Discrete Basis Parameterization for the Gauge Theory Bootstrap

TL;DR

This paper advances the Gauge Theory Bootstrap by employing a discrete basis for the S-matrix, significantly improving computational efficiency and enabling detailed analysis of resonance poles in pion scattering.

Contribution

It introduces a discrete basis parametrization for the GTB framework, reducing computation time and allowing precise analysis of resonance poles.

Findings

Reduced computational time from 30 minutes to under 1 minute.

Enabled detailed analysis of the $ ho(770)$, $f_2(1270)$, and $\sigma$ meson poles.

Facilitated evaluation of the S-matrix on the complex sheet.

Abstract

We implement the Gauge Theory Bootstrap (GTB) framework, initiated by He and Kruczenski in arXiv:2309.12402 and arXiv:2403.10772, using a discrete basis parametrization of the 2-to-2 pion scattering S-matrix, the spectral densities and the form factors. This approach enables a refined analysis of the convergence of the GTB and drastically reduced computational time --from approximately half an hour in arXiv:2403.10772 to under one minute in ours. The discrete basis also facilitates the evaluation of the S-matrix across the complex sheet resulting, in additional of the dominant $\rho(770)$ and $f_2(1270)$ resonances identified in arXiv:2403.10772, in the extraction of the $\sigma$ meson pole located far from the real axis.