Changes

\frac{d^8\sigma}{d\Omega_{b1}\,d\Omega_\omega\,d\Omega_\rho\,d\Omega_\pi} =

\frac{d^8\sigma}{d\Omega_{b1}\,d\Omega_\omega\,d\Omega_\rho\,d\Omega_\pi} =

\frac{1}{m_Xk_i}|T_{fi}|^2

\frac{1}{m_Xk_i}|T_{fi}|^2

\left(\frac{q_{b1}}{16\pi^2m_X}\right)

\left(\frac{q_{b1}dm_X}{16\pi^3}\right)

\left(\frac{q_{\omega}}{16\pi^2m_{b1}}\right)

\left(\frac{q_{\omega}dm_{b1}}{16\pi^3}\right)

\left(\frac{q_{\rho}}{16\pi^2m_\omega}\right)

\left(\frac{q_{\rho}dm_\omega}{16\pi^3}\right)

\left(\frac{q_{\pi}}{16\pi^2m_\rho}\right)

\left(\frac{q_{\pidm_\rho}}{16\pi^2}\right)

</math>

</math>

where <math>k_i</math> is the beam photon momentum in the G-J frame.  The explicit kinematic factors from the initial-state flux and the density of final states for each of the decays are not factored into the T matrix so that we can make sure that it explicitly respects unitarity in each partial wave. In terms of the individual decay matrix elements introduced earlier, the T matrix element can be written as

where <math>k_i</math> is the beam photon momentum in the G-J frame.  The explicit kinematic factors from the initial-state flux and the density of final states for each of the decays are not factored into the T matrix so that we can make sure that it explicitly respects unitarity in each partial wave. In terms of the individual decay matrix elements introduced earlier, the T matrix element can be written as