Changes

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

\left(\frac{q_\pi dm_\rho}{16\pi^3}\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>p_i</math> [<math>p_f</math>] is the target [recoil] nucleon momentum in the center of mass frame of the overall reaction.  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

:<math>

:<math>

T_{fi} = \sum_{R,\lambda_R\lambda_{b_1},\lambda_\omega,\lambda_\rho}

T_{fi} = \sum_{R,\lambda_R\lambda_{b_1},\lambda_\omega,\lambda_\rho}