An 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 ${\varphi }_{2;\pi }(x,\mu )$ by improving the traditional light-cone harmonic oscillator model within the reconstruction of the function ${\phi }_{2;\pi }(x)$. In order to constraining the model parameters, we calculate its moments $⟨{\xi }^n{⟩}_{2;\pi }{|}_{\mu }$ in the framework of QCD background field theory sum rule (BFTSR) up to $10^{\mathrm{th}}$ order. Considering the fact that the sum rule of the $0^{\mathrm{th}}$ moment $⟨{\xi }^0{⟩}_{2;\pi }{|}_{\mu }$ cannot be normalized, we suggest a more reasonable sum rule formula for $⟨{\xi }^n{⟩}_{2;\pi }{|}_{\mu }$. Then, we obtain the values of $⟨{\xi }^n{⟩}_{2;\pi }{|}_{{\mu }_0}$ with $n=(2,4,6,8,10)$ at the initial scale ${\mu }_0=1\mathrm{GeV}$. The first two moments are: $⟨{\xi }^2{⟩}_{2;\pi }{|}_{{\mu }_0}=0.271\pm 0.013$, $⟨{\xi }^4{⟩}_{2;\pi }{|}_{{\mu }_0}=0.138\pm 0.010$; and the corresponding Gegenbauer moments are $a_2^{2;\pi }({\mu }_0)=0.206\pm 0.038$, $a_4^{2;\pi }({\mu }_0)=0.047\pm 0.011$, respectively. After fitting the moments $⟨{\xi }^n{⟩}_{2;\pi }{|}_{\mu }$, we obtained the appropriate model parameters by using the least square method. The resultant behavior for twist-2 pion DA is more closely to the AdS/QCD and lattice result, but is narrower than that by Dyson-Schwinger equation. Furthermore, we calculate the pion-photon transition form factors (TFF) and $B\to \pi$ TFF within light-cone sum rule approach, which are conform with experimental and theoretical results.

15 pages, 6 figures, matches the version to appear in PRD