= Solution
For a massless <fermion>, <chirality> is fixed by <helicity>. For a massless <antifermion>, the field-chirality label is opposite to its physical <helicity>: a left-chiral field creates negative-helicity particles and positive-helicity antiparticles. At $E\gg m$, wrong-chirality amplitudes are suppressed by $m/E$, so chirality-preserving vector vertices conserve <helicity> along a physical fermion line up to these corrections.
For <electron-positron annihilation into a muon pair> through a vector mediator, each annihilating or created pair therefore has opposite physical <helicities>. Writing each pair in the order (negative particle, positive particle), the nonzero possibilities are
$$
\boxed{(L,R)_e\to(L,R)_\mu,\quad(L,R)_e\to(R,L)_\mu,\quad(R,L)_e\to(L,R)_\mu,\quad(R,L)_e\to(R,L)_\mu.}
$$
Here $L,R$ refer to physical <helicity> along each particle's own <momentum>, not to the sign of its spin projected on a single common axis. The incoming pair has total spin projection $m=\pm1$ along the <electron> beam; the outgoing pair has $m'=\pm1$ along the <muon> direction. Same-helicity pairs vanish in the strictly massless vector-current limit.
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