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) ${\varphi }_{p,\sigma }^K$ within the QCD background field approach. The $S{U}_f(3)$-breaking effects are studied in detail under a systematical way, especially the sum rules for the moments of ${\varphi }_{p,\sigma }^K$ 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 ${\varphi }_{p,\sigma }^K$ are $a_{K,p}^1(1\mathrm{GeV})=-0.376_{-0.148}^{+0.103}$, $a_{K,p}^2(1\mathrm{GeV})=0.701_{-0.491}^{+0.481}$, $a_{K,\sigma }^1(1\mathrm{GeV})=-0.160_{-0.074}^{+0.051}$ and $a_{K,\sigma }^2(1\mathrm{GeV})=0.369_{-0.149}^{+0.163}$, respectively. Their normalization parameters ${\mu }_K^p{|}_{1\mathrm{GeV}}=1.188_{-0.043}^{+0.039}$ GeV and ${\mu }_K^{\sigma }{|}_{1\mathrm{GeV}}=1.021_{-0.055}^{+0.036}$ GeV. A detailed discussion on the properties of ${\varphi }_{p,\sigma }^K$ 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 ${\Psi }_{p,\sigma }^K(x,{\mathbf{k}}_{\perp })$ 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.

Comments: 11 pages, 3 figures. To match the printed version. To be published in Communications in Theoretical Physics