Contributor info: Mr Kelian Häring

Andrea Guerrieri, Kelian Häring, Ning Su

SciPost Phys. 20, 034 (2026) · published 9 February 2026 | Toggle abstract · pdf

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.

Kelian Häring, Alexander Zhiboedov

SciPost Phys. 16, 034 (2024) · published 26 January 2024 | Toggle abstract · pdf

We review the basic assumptions and spell out the detailed arguments that lead to the bound on the Regge growth of gravitational scattering amplitudes. The minimal extra ingredient compared to the gapped case - in addition to unitarity, analyticity, subexponentiality, and crossing - is the assumption that scattering at large impact parameters is controlled by known semi-classical physics. We bound the Regge growth of amplitudes both with the fixed transferred momentum and smeared over it. Our basic conclusion is that gravitational scattering amplitudes admit dispersion relations with two subtractions. For a sub-class of smeared amplitudes, black hole formation reduces the number of subtractions to one. Finally, using dispersion relations with two subtractions we derive bounds on the local growth of relativistic scattering amplitudes. Schematically, the local bound states that the amplitude cannot grow faster than $s^2$. The results obtained in the paper are valid for $d> 4$ for which the $2\to2$ scattering amplitude is well-defined.