A new parametrization for the scalar pion form factors

We derive a new parametrization for the scalar pion form factors that allows us to analyze data over a large energy range via the inclusion of resonances, and at the same time to ensure consistency with the high-accuracy dispersive representations available at low energies. As an application the formalism is used to extract resonance properties of excited scalar mesons from data for \(\bar B^0_s\to J/\psi \pi\pi\). In particular we find for the pole positions of \(f_0(1500)\) and \(f_0(2020)\) \(1465\pm 18 - i (50\pm 9)\,\text{MeV}\) and \(1910\pm 50 - i(199\pm 40)\,\text{MeV}\), respectively. In addition, from their residues we calculate the respective branching ratios into \(\pi\pi\) to be \((58\pm31)\%\) and \((1.3\pm1.8)\%\).