An analytical toolkit for the S-matrix bootstrap

DOI10.1007/JHEP03(2021)013zbMATH Open1461.81138arXiv2006.08221MaRDI QIDQ2028221

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Publication date: 31 May 2021

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Abstract: We revisit analytical methods for constraining the nonperturbative $S$-matrix of unitary, relativistic, gapped theories in $dgeq3$ 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.

Full work available at URL: https://arxiv.org/abs/2006.08221

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