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arXiv · 2512.13780

Positivity with Long-Range Interactions

B. Bellazzini·J. Berman·G. Isabella·F. Riva·M. Romano·F. Sciotti
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Abstract

We introduce infrared finite, analytic, crossing symmetric, Regge behaved, and Lorentz invariant amplitudes $\mathcal{M}_{\mathcal {E}}$, labeled by the experimental energy resolution $\mathcal{E}$ for detecting soft photons and gravitons. For $\mathcal{E}$ 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 $\mathcal{M}_{\mathcal{E}}$ 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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B. Bellazzini, J. Berman, G. Isabella, F. Riva, M. Romano, F. Sciotti. 2025-12-15. Positivity with Long-Range Interactions. https://arxiv.org/abs/2512.13780

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