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Summary
The paper discusses improving ππ dispersive analyses and resonance determination using Forward Dispersion Relations (FDR). The authors present preliminary results of an improved pion-pion scattering dispersive analysis, including a refined treatment of inelasticities and the introduction of G-waves.
Highlights
- Improved ππ dispersive analysis with FDR constraints up to 1.6 GeV.
- Refined treatment of inelasticities and introduction of G-waves.
- Preliminary results for three reliable solutions corresponding to different datasets.
- Extraction of resonance pole parameters using continued fractions.
- No evidence for the ρ(1250) resonance.
- Improved precision in the determination of resonance parameters.
- Results are stable against variations in the analysis parameters.
Key Insights
- The use of FDR constraints up to 1.6 GeV allows for a more precise determination of the ππ scattering amplitude, particularly at higher energies.
- The introduction of G-waves is necessary to describe the interaction up to higher energies, and their inclusion improves the overall fit to the data.
- The continued fraction method provides a robust and model-independent way to extract resonance pole parameters from the FDR output.
- The absence of evidence for the ρ(1250) resonance suggests that its existence may be doubtful.
- The improved precision in the determination of resonance parameters has implications for our understanding of the light meson spectrum.
- The stability of the results against variations in the analysis parameters gives confidence in the reliability of the method.
- The results of this analysis have the potential to shed new light on the long-standing problem of the σ meson and its relationship to the f0(500) resonance.
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Citation
Peláez, J. R., Rabán, P., & de Elvira, J. R. (2024). Improving $\pi\pi$ dispersive analyses and resonance determination with Forward Dispersion Relations (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.17932