  Chiral-scale perturbation theory $\chi$PT$_\sigma$ has been proposed as an
alternative to chiral $SU(3)_L\times SU(3)_R$ perturbation theory which
explains the $\Delta I = 1/2$ rule for kaon decays. It is based on a low-energy
expansion about an infrared fixed point in three-flavor QCD. In
$\chi$PT$_\sigma$, quark condensation $\langle\bar q q \rangle_\mathrm{vac}
\neq 0$ induces nine Nambu-Goldstone bosons: $\pi, K, \eta$ and a QCD dilaton
$\sigma$ which we identify with the $f_0(500)$ resonance. Partial conservation
of the dilatation and chiral currents constrains low-energy constants which
enter the effective Lagrangian of $\chi$PT$_\sigma$. These constraints allow us
to obtain new phenomenological bounds on the dilaton decay constant via the
coupling of $\sigma/f_0$ to pions, whose value is known precisely from
dispersive analyses of $\pi\pi$ scattering. Improved predictions for $\sigma
\to \gamma \gamma$ and the $\sigma NN$ coupling are also noted. To test
$\chi$PT$_\sigma$ for kaon decays, we revive a 1985 proposal for lattice
methods to be applied to $K \to \pi$ on-shell.
