Twist-3 distribution amplitudes of the pion and kaon from the QCD sum   rules
  Twist-3 distribution amplitudes of the pion and kaon are studied in this paper. We calculate the fist several moments for the twist-3 distribution amplitudes (\phi_{p,\sigma}^\pi and \phi_{p,\sigma}^K) of the pion and kaon by applying the QCD sum rules. Our results show that, (i) the first three moments of \phi_p^K and the first two moments of \phi_p^\pi and \phi_\sigma^{\pi,K} of the pion and kaon can be obtained with 30% uncertainty; (ii) the fourth moment of the \phi_p^\pi and the second moment of the \phi_\sigma^K can be obtained when the uncertainty are relaxed to 35%; (iii) the fourth moment of the \phi_\sigma^\pi can be obtained only when the uncertainty are relaxed to 40%; (iv) we have m_{0\pi}^p=1.10\pm 0.08 {\rm GeV} and m_{0K}^p=1.25\pm 0.15 {\rm GeV} after including the \alpha_s-corrections to the perturbative part. These moments will be helpful for constructing the twist-3 wave functions of the pion and kaon. 
Tao Huang, Ming-Zhen Zhou, Xing-Hua Wu