(and some things about the weak interaction) Nuclear b-Decay (and some things about the weak interaction) Tomas Janssen Povh/Rith: Chapter 10 (Weak interaction) Chapter 15.5 (b-decay of the neutron) Chapter 17.6 (Nuclear b-decay)

Overview of the talk Weak Interaction V-A coupling Cabibbo angle b-decay of the neutron Phase space Fermi and Gamow-Teller transitions Nuclear b-decay Different decay types (allowed, forbidden, …) Physics beyond the standard model

V-A coupling Parity is not conserved Spin flip should be possible Neutrino has a definite handedness  V -A

Cabibbo angle 1 Quarks from one family: weak isospin doublet Operator I+ changes weak isospin I+|u> = |d> ; I+|d> = |u> ; I+|s> = |c> ; etc. N No mixing of family’s! General weak decay involving quarks: Quark emits W+/- and changes it’s weak isospin. W+/- decays to: Lepton / anti-lepton (semi-leptonic) Quark / anti-quark (non-leptonic)

Cabibbo angle 2 So mixing of family’s should be possible! W- p  - So mixing of family’s should be possible! Mixing matrix of eigenstates of the same weak isospin. W- T+ = I+cosC d u W- T+ = I+sinC s u

b-Decay of the neutron 1 Phase space

b-Decay of the neutron 2 Fermi transitions Case 1: pure vector transitions (“Fermi”)  No spin flip; DJ=0 Independent of nuclear structure!

b-Decay of the neutron 3 Gamow-Teller transitions Case 2: pure axial transitions (“Gamow-Teller”) Spin flip; DJ=0, ±1 Matrix element depends on overlap of spin-wavefunctions Use:

b-Decay of the neutron 4 Total matrix element We cannot measure individual quarks, so we need the complete nucleon wave functions and

Nuclear b-decay 1 Nucleon is contained in a nucleus Matrix element contains overlap of nuclear wave functions Difference in binding energy fixes phase space Phase space is modified by Coulomb interaction

Nuclear b-decay 2 Phase Space Fermi function: Coulomb parameter for :

Nuclear b-decay 3 ft-Value Since We can define ft-value: only a function of the matrix element ft-value ranges from 103 – 1022 sec. ! The difference between vector and axial transitions can’t explain this  Look at orbital angular momentum.

Nuclear b-decay 4 l-dependence Plane wave: For spinless particle: partial wave: So we can associate each term in the plane wave expansion with a unit of l

Nuclear b-decay 4 Types of decay Since p ~ MeV, x ~ fm px ~10-2 The matrix element occurs squared in the decay rate, So each unit of l suppresses the decay with 10-4 l = 0 DP=0 Allowed l = 1 DP=1 Forbidden l = 2 Double forbidden l =3 Triple forbidden e.g: 1-  0+ : Once forbidden Gamow-Teller

Nuclear b-decay 5 Superallowed b-decay Initial and final states overlap perfectly Proton and neutron have the same q-numbers Initial and final states are in the same isospin multiplet “Only” with b+ Decay to highly excited state

Nuclear b-decay 6 Forbidden b-decay Due to selection rules: the allowed decays are ruled out.

Nuclear b-decay 7 Kurie Plot Gives:  Straight line, if Mfi is constant (only if l=0; allowed)

Beyond the standard model 1 Measuring the neutrino mass Nonzero neutrino mass alters phase space: Gives: The intersection with the K=0 axis gives the neutrino mass Also puts a limit on the tau and muon neutrino’s (neutrino oscillations)

Beyond the standard model 2 Measuring a S or T coupling If the neutrino is massive, we need righthanded neutrino’s We can’t have pure V-A Consider Fermi decay: DJ=0. Can only happen with V or S Angular dependence of Matrix element: Where:

Beyond the standard model 2 Measuring a S or T coupling But we can’t measure so instead look at:

Summary (please think of some questions!)