Remote Nordic HET seminar: Miguel Correia

Speaker: Miguel Correia

Title: An analytical toolkit for the S-matrix bootstrap

Abstract: I will revisit analytical methods for constraining the nonperturbative S-matrix of unitary, relativistic, gapped theories in d > 2 spacetime dimensions. Assuming extended analyticity of the two-to-two scattering amplitude together with elastic unitarity I will prove Aks' theorem: Particle production is necessary if there is scattering. To quantify the required inelasticity we consider 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.