|
This formed the matrix element that completed the Fermi theory of β decay and described parity violation, neutrino helicity, muon decay properties along with the concept of lepton universality. Before the [[Standard Model| Standard Model of Particle Physics]] was developed, [[George Sudarshan]] and [[Robert Marshak]], and also independently [[Richard Feynman]] and [[Murray Gell-Mann]], determined the correct [[tensor]] structure ([[vector (geometric)|vector]] minus [[axial vector]], {{nowrap|''V'' − ''A''}}) of the four-fermion interaction.
From there modern [[Quantum Field Theory|electroweak theory]] was developed, which described the [[weak interaction]] in terms of massive [[W and Z Bosons|Gauge Bosons]] which was required for describing high energy particle cross-sections.
== Conservation rules for beta decay ==
=== Baryon number is conserved===
:<math>B = \frac{n_q - n_{\bar{q}}}{3}</math>
where
: <math>n_q</math> is the number of constituent quarks, and
: <math>n_{\overline{q}}</math> is the number of constituent antiquarks.
Beta decay just changes [[neutron]] to [[proton]] or, in the case of negative beta decay ([[electron capture]]) [[proton]] to [[neutron]] so the number of individual [[quarks]] don't change. It is only the baryon flavor that changes, here labelled as the [[isospin]].
Up and down [[quarks]] have total isospin <math>I = \frac{1}{2}</math> and isospin projections
:<math>I_\text{z} = \begin{cases} \frac{1}{2} & \text{up quark} \\ -\frac{1}{2} & \text{down quark} \end{cases}</math>
All other quarks have ''I'' = 0.
In general
:<math>I_\text{z} = \frac{1}{2} (n_\text{u} - n_\text{d})</math>
===Lepton number is conserved===
::<math>L \equiv n_{\ell} - n_{\bar{\ell}}</math>
so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0.
:<math>\begin{matrix}
& \text{n} & \rightarrow & \text{p} & + & \text{e}^- & + & \bar{\nu}_\text{e} \\
L: & 0 & = & 0 & + & 1 & - & 1 \end{matrix}</math>
=== Angular momentum===
For allowed decays, the net orbital angular momentum is zero, hence only spin quantum numbers are considered.
The electron and antineutrino are [[fermions]], spin-1/2 objects, therefore they may couple to total <math>S=1</math> (parallel) or <math>S=0</math> (anti-parallel).
For forbidden decays, orbital angular momentum must also be taken into consideration.
== Fermi transitions ==
| 