The Phases of the Scalar S-Matrix Island
Joan Elias Miro, Andrea Guerrieri, Mehmet Asim Gumus
TLDR
This paper tightens S-matrix bounds for scalar scattering, revealing distinct phases on the boundary related to UV mechanisms of gapped scalars.
Key contributions
- Tightens non-perturbative bounds for scalar scattering amplitudes via S-matrix bootstrap.
- Analyzes asymptotic Regge behavior and resonance spectrum to uncover boundary physics.
- Discovers universal S-matrix behavior along boundary edges, contrasting with other edges.
- Classifies the boundary into distinct phases linked to different UV mechanisms for gapped scalars.
Why it matters
This work deepens our understanding of fundamental scalar interactions and the structure of allowed S-matrices. The classification of boundary phases provides new insights into how gapped scalars emerge from different UV physics, advancing the S-matrix bootstrap program.
Original Abstract
The two-to-two four-dimensional scattering amplitude of identical scalars obeys rigorous two-sided non-perturbative bounds derived via the modern numerical S-matrix bootstrap. These bounds carve out an allowed region with a rich boundary structure, featuring edges and vertices. In this work we further tighten this region and uncover the physics of its boundary by analyzing the asymptotic Regge behavior of the amplitude and the spectrum of resonances and virtual states. We find that the S-matrices along a given edge exhibit universal behavior, sharply contrasting with that on other edges. This reveals a classification of the boundary into distinct phases, corresponding to different UV mechanisms by which a gapped scalar arises.
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