On the importance of measuring $\rho$ at $\sqrt{s}>1$ TeV

Abstract

We show that, even for a soft collision like forward elastic scattering, the phase of the amplitude is extremely sensitive to a breakdown of strict causality in local QFT. This is especially the case when the breakdown is manifested by a failure of polynomial boundedness which leads to amplitudes that in some complex direction have order 1 exponential growth in $|\sqrt{s}|$.