AbstractWe provide global parameterizations of $$\pi \pi \rightarrow \pi \pi $$ππ→ππ scattering S0 and P partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of $$\pi \pi \rightarrow \pi \pi $$ππ→ππ, both in the real axis up to 1.12 $${\mathrm {\,GeV}}$$GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 $${\mathrm {\,GeV}}$$GeV. Above that energy we just describe the available experimental data. Moreover, the analytic continuations of these global parameterizations also describe accurately the dispersive determinations of the $$\sigma /f_0(500)$$σ/f0(500), $$f_0(980)$$f0(980) and $$\rho (770)$$ρ(770) pole parameters.
Probing modified dispersion relations in vacuum with high-energy γ-ray sources: review and prospects
