The width of $f_{0}(980)$ in isospin-symmetry-breaking decays

Abstract

The scalar meson $f_{0}(980)$ has long posed a perplexing puzzle within the realm of light hadron physics. Conventionally, its mass and width in normal decay processes have been estimated as $M=990\pm20$~MeV/$c^2$ and $\Gamma=40-100$~MeV, respectively. Theoretical explanations regarding the internal structure of $f_{0}(980)$ range from it being a conventional quark-antiquark meson to a tetraquark state, a $K\overline{K}$ molecule, or even a quark-antiquark gluon hybrid. However, a definitive consensus has remained elusive over a considerable duration. Recent observations by the BESIII experiment have unveiled anomalously narrow widths of $f_{0}(980)$ in five independent isospin-symmetry-breaking decay channels. Harnessing these experimental findings, we performed a simultaneous fit to the $\pi\pi$ invariant mass distributions, resulting in a refined determination of the mass and width in isospin-symmetry-breaking decays as $M=990.0\pm0.4(\text{stat})\pm0.1(\text{syst})$~MeV/$c^2$ and $\Gamma=11.4\pm1.1(\text{stat})\pm0.9(\text{syst})$~MeV, respectively. Here, the first errors are statistical and the second are systematic. Furthermore, by employing the parameterized Flatt\'{e} formula to fit the same $\pi\pi$ invariant mass distributions, we ascertained the values of the two coupling constants, $g_{f\pi\pi}$ and $g_{fK\overline{K}}$, as $g_{f\pi\pi}=0.46\pm0.03$ and $g_{fK\overline{K}}=1.24\pm0.32$, respectively. Based on the joint confidence regions of $g_{f\pi\pi}$ and $g_{fK\overline{K}}$, we draw the conclusion that the experimental data exhibit a propensity to favor the $K\overline{K}$ molecule model and the quark-antiquark ($q\bar{q}$) model, while offering relatively less support for the tetraquarks ($q^{2}\bar{q}^{2}$) model and the quark-antiquark gluon ($q\bar{q}g$) hybrid model.