Abstract
We revisit analytical methods for constraining the nonperturbative S-matrix of unitary, relativistic, gapped theories in d ≥ 3 spacetime dimensions. We assume extended analyticity of the two-to-two scattering amplitude and use it together with elastic unitarity to develop two natural expansions of the amplitude. One is the threshold (non-relativistic) expansion and the other is the large spin expansion. The two are related by the Froissart-Gribov inversion formula. When combined with crossing and a local bound on the discontinuity of the amplitude, this allows us to constrain scattering at finite energy and spin in terms of the low-energy parameters measured in the experiment. Finally, we discuss the modern numerical approach to the S-matrix bootstrap and how it can be improved based on the results of our analysis.
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Correia, M., Sever, A. & Zhiboedov, A. An analytical toolkit for the S-matrix bootstrap. J. High Energ. Phys. 2021, 13 (2021). https://doi.org/10.1007/JHEP03(2021)013
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DOI: https://doi.org/10.1007/JHEP03(2021)013