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

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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 $|\sqrt{s}|$.
8 pages, including one postscript figure, latex with epsf.sty

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