino mass comes in here Endpoint energy: Kai Zuber 20

21 Phase space (see Otten, Weinheimer, Rep. Prog. Phys. 71 (2008)) Number of states in a momentum range p+dp Neutrino and electron momenta are not correlated Equation from previous slide (omitting subscript e) Kai Zuber 21

22 A few things to add Modification due to shell electrons: Fermi-function Nonrelativistic approximation (Primakoff-Rosen) with Modification due to neutrino oscillations and excited states Kai Zuber 22

23 Neutrino mixing Known in the quark - sector for more than 40 years U ν i = U αi ν α 2 Flavour Scenario = cosθ sin Θ sin Θ cosθ 3 Flavour Scenario cosθ 12 sinθ 12 0 U = sinθ 12 cosθ cosθ 13 0 sinθ 13 e iδ cosθ 23 sinθ 23 sinθ 13 e iδ 0 cosθ 13 0 sinθ 23 cosθ 23

24 Paramatrisation of CKM- and PMNS matrix NB : Later in double beta decay this will be multiplied by a diagonal matrix Measured quantity in beta decay: Experimentally it is a fit parameter to spectral shape in the endpoint region Kai Zuber 24