TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.20.2.034
TI  - From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude
PY  - 2026/02/09
UR  - https://scipost.org/SciPostPhys.20.2.034
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 20
IS  - 2
SP  - 034
A1  - Guerrieri, Andrea
AU  - Häring, Kelian
AU  - Su, Ning
AB  - Quantum Chromodynamics (QCD) governs the strong interactions of hadrons, but extracting its physical spectrum remains a significant challenge due to its non-perturbative nature. In this Letter, we introduce a novel data-driven approach that systematically enforces the fundamental principles of analyticity, crossing symmetry, and unitarity while fitting experimental data. Our Bootstrap Fit method combines S-matrix Bootstrap techniques with non-convex numerical optimization, allowing for the construction of a scattering amplitude that adheres to first-principles constraints. We apply this framework to pion-pion scattering, demonstrating that it accurately reproduces low-energy predictions from Chiral Perturbation Theory ($\chi$PT) while also providing a non-perturbative determination of the total cross-section that is consistent with experiment. A key feature of our approach is its ability to dynamically generate physical states, yielding a spectrum of resonances consistent with QCD. Most notably, we predict the existence of a genuine doubly charged tetraquark resonance around 2 GeV, which could be observed in B-meson decays at LHCb. These results establish a robust new pathway for extracting hadronic properties directly from scattering data while enforcing fundamental physical constraints.
ER  -

@Article{10.21468/SciPostPhys.20.2.034,
	title={{From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude}},
	author={Andrea Guerrieri and Kelian Häring and Ning Su},
	journal={SciPost Phys.},
	volume={20},
	pages={034},
	year={2026},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.20.2.034},
	url={https://scipost.org/10.21468/SciPostPhys.20.2.034},
}