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_00009v1 (pdf) |
| Date submitted: | Oct. 7, 2025, 10:55 a.m. |
| Submitted by: | Häring, Kelian |
| 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
Current status:
Reports on this Submission
Strengths
1- Tetraquark new prediction. 2- New AI method (PSO) in the numerical toolbox 3- Successful input of experimental multi-particle data 4- Match to chiPT a posteriori 5- Improved understanding of the sigma resonance
Report
The paper easily meets criteria for publication in scipost physics.
Requested changes
One thing that was maybe not discussed: how sensitive is the amplitude and the tetraquark prediction in particular to the choice of inelastic profile? A comment on this would be helpful, as an analysis of this fact would probably require an entire separate study.
It wasn't immediately clear to me how you could do any assumption on the spectrum? How exactly are the resonance input? As exact zeros of the partial waves in the complex plane? That sounds like a dangerous numerical procedure?
Fig. 3 is not so easy to understand on its own, for instance why would a big red cross appear to lie outside of "allowed space", or any kink for that matter. I understand the matter is complex, but maybe the figure or the caption could be improved.
Could you comment more precisely the number of parameters you're fixing and their effect? You mention that it would be good to let the bootstrap figure them all out, but why exactly did you chose the specific parameters you fixed?
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)