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arXiv · 2606.19432

Partial-wave unitarity and long-range interactions

Ryan Plestid·Pablo Quílez Lasanta
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Abstract

Theories with massless particles contain $t$-channel (forward scattering) singularities that cause standard fixed order expressions for partial-wave amplitudes to be ill-defined. This presents an obstruction to systematically improvable partial-wave unitarity bounds. In this work, we study the construction of partial-wave amplitudes in a modified perturbation theory that incorporates long-range interactions focusing on the role of off-shell Coulomb modes. We find that there exists a universal description of the forward scattering region that renders the amplitudes renormalization scale independent. The resulting partial-wave amplitudes become well defined single-scale objects without spurious dependence on the infrared regulator, and we present a practical method for their computation order-by-order in perturbation theory.

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Ryan Plestid, Pablo Quílez Lasanta. 2026-06-17. Partial-wave unitarity and long-range interactions. https://arxiv.org/abs/2606.19432

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