2004/11/30 by J. R. Peláez, J. R. Pelaez, F. J. Yndurain +1 · 3 citations
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph
paper · pdf · doi:10.1103/physrevd.71.074016
published as Phys.Rev. D71 (2005) 074016 · Version to be published in Phys. Rev. D. Plain TeX file. (minor changes). 16 figures (some multiple)
arxiv created 2005/03/03 · openalex publication_date 2005/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We obtain reliable \ensuremathπ\ensuremathπ scattering amplitudes consistent with experimental data, both at low and high energies, and fulfilling appropriate analyticity properties. We do this by first fitting experimental low energy (s1/2\ensuremath≤1.42 GeV) phase shifts and inelasticities with expressions that incorporate analyticity and unitarity. In particular, for the S wave with isospin 0, we discuss in detail several sets of experimental data. This provides low energy partial wave amplitudes that summarize the known experimental information. Then, we impose Regge behavior as follows from factorization and experimental data for the imaginary parts of the scattering amplitudes at higher energy, and check fulfillment of dispersion relations up to 0.925 GeV. This allows us to improve our fits. The ensuing \ensuremathπ\ensuremathπ scattering amplitudes are then shown to verify dispersion relations up to 1.42 GeV, as well as s\ensuremath-t\ensuremath-u crossing sum rules and other consistency conditions. The improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test chiral perturbation theory calculations, pionium decays, or use as input for CP-violating K decays. In this respect, we find [a0(0)\ensuremath-a0(2)]2=(0.077\ifmmode±\else\textpm\fi0.008)M_\ensuremathπ^\ensuremath-2 and \ensuremathδ0(0)(mK2)\ensuremath-\ensuremathδ0(2)(mK2)=52.9\ifmmode±\else\textpm\fi1.6o.