Global parametrizations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math> scattering with dispersive constraints: Beyond the S0 wave

We provide new global parametrizations of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>π</a:mi><a:mi>π</a:mi><a:mo stretchy="false">→</a:mo><a:mi>π</a:mi><a:mi>π</a:mi></a:mrow></a:math> scattering for the S2, P, D, F, and G partial waves up to at least 1.8 GeV, easy to implement for phenomenological use. With earlier S0-wave parametrizations, slightly updated here, they reproduce previous partial wave dispersion analyses up to the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>π</d:mi><d:mi>ω</d:mi></d:math> threshold. In addition, these new parametrizations have improved their description of recent P-wave data, the inelasticity in various waves, and their fulfillment of Roy-like and forward dispersion relations. The latter now test very high partial waves and have an improved matching with the Regge regime, extending those with P-wave contributions up to 1.6 GeV. Above 1.6 GeV and up to 1.8 GeV, or sometimes somewhat beyond, the parametrizations are simple unconstrained fits to data.