How adding zero to the complex relation between production and scattering amplitudes found by van Beveren and Rupp gives the expected real relation

Abstract

If a hadronic production process is dominated by two body final state interactions, the amplitude $A$ for the production process can be expanded as a sum of the scattering amplitudes $T$ for the relevant two body channels. Van Beveren and Rupp have claimed that the unitarity relation ${\rm {Im}} A= T^\dag A$ can be satisfied if the coefficients in this expansion are complex. We demonstrate that the coefficients have to be real if the scattering amplitudes $T$ satisfy unitarity. Van Beveren and Rupp have merely written real coefficients as a sum of complex numbers.