Twist-3 pion and kaon distribution amplitudes from the instanton vacuum   with flavor SU(3) symmetry breaking
  We investigate the twist-3 pion and kaon distribution amplitudes of the pseudoscalar (phi^p_{pi,K}) and pseudotensor (phi^{sigma}_{pi,K}) types, based on the effective chiral action from the instanton vacuum. Effects of flavor SU(3) symmetry breaking are explicitly taken into account. The Gegenbauer moments and the moments of the distribution amplitudes (<xi^m>) are also computed. Our results are summarized as follows: a^p_{2,pi} ~ 0.4, a^p_{1,K} ~ 0.02 and a^p_{2,K} ~ 0.14, and a^{sigma}_{2,pi} ~ 0.02 and a^{sigma}_{1,K} ~ a^{sigma}_{2,K} ~ 0; <xi^2>^p_{\pi} ~ <xi^2>^p_K ~ 0.37 and <xi>^p_K ~ 0, and <xi^2>^{sigma}_{pi} ~ <xi^2>^{sigma}_K ~ 0.20 and <xi>^{sigma}_K ~ 0. We compare our results with those from the QCD sum rules. We also discuss the relevant Wilson coefficients which were analyzed recently in chiral perturbation theory. 
Seung-il Nam and Hyun-Chul Kim