\, \, \, ,$$ where $p_f$ denotes the modulus of the CM $3$-momentum in the final state. (Regarding the details relating to the Lorentz invariant phase space, see Ref. [@ah].) In Sections \[sec:D1\]-\[sec:D5\], $p_f=\sqrt{s}/2$ and $$\label{eq:EQ105}
\frac{d\sigma}{d\Omega} = \frac{\lvert \mathscr{T} \rvert^2}{(8 \pi)^2 s} \, \, \, .$$ In Sections \[sec:D6\] and \[sec:D7\], $p_f=(s-m_e^2)/(2\sqrt{s})$ and Eq. (\[eq:EQ105\]) also holds. In Section \[sec:D8\], $p_f=\sqrt{s/4-m_e^2}$ and $$\frac{d\sigma}{d\Omega} = \frac{\lvert \mathscr{T} \rvert^2}{(8 \pi)^2 s} \sqrt{1-\frac{4 m_e^2}{s}} \, \, \, .$$

I will finally list a number of helpful relations obeyed by the matrix operator Tr, which returns the trace of a square matrix, i.e., the sum of its diagonal elements. Put forth by Richard Feynman, the trace technique comprises a set of operations enabling the speedy derivation of the sum of the contributions to the scattering amplitude from all spin orientations pertaining to the scattering process in question. $$\begin{aligned}
{\rm Tr} [A+B] &= {\rm Tr} [A] + {\rm Tr} [B]\\
{\rm Tr} [AB] &= {\rm Tr} [BA]\\
{\rm Tr} [ABC] &= {\rm Tr} [CAB] = {\rm Tr} [BCA]\\
{\rm Tr} [g_{ab}] &= 4 g_{ab}\\
{\rm Tr} [\gamma_a \gamma_b] &= {\rm Tr} [2 g_{a b} - \gamma_b \gamma_a] = {\rm Tr} [2 g_{a b} - 