S-matrix bootstrap for resonances

TL;DR

This paper establishes analytical bounds on how strongly unstable particles can couple to asymptotic states in 1+1 dimensional quantum field theories, and develops a numerical method that can be extended to higher dimensions.

Contribution

It derives an analytical bound on resonance couplings and introduces a numerical framework that can be generalized to 3+1 dimensions.

Findings

Analytical bound on resonance coupling strength.

Numerical method for bound recovery.

Framework extendable to higher dimensions.

Abstract

We study the $2\rightarrow2$ $S$-matrix element of a generic, gapped and Lorentz invariant QFT in $d=1+1$ space time dimensions. We derive an analytical bound on the coupling of the asymptotic states to unstable particles (a.k.a. resonances) and its physical implications. This is achieved by exploiting the connection between the S-matrix phase-shift and the roots of the S-matrix in the physical sheet. We also develop a numerical framework to recover the analytical bound as a solution to a numerical optimization problem. This later approach can be generalized to $d=3+1$ spacetime dimensions.