SciPost Submission Page
From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude
by Andrea Guerrieri, Kelian Häring, Ning Su
Submission summary
| Authors (as registered SciPost users): | Kelian Häring |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202510_00009v2 (pdf) |
| Date submitted: | Dec. 1, 2025, 10:35 a.m. |
| Submitted by: | Kelian Häring |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational, Phenomenological |
Abstract
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 \textit{analyticity, crossing symmetry, and unitarity} while fitting experimental data. Our \textit{Bootstrap Fit} method combines \textit{S-matrix Bootstrap techniques} with \textit{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 \textit{genuine doubly charged tetraquark resonance} around \textit{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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We are pleased to resubmit our manuscript "From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude" for publication in SciPost Physics.
We would like to thank the editor and the referees for their positive feedback and the constructive comments made on our work. Following their questions and comments we modified the manuscript as detailed in "List of changes". The referee’s questions have been addressed in the dedicated section.
We believe that the revised version addresses the question raised and improves the clarity of the manuscript.
Kind regards,
Kelian Häring (on behalf of the authors)
List of changes
- Figure 3: We have improved the color scheme and clarified the caption to better explain the role of each element in the plot.
- Section II.C: We rephrased section II.C starting from "The physical spectrum is...". We agree that the previous version was potentially confusing regarding which resonances are assumed and which are dynamically generated. We have therefore revised the paragraph to make this distinction explicit.