| In this paper, we make use of the QCD light-cone sum rule method to study the second moments〈ξp2〉,〈ξσ2〉and the fourth moments〈ξp4〉,〈ξσ4〉and the zero moments'normalization constant m0πp,m0πσof the twist-3 distribution amplitudesφp,φσof the pion.We get their sum rules, make numerical analysis, discuss the influence on them when the continue threshold value sπp or sπσtakes different values. We find , if we take the continue threshold value as sπp = sπσ= 1.69GeV2 without considering the correction to the perturbative partαs, the normalization consta m0πp = 1.01±0.02GeV is greater than the result m0πp = 0.96±0.03GeVobtained previously; when we take the correction to the perturbative partαs into account, the normalization constant m0πp = 1.09±0.03GeV is consistent with previous result m0πp = 1.10±0.08GeV, but is smaller than ( )mπ2 mu + md = 1.48GeV. In addition, we still find the bigger the continue threshold value is , the bigger the corresponding Borel window becomes; and normalization constants m0πp and m0πσwill increase with the continue threshold value increasing, but the the second moments〈ξp2〉,〈ξσ2〉and the fourth moments〈ξp4〉,〈ξσ4〉of the distribution amplitudesφp,φσof the pion will reduce with the continue threshold value increasing. Twist-3 distribution amplitudesφpandφσof the pion can be expanded on the basis of Gegenbauer polynomials, and we can further to calculate the approximate expressions to first few terms in expansion of the distribution amplitudes using the numerical results obtained in the paper.This is the basis of calculating weak form factor from B to pion and further determining the element of CKM matrix.
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