About the lower bound on the fixed-angle scattering amplitude at high energy

Assuming that the phase is small we prove that the fixed-angle scattering amplitude in potential scattering cannot decrease faster than exp(-Ckθlogk), where θ is the scattering angle and k the centre-of-mass momentum. This result agrees with the explicit calculation of Wu for the gaussian potential [exp(-Cθk√logk)] and with a previous bound derived from the Mandelstam representation with a finite number of subtractions. The applicability of this result outside the framework of potential scattering is discussed. (orig.)