Improved light-cone harmonic oscillator model for the pionic leading-twist distribution amplitude

Abstract

In this paper, we study the pion leading-twist distribution amplitude (DA) ${\ensuremath{\phi}}_{2;\ensuremath{\pi}}(x,\ensuremath{\mu})$ by improving the traditional light-cone harmonic oscillator model within the reconstruction of the function ${\ensuremath{\varphi}}_{2;\ensuremath{\pi}}(x)$. In order to constrain the model parameters, we calculate its moments $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$ in the framework of the QCD background field theory sum rule up to tenth order. Considering the fact that the sum rule of the zeroth moment $⟨{\ensuremath{\xi}}^{0}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$ cannot be normalized, we suggest a more reasonable sum rule formula for $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$. Then, we obtain the values of $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{{\ensuremath{\mu}}_{0}}$ with $n=(2,4,6,8,10)$ at the initial scale ${\ensuremath{\mu}}_{0}=1\text{ }\text{ }\mathrm{GeV}$. The first two moments are $⟨{\ensuremath{\xi}}^{2}{⟩}_{2;\ensuremath{\pi}}{|}_{{\ensuremath{\mu}}_{0}}=0.271\ifmmode\pm\else\textpm\fi{}0.013$ and $⟨{\ensuremath{\xi}}^{4}{⟩}_{2;\ensuremath{\pi}}{|}_{{\ensuremath{\mu}}_{0}}=0.138\ifmmode\pm\else\textpm\fi{}0.010$, and the corresponding Gegenbauer moments are ${a}_{2}^{2;\ensuremath{\pi}}({\ensuremath{\mu}}_{0})=0.206\ifmmode\pm\else\textpm\fi{}0.038$ and ${a}_{4}^{2;\ensuremath{\pi}}({\ensuremath{\mu}}_{0})=0.047\ifmmode\pm\else\textpm\fi{}0.011$, respectively. After fitting the moments $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$, we obtain the appropriate model parameters by using the least squares method. The resultant behavior for the twist-2 pion DA is closer to the AdS/QCD and lattice results, but narrower than that obtained using the Dyson-Schwinger equation. Furthermore, we calculate the pion-photon transition form factors (TFFs) and $B\ensuremath{\rightarrow}\ensuremath{\pi}$ TFFs within the light-cone sum rule approach, which conform with experimental and theoretical results.