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

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