  In this paper, we study the pion leading-twist distribution amplitude
$\phi_{2;\pi}(x,\mu)$ by improving the traditional light-cone harmonic
oscillator model within the reconstruction of the function
$\varphi_{2;\pi}(x)$. In order to constraining the model parameters, we
calculate its moments $\langle\xi^n\rangle_{2;\pi}|_\mu$ in the framework of
QCD background field theory sum rule (BFTSR) up to $10^{\rm th}$ order.
Considering the fact that the sum rule of the $0^{\rm th}$ moment
$\langle\xi^0\rangle_{2;\pi}|_\mu$ cannot be normalized, we suggest a more
reasonable sum rule formula for $\langle\xi^n\rangle_{2;\pi}|_\mu$. Then, we
obtain the values of $\langle\xi^n\rangle_{2;\pi}|_{\mu_0}$ with
$n=(2,4,6,8,10)$ at the initial scale $\mu_0 = 1~{\rm GeV}$. The first two
moments are: $\langle \xi^2\rangle_{2;\pi}|_{\mu_0} = 0.271 \pm 0.013$,
$\langle\xi^4\rangle_{2;\pi}|_{\mu_0} = 0.138 \pm 0.010$; and the corresponding
Gegenbauer moments are $a^{2;\pi}_2(\mu_0) = 0.206 \pm 0.038$,
$a^{2;\pi}_4(\mu_0) = 0.047 \pm 0.011$, respectively. After fitting the moments
$\langle\xi^n\rangle_{2;\pi}|_{\mu}$, 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.

High Energy Physics - Phenomenology