Sign of the Absorptive Elastic Amplitude below the Physical Threshold

We show that for elastic processes which have absorptive channels below the physical threshold, the absorptive partial-wave amplitude aₗ(s) has the sign of (-1)ˡ for s below the physical threshold, where l is the orbital angular momentum. The result is valid for any stable particles of arbitrary spins. More generally, for elastic partial wave transitions between states of definite parity P=εη₁η₂ (where η₁ and η₂ are the intrinsic parities and ε=±1), the sign of the absorptive amplitude below threshold is that of ε.