A new parametrization for the scalar pion form factors

Abstract

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 $${\bar{B}}^0_s\rightarrow J/\psi \pi \pi $$ B¯s0→J/ψππ . In particular we find for the pole positions of $$f_0(1500)$$ f0(1500) and $$f_0(2020)$$ f0(2020) $$1465\pm 18 - i (50\pm 9)\,\text {MeV}$$ 1465±18-i(50±9)MeV and $$1910\pm 50 - i(199\pm 40)\,\text {MeV}$$ 1910±50-i(199±40)MeV , respectively. In addition, from their residues we calculate the respective branching ratios into $$\pi \pi $$ ππ to be $$(58\pm 31)\%$$ (58±31)% and $$(1.3\pm 1.8)\%$$ (1.3±1.8)% .