1. By: Christopher Hayes November 29, 2012
Neutron Beta Decay
By: Christopher Hayes
November 29, 2012

2. Fermi’s Original Theory
First Theory of beta decay developed by
Fermi (1933)
Point-like four fermion vertex
Could be applied to any nucleus. Also works for neutron decay and muon decay
Historical document---First succesful theory of the creation of massive particles

3. Muon Decay Theory of muon decay is similar to neutron beta decay
Muon decay is a pure weak interaction ---defines the strength of the weak coupling constant
Precision of GF determined by precision of muon lifetime calculation

4. First Order Calculation of Neutron Decay Rate
Treats neutron and proton as point-like
Dirac particles which couple to W --
Feynman Diagram similar to muon decay
Matrix element exactly the same as muon decay

5. Matrix Element Propagator for a massive vector boson:
Weak force V-A vertex factor:
Matrix Element:

6. Decay Distribution and Lifetime

7. Theory of Neutron Decay with Spectator Quarks
Presence of spectator quarks modifies the calculation of the matrix element at the quark-quark vertex
Generational mixing at the quark-quark vertex requires and additional factor of Vud from the CKM matrix

8. Calculation of Lifetime
Δ = 2.5%

9. Further extensions of the theory of neutron beta decay
More sophisticated theory includes terms which couple directly to the neutron spin vector.
Particle Data Booklet lists values for a, A, B, D
Constants A,B, D determined by experiments with polarized neutrons
Nab experiment at SNS will measure the constants a, b.