### Speaker

### Description

Three-flavor chiral perturbation theory with $t,b,c$ quarks decoupled tests the infrared limit of three-flavor QCD. The standard theory $\chi$PT$_3$ (before being unitarized) assumes that there is no infrared fixed point $\alpha_{\mathrm{IR}}$. If $\alpha_{\mathrm{IR}}$ exists, we get chiral-scale perturbation theory $\chi$PT$_\sigma$ about a scale-invariant theory where the quark condensate is also a scale condensate with nine Nambu-Goldstone (NG) bosons: a massless $0^{++}$ dilaton $\sigma$ ($f_0(500)$ in the real world) as well as $\pi,K,\eta$. The effective Lagrangian for $\chi$PT$_\sigma$ is the standard one modified by $\sigma$-dependent terms and factors required to give the correct scaling dimensions, and can be systematically extended to include higher-order and electroweak corrections. The most important result is a neat explanation of the $\Delta I=1/2$ puzzle for kaon decays; we propose to test it on the lattice via $K\to \pi$ with both on shell.