Unquenching the Scalar Glueball

Computations in the quenched approximation on the lattice predict the lightest glueball to be a scalar in the $1.5–1.8\mathrm{GeV}$ region. Here we calculate the dynamical effect the coupling to two pseudoscalars has on the mass, width, and decay pattern of such a scalar glueball. Modeling this nonperturbative interaction reveals that, if the pure glue state has a width to two pseudoscalars of $\sim 100\mathrm{MeV}$ as predicted on the lattice, the resulting hadron has a width to these channels of only $\sim 30\mathrm{MeV}$ with a large $\eta \eta$ component. Experimental results need to be reanalyzed in light of these predictions to decide if either the $f_0\left(1500\right)$ or an $f_0\left(1710\right)$ coincides with this dressed glueball.