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  • Open Access

Resonances: Universality and factorization on higher Riemann sheets

Miguel Correia and Celina Pasiecznik

  • Department of Physics, McGill University, 3600 Rue University, Montréal, Quebec H3A 2T8, Canada

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Phys. Rev. D 114, 076027 – Published 28 October, 2026

DOI: https://doi.org/10.1103/xlzf-36z4

Abstract

Most particles in nature are unstable, manifesting as resonances in scattering processes. Using analyticity and unitarity, we show nonperturbatively that resonances, defined as poles on higher Riemann sheets of scattering amplitudes, share basic properties with stable particles: (i) universality, that a resonance generically appears in every S-matrix element; and (ii) factorization, that amplitudes factorize on resonance poles. Our framework applies in any spacetime dimension and across arbitrarily many two-particle cuts, including cases where the kinematic Riemann surface becomes infinitely sheeted. Importantly, we find that resonance data (spin, mass, width, couplings, and sheet index) are fully encoded on the physical sheet, where causality can impose additional constraints. These results are relevant for extending S-matrix bootstrap studies beyond elastic scattering.

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Phys. Rev. D 114, 076027– Published 28 October, 2026
  • Received 18 May 2026
  • Accepted 9 September 2026
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