Solution (source code)

= Solution

The charged <pion> has valence content $\pi^-=d\bar u$. Its constituents annihilate into a virtual <W boson>, followed by the lepton pair:
$$
d+\bar u\longrightarrow W^{-*}\longrightarrow\ell^-+\bar\nu_\ell,
\qquad \ell=e,\mu.
$$
\Image[/past-exam-of-the-particle-and-nuclear-physics-course-of-the-university-of-cambridge/2021-pion-leptonic-diagram.png]
{title=The leading quark-level charged-pion leptonic decay diagram}

The quark vertex carries the $u$--$d$ <Cabibbo-Kobayashi-Maskawa matrix> element, and the leptonic vertex is the <weak charged current>. The pion's nonperturbative spatial structure is encoded in the <pion decay constant> when evaluating the <decay amplitude>.