Another possibility, within QFT, is along nrqed's remark that the Z or W is very
off-shell (E<<m). The difference should be due to the Weak interaction
then. This is where things become indeed more complicated to write down
mathematically.
For the Beta decay you were probably thinking about we get according
to "Diagrammatica, Apendix E" :
The vertex function for u --> W-, d Veltman gives:
ig\frac{1}{2\sqrt{2}} \gamma^\mu(1+\gamma^5)V_{ud}
So, there's the chiralty selection and the the Vud which denotes the factor
from the Cabibbo-Kobayashi-Maskawa matrix. The propagator for W is
given by:
\frac{\delta_{\mu\nu}}{p^2+M^2-i\epsilon}
So, well, this still hides the complexity. But the interaction term should
be the product of the u-quark spinor plane wave with the W-plane wave
where W- is:
W^-\ =\ \frac{1}{\sqrt{2}}\left(A^\mu_1-iA^\mu_2 \right)
(Weinberg 21.3.13, Volume 2) Where A is from the Yang Mills field. The
interaction can be found in the Yang Mills equivalent of the normal
covariant derivative:
\def\pds{\kern+0.1em /\kern-0.55em \partial}<br />
\def\lts#1{\kern+0.1em /\kern-0.65em #1}<br />
\lts{D}_\mu \ \equiv\ \pds_\mu - ie\kern+0.25em /\kern-0.75em A_\mu
Which in the Electroweak case becomes:
\def\pds{\kern+0.1em /\kern-0.55em \partial}<br />
\def\lts#1{\kern+0.1em /\kern-0.65em #1}<br />
\left( \pds_\mu - i\kern+0.25em /\kern-0.75em {\vec A}_\mu \cdot {\vec t}_L\right) u
Which can be read from the YM Lagrangian (Weinberg 21.3.11) where
t is the isospin. The real task is now to establish if this interaction can
be enough to mostly cancel the rest-mass energy...
Regards, Hans
