Global parameterization of $\pi \pi$ scattering up to 2 GeV

Understand

We provide global parameterizations of $\pi\pi$ 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 $\pi\pi$, both in the real axis up to 1.12 GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 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 $\sigma/f_0(500)$, $f_0(980)$ and $\rho(770)$ pole parameters.