= Massless fermion Z decay spin sum
{title2=$\sum|\mathcal M|^2=\frac{g^2M_Z^2}{c_W^2}(c_v^2+c_a^2)$}
For the <Z boson> vertex $g\gamma^\mu(c_v-c_a\gamma^5)/(2c_W)$, sum over the three initial polarizations and final <fermion> spins. The symmetric <Dirac trace> is $4(c_v^2+c_a^2)(k_1^\mu k_2^\nu+k_1^\nu k_2^\mu-g^{\mu\nu}k_1\cdot k_2)$. The vector-axial interference is antisymmetric and drops out of the <massive vector polarization sum>. The longitudinal term drops out by current conservation for massless final particles. Contracting the remaining trace gives the displayed result. The <massive-vector spin average> divides it by three; <two-body Lorentz-invariant phase space> then gives $\Gamma=g^2M_Z(c_v^2+c_a^2)/(48\pi c_W^2)$ per color. These coefficients are twice those used with a vertex prefactor $g/c_W$.
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