Revisiting the Twist-3 Distribution Amplitudes of K Meson Within the QCD Background Field Approach

In the present paper, we investigate the kaon twist-3 distribution amplitudes (DAs) φ p,σ K within the QCD background field approach. The SU f (3)-breaking effects are studied in detail under a systematical way, especially the sum rules for the moments of φ K p,σ are obtained by keeping all the mass terms in the s-quark propagator consistently. After adding all the uncertainties in quadrature, the first two Gegenbauler moments of φp,σ K are a K,p 1 (1 GeV)=0.376-0.148+0.103, a K,p 2(1 GeV) =0.701-10.491+0.48 , a K,σ1 (1 GeV) = 0.160-0.074+0.051, and a K,σ 2(1 GeV)=0.369-0.149+0.163 , respectively. Their normaliza- tion parameters μ K p |1 GeV=1.188-0.043+0.039 GeV and μ K σ |1 GeV=1.021-0.055+0.036 GeV. A detailed discussion on the properties of φ p,σ K moments shows that the higher-order s-quark mass terms can indeed provide sizable contributions. Furthermore, based on the newly obtained moments, a model for the kaon twist-3 wavefunction Ψ p,σ K (x, k ⊥ ) with a better end-point behavior is constructed, which shall be useful for perturbative QCD calculations. As a byproduct, we make a discussion on the properties of the pion twist-3 DAs.