Solution (source code)

= Solution

Read the line styles and fermion-number arrows in the original PDF: a wavy line is a <photon>, and a coiled line is a <gluon>. The valid fundamental <interaction vertices> are
$$
\boxed{\text{QED: (a), (f).}\qquad\text{QCD: (b), (g).}}
$$
Both (a) and (f) have one electron-line arrow entering and one leaving a photon vertex; changing the drawing's orientation does not change the <quantum electrodynamics> interaction. The <Quantum chromodynamics> vertices (b) and (g) are the cubic and quartic <gluon> self-interactions.

The remaining cases fail for different reasons. Diagram (c) couples an isolated electron line to gluons and is not an allowed fermion vertex. Diagram (d) changes an <Electron> to a <muon> at a photon vertex, violating the flavour-diagonal electromagnetic coupling. Diagram (e) couples a colourless <Electron> to a <gluon>. Diagram (h) changes an <up quark> into a <down quark> at a gluon vertex, whereas <Quantum chromodynamics> preserves quark flavour; that assignment also fails <electric charge conservation>.

One measurement of the <strong coupling constant> uses the fraction of resolved <three-jet events> in $e^+e^-\to q\bar qg$: with a fixed jet-resolution definition, its leading ratio to two-jet production is proportional to $\alpha_s$, with calculable higher-order corrections.

\Image[/past-exam-of-the-particle-and-nuclear-physics-course-of-the-university-of-cambridge/2021-three-jet-diagrams.png]
{title=The two leading gluon-emission diagrams for a three-jet measurement}

The intermediate current is $\gamma^*$ or $Z^*$, and the extra <gluon> can be emitted from either the <quark> or the <antiquark>. Both <Feynman diagrams> contribute coherently. The observed jets arise from <hadronization>; a resolved-jet definition is needed because arbitrarily soft or collinear radiation is not a separate measurable third jet.