Positivity with Long-Range Interactions
Abstract
We introduce infrared finite, analytic, crossing symmetric, Regge behaved, and Lorentz invariant amplitudes M E, labeled by the experimental energy resolution E for detecting soft photons and gravitons. For E exponentially smaller than any hard scale, they also satisfy unitarity and their associated cross sections reproduce the inclusive, infrared-finite cross sections of ordinary amplitudes. These properties make ME suitable for deriving infrared-safe positivity bounds on effective field theories in the presence of long-range forces even in D=4. As an illustration, we present explicit bounds in the low-energy theory of pions coupled to electromagnetism and gravity.
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