Two-body symmetry factors and massless daughter rate units

Given: Assume Countable Choice ${\mathrm{A}\mathrm{C}}_{\omega }$ The Axiom of Countable Choice (${\mathrm{A}\mathrm{C}}_{\omega }$). Use the formal scalar coefficient conventions of Scalar symmetry factors and decay coefficient units and Complete two-body phase space and coefficient flux map. Set the equal scalar rest energy to $m=0$ and take $s>0$. For scattering, write $p_i=(E_i,{\mathbf{p}}_i)$ and $k_i=({\epsilon }_i,{\mathbf{k}}_i)$ with $E_i=\mathrm{\mid }{\mathbf{p}}_i\mathrm{\mid }>0$ and ${\epsilon }_i=\mathrm{\mid }{\mathbf{k}}_i\mathrm{\mid }>0$, and require $P=p_1+p_2=k_1+k_2$ and $h(P,P)=s$, evaluating the scattering coefficients in the center-of-momentum frame of Complete two-body phase space and coefficient flux map. For decay, take both daughters on that same positive shell with total parent $P_0=({\mathsf{M}}_0,\mathbf{0})$, ${\mathsf{M}}_0>0$. Let the constant quartic amplitude $\lambda \in \mathbb{R}$ and cubic parent amplitude $G_E\in \mathbb{C}$ have the units specified by those suppliers.

Countable Choice ${\mathrm{A}\mathrm{C}}_{\omega }$ The Axiom of Countable Choice (${\mathrm{A}\mathrm{C}}_{\omega }$) is assumed; no stronger choice axiom is used.

Scalar symmetry factors and decay coefficient units: identical and distinguishable scalar scattering coefficients and the equal-daughter decay-rate coefficient.

Complete two-body phase space and coefficient flux map: the phase-space integral and the units and definitions of the formal coefficient maps.