A new parametrization for the scalar pion form factors

Abstract

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

Comments: 18 pages, 11 figures; v2: discussion+figure on pi pi --> K Kbar added, version published in EPJC