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An Analytical Toolkit for the S-matrix Bootstrap

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arxiv 2006.08221 v1 pith:VM3CD73A submitted 2020-06-15 hep-th

Miguel Correia , Amit Sever , Alexander Zhiboedov This is my paper · ORCID
classification hep-th
keywords amplitudeanalyticalbootstrapexpansionmatrixscatteringspinallows
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We revisit analytical methods for constraining the nonperturbative $S$-matrix of unitary, relativistic, gapped theories in $d \geq 3$ 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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Cited by 11 Pith papers

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