= Solution
At <energies> large compared with <fermion masses>, the <gauge interactions> preserve <chirality> on each <fermion> line. A <photon> couples to charged <fermions> with equal left and right coefficients $eQ_f$. A <gluon> couples to either <quark> <chirality> with coefficient $g_sT^a$. A <Z boson> couples to both, with coefficients $(g/\cos\theta_W)(T_3-Q_f\sin^2\theta_W)$ on left-chiral fields and $(g/\cos\theta_W)(-Q_f\sin^2\theta_W)$ on right-chiral fields. A <W boson> couples only to left-chiral <fermions> and the associated right-helicity <antifermions>: $W^-\to\ell^-_L\bar\nu_R$ or $d_L\bar u_R$, and the charge-conjugate $W^+$ channels. For <quarks> the coefficient includes the <CKM matrix>. There is no <Standard Model> right-chiral <neutrino> gauge vertex.
For outgoing pairs at a neutral vertex, the allowed <helicities> are $f^-_L\bar f^+_R$ and $f^-_R\bar f^+_L$; the latter labels <helicity>, not the <chirality> of the corresponding antifield. Only the $s$-channel <photon> and <Z boson> diagrams contribute to $e^+e^-\to\mu^+\mu^-$ at tree level among these gauge exchanges. A <W boson> changes charged <leptons> into <neutrinos>, and <gluons> do not couple to <leptons>.
\Image[/past-exam-of-the-particle-physics-course-of-the-university-of-oxford/2015-gauge-and-decay-diagrams.png]
{title=<Feynman diagrams> for chiral gauge vertices, annihilation, charm production and tau decay}
{description=Original diagrams. Fermion arrows denote fermion-number flow; dashed binding brackets indicate a meson projection, not a perturbative vertex. Neutral vertices allow the two opposite-helicity outgoing pairs listed in the solution.}
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