An analytical toolkit for the S-matrix bootstrap

Miguel Correia, Amit Sever*, Alexander Zhiboedov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number13
JournalJournal of High Energy Physics
Issue number3
StatePublished - Mar 2021


  • Nonperturbative Effects
  • Scattering Amplitudes
  • Space-Time Symmetries


Dive into the research topics of 'An analytical toolkit for the S-matrix bootstrap'. Together they form a unique fingerprint.

Cite this