Chiral Suppression of Scalar-Glueball Decay

Since glueballs are $SU(3{)}_{\mathrm{Flavor}}$ singlets, they should couple equally to $u$, $d$, and $s$ quarks, so that equal coupling strengths to ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ are expected. However, we show that chiral symmetry implies the scalar-glueball amplitude for $G_0\to \overline{q}q$ is proportional to the quark mass, so that mixing with $\overline{s}s$ mesons is enhanced and decays to $K^{+}{K}^{-}$ are favored over ${\pi }^{+}{\pi }^{-}$. Together with evidence from lattice calculations and experiment, this supports the hypothesis that $f_0(1710)$ is the ground state scalar glueball.