From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude
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| Format: | Preprint |
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2024
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| _version_ | 1866909399564419072 |
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| author | Guerrieri, Andrea Häring, Kelian Su, Ning |
| author_facet | Guerrieri, Andrea Häring, Kelian Su, Ning |
| contents | We propose a novel strategy to fit experimental data using a UV complete amplitude ansatz satisfying the constraints of Analyticity, Crossing, and Unitarity. We focus on $ππ$ scattering combining both experimental and lattice data. The fit strategy requires using S-matrix Bootstrap methods and non-convex Particle Swarm Optimization techniques. Using this procedure, we numerically construct a full-fledged scattering amplitude that fits the data and contains the known QCD spectrum that couples to $ππ$ states below $1.4$ GeV. The amplitude constructed agrees below the two-particle threshold with the two-loop $χ$PT prediction. Moreover, we correctly predict the $D_2$ phase shift, the appearance of a spin three state, and the behavior of the high-energy total cross-section. Finally, we find a genuine tetraquark resonance around 2 GeV, which we argue might be detected by looking into the decays of B mesons. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_23333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude Guerrieri, Andrea Häring, Kelian Su, Ning High Energy Physics - Theory High Energy Physics - Lattice High Energy Physics - Phenomenology We propose a novel strategy to fit experimental data using a UV complete amplitude ansatz satisfying the constraints of Analyticity, Crossing, and Unitarity. We focus on $ππ$ scattering combining both experimental and lattice data. The fit strategy requires using S-matrix Bootstrap methods and non-convex Particle Swarm Optimization techniques. Using this procedure, we numerically construct a full-fledged scattering amplitude that fits the data and contains the known QCD spectrum that couples to $ππ$ states below $1.4$ GeV. The amplitude constructed agrees below the two-particle threshold with the two-loop $χ$PT prediction. Moreover, we correctly predict the $D_2$ phase shift, the appearance of a spin three state, and the behavior of the high-energy total cross-section. Finally, we find a genuine tetraquark resonance around 2 GeV, which we argue might be detected by looking into the decays of B mesons. |
| title | From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude |
| topic | High Energy Physics - Theory High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2410.23333 |