Eur. Phys. J. C (2022) 82: 603
https://doi.org/10.1140/epjc/s10052-022-10555-y

Regular Article - Theoretical Physics

$a_1(1260)$-meson longitudinal twist-2 distribution amplitude and the $D\to a_1(1260){\ell }^{+}{\nu }_{\ell }$ decay processes

¹ Department of Physics, Guizhou Minzu University, 550025, Guiyang, People’s Republic of China
² Department of Physics, Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, 401331, Chongqing, People’s Republic of China

^b fuhb@cqu.edu.cn

Received: 23 December 2021
Accepted: 26 June 2022
Published online: 9 July 2022

Abstract

In the paper, we investigate the moments $⟨{\xi }_{2;a_1}^{\Vert ;n}⟩$ of the axial-vector $a_1(1260)$-meson distribution amplitude by using the QCD sum rules approach under the background field theory. By considering the vacuum condensates up to dimension-six and the perturbative part up to next-to-leading order QCD corrections, its first five moments at an initial scale ${\mu }_0=1\mathrm{GeV}$ are $⟨{\xi }_{2;a_1}^{\Vert ;2}⟩{|}_{{\mu }_0}=0.223\pm 0.029$, $⟨{\xi }_{2;a_1}^{\Vert ;4}⟩{|}_{{\mu }_0}=0.098\pm 0.008$, $⟨{\xi }_{2;a_1}^{\Vert ;6}⟩{|}_{{\mu }_0}=0.056\pm 0.006$, $⟨{\xi }_{2;a_1}^{\Vert ;8}⟩{|}_{{\mu }_0}=0.039\pm 0.004$ and $⟨{\xi }_{2;a_1}^{\Vert ;10}⟩{|}_{{\mu }_0}=0.028\pm 0.003$, respectively. We then construct a light-cone harmonic oscillator model for $a_1(1260)$-meson longitudinal twist-2 distribution amplitude ${\varphi }_{2;a_1}^{\Vert }(x,\mu )$, whose model parameters are fitted by using the least squares method. As an application of ${\varphi }_{2;a_1}^{\Vert }(x,\mu )$, we calculate the transition form factors (TFFs) of $D\to a_1(1260)$ in large and intermediate momentum transfers by using the QCD light-cone sum rules approach. At the largest recoil point ($q^2=0$), we obtain $A(0)=0.{130}_{-0.013}^{+0.015}$, $V_1(0)=1.{898}_{-0.121}^{+0.128}$, $V_2(0)=0.{228}_{-0.021}^{+0.020}$, and $V_0(0)=0.{217}_{-0.025}^{+0.023}$. By applying the extrapolated TFFs to the semi-leptonic decay $D^{0(+)}\to a_1^{-(0)}(1260){\ell }^{+}{\nu }_{\ell }$, we obtain $\mathcal{B}(D^0\to a_1^{-}(1260)e^{+}{\nu }_e)=(5.{261}_{-0.639}^{+0.745})\times {10}^{-5}$, $\mathcal{B}(D^{+}\to a_1^0(1260)e^{+}{\nu }_e)=(6.{673}_{-0.811}^{+0.947})\times {10}^{-5}$, $\mathcal{B}(D^0\to a_1^{-}(1260){\mu }^{+}{\nu }_{\mu })=(4.{732}_{-0.590}^{+0.685})\times {10}^{-5}$, $\mathcal{B}(D^{+}\to a_1^0(1260){\mu }^{+}{\nu }_{\mu })=(6.{002}_{-0.748}^{+0.796})\times {10}^{-5}$.