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 $${\bar{B}}^0_s\rightarrow J/\psi \pi \pi $$. 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 $$(58\pm 31)\%$$ and $$(1.3\pm 1.8)\%$$