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

We replace ordinary chiral SU(3)_L * SU(3)_R perturbation theory CHPT_3 by a new theory CHPT_sigma based on a low-energy expansion about an infrared fixed point alpha_IR for 3-flavor QCD. At alpha_IR, the quark condensate <bar{q}q>_vac =\= 0 induces nine Nambu-Goldstone bosons: pi, K, eta and a 0++ QCD dilaton sigma. Physically, sigma appears as the f_0(500) resonance, a pole at a complex mass with real part < m_K. The ΔI = 1/2 rule for nonleptonic K-decays is then a consequence of CHPT_sigma, with a K_S-sigma coupling fixed by data for K_S^0 --> gamma gamma and gamma gamma --> pi pi. We estimate R_IR ~ 5 for the nonperturbative Drell-Yan ratio R = sigma(e+e- --> hadrons)/sigma(e+e- --> mu+mu-) at alpha_IR.

preprint2012arXivOpen access
R. J. CrewtherLewis C. Tunstall
hep-phnucl-th
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R. J. CrewtherLewis C. Tunstall

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