  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 $(1.3\pm1.8)\%$.
