A new parametrization for the scalar pion form factors

TL;DR

This paper introduces a new parametrization for scalar pion form factors that effectively combines high-precision low-energy dispersive data with resonance analysis at higher energies, enabling extraction of scalar meson properties from B meson decay data.

Contribution

The paper presents a novel parametrization method for scalar pion form factors that unifies low-energy dispersive analysis with high-energy resonance modeling, facilitating detailed resonance property extraction.

Findings

Resonance pole positions for $f_0(1500)$ and $f_0(2020)$ determined.

Branching ratios into $ ext{pi} ext{pi}$ calculated for these resonances.

Formalism successfully analyzes $ar B^0_s o J/\psi ext{pi} ext{pi}$ decay data.

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 $\bar B^0_s\to J/\psi \pi\pi$. 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 $(1.3\pm1.8)\%$.