S-matrix bootstrap for resonances

Abstract

We study the $2\to 2$ $S$-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.

arXiv commentMinor typos corrected, matches published version

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• Rigorous bounds on the Analytic $S$-matrix
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• Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d\ge 2$
• Bootstrapping the $a$-anomaly in $4d$ QFTs
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• The QCD $\beta$-function On The String Worldsheet
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• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
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