1203.1321 (R. J. Crewther et al.)

Origin of ΔI=1/2 Rule for Kaon Decays: QCD Infrared Fixed Point    [PDF]

R. J. Crewther, Lewis C. Tunstall

We propose that 3-flavor QCD has an infrared fixed point $\alpha_IR$. Ordinary chiral $SU(3)_L \times SU(3)_R$ perturbation theory $\chi PT_3$ is replaced by a new theory $\chi PT_\sigma$ based on a low-energy expansion about $\alpha_IR$, where the quark condensate $<\bar{q}q>_vac \neq 0$ induces nine Nambu-Goldstone bosons: $\pi, K, \eta$ and a 0^{++} QCD dilaton $\sigma$. Physically, $\sigma$ appears as the f_{0}(600) resonance, a pole at a complex mass with real part $\lesssim m_K$. The \Delta I=1/2 rule for non-leptonic K-decays is then a consequence of $\chi PT_\sigma$, with a $K\sigma$ coupling fixed by data for $K_{S}^{0} \to \gamma\gamma$ and $\gamma\gamma \to \pi\pi$. We estimate $R_IR \approx 5$ for the non-perturbative Drell-Yan ratio $R = \sigma(e^{+}e^{-} \to hadrons)/\sigma(e^{+}e^{-} \to \mu^{+}\mu^{-})$ at $\alpha_IR$.

View original: http://arxiv.org/abs/1203.1321