Origin of \Delta I=1/2 Rule for Kaon Decays: QCD Infrared Fixed Point
Abstract
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 \Delta I = 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.
Keywords
Cite
@article{arxiv.1203.1321,
title = {Origin of \Delta I=1/2 Rule for Kaon Decays: QCD Infrared Fixed Point},
author = {R. J. Crewther and Lewis C. Tunstall},
journal= {arXiv preprint arXiv:1203.1321},
year = {2012}
}
Comments
5 pages, 3 figures. v3: new remarks about f_0(500) pole amplitudes and CHPT_3, expanded discussion on convergence of chiral-scale expansion, added emphasis on chiral SU(2) limit, references adjusted, conclusions unchanged