$2+3$ system, $$\label{Eq:2}
\widetilde{p}_2 = \frac{\lambda^{1/2}(M_{23}^2,m_2^2,m_3^2)}{2M_{23}},$$ and $M_{23}$ is the invariant mass of the $2+3$ system. Fixing the Mandelstam variables $s$ and $t$, $s=(p_a + p_b)^2$, $t=(p_a - p_1)^2$, the $T$ matrix in Eq. (\[Eq:1\]) will be of the type ($M_{\rm inv} \equiv M_{23}$): $$\label{Eq:3}
  T \equiv C \, \frac{1}{M_{\rm inv}^2 - M_R^2 + i M_R \Gamma_R} \, g_{R,23}\, ,$$ where we have put a coupling $g_{R,23}$ for the resonance $R$ to the $2+3$ system. The width for the resonance going to $2+3$ is given in this case by $$\label{Eq:4}
  \Gamma_{R,23} = \frac{1}{8\pi} \frac{1}{M_{\rm inv}^2} \, \widetilde{p}_2 \,g_{R,23}^2 \, ,$$ which allows one to write Eq. (\[Eq:1\]) as $$\label{Eq:5}
  \frac{\mathrm{d}^2\sigma}{\mathrm{\rm d} t \,\mathrm{d} M_{\rm inv} } = \frac{\prod(2m_F)}{32\, p_a^2 \, s}\, \frac{1}{(2\pi)^3}\, C^2  \frac{8 \pi M_{\rm inv}^2 \Gamma_{R,23}}{|M_{\rm inv}^2 - M_R^2 + i M_R \Gamma_R|^2}.$$

This equation is also good when we sum and average over polarizations of the particles in a more general case of $|T|^2$. The sum over polarizations of 2 and 3 will go into $\Gamma_{R,23}$ and the sum and average over polarizations of the other particles can be absorbed in the constant $C$ (for fixed $s$ and $t$). Eq. (\[Eq:5\]) can also be used for any 