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

Abstract

In the present paper, we investigate the kaon twist-3 distribution amplitudes (DAs) φKp,σ within the QCD background field approach. The SUf (3)-breaking effects are studied in detail under a systematical way, especially the sum rules for the moments of φKp,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 φKp,σ are a1K,p(1 GeV) = − 0.376+0.103−0.148, a2K,p(1 GeV) = 0.701+0.481−0.491, a1K,σ(1 GeV) = −0.160+0.051−0.074, and a2K,σ(1 GeV) = 0.369+0.163−0.149, respectively. Their normalization parameters μpK|1 GeV = 1.188+0.039−0.043 GeV and μσK|1 GeV = 1.021+0.036−0.055 GeV. A detailed discussion on the properties of φKp,σ 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 ΨKp,σ (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.