= Massive vector-current annihilation kernel
{title2=$F=t^2+u^2+4s\Sigma-2\Sigma^2$}
For an initial <Dirac field> of mass $m$ annihilating into a distinct <Dirac field> of mass $M$ through a vector current, put $\Sigma=m^2+M^2$. With <Mandelstam variables> satisfying $s+t+u=2\Sigma$, the <spin average> of the two contracted vector currents is $2F$, where $F=(\Sigma-t)^2+(\Sigma-u)^2+2s\Sigma=t^2+u^2+4s\Sigma-2\Sigma^2$. The <gamma-matrix trace> proof uses $\operatorname{tr}[(\not p_2-m)\gamma^\mu(\not p_1+m)\gamma^\nu]=4[p_2^\mu p_1^\nu+p_2^\nu p_1^\mu-(s/2)g^{\mu\nu}]$ and the analogous final tensor. Couplings, the mediator denominator and <color charge> factors multiply this common kinematic expression.
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