Neutron
Beta
Decay
By: Christopher Hayes
November 29, 2012
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• Historical document---First succesful theory of the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
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
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
Matrix Element
Propagator for a massive vector boson:
Weak force V-A vertex factor:
Matrix Element:
Decay Distribution and Lifetime
Theory of Neutron Decay with
Spectator Quarks
• Presence of spectator quarks
modifies the calculation of the
matrix element at the quarkquark vertex
• Generational mixing at the quark-quark vertex requires and
additional factor of Vud from the CKM matrix
Calculation of Lifetime
Δ = 2.5%
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.