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

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 $\mathcal{B}(D^0\to a_1^{-}(1260)e^{+}{\nu }_e)=(5.261_{-0.639}^{+0.745})\times 10^{-5}$, $\mathcal{B}(D^{+}\to a_1^0(1260)e^{+}{\nu }_e)=(6.673_{-0.811}^{+0.947})\times 10^{-5}$, $\mathcal{B}(D^0\to a_1^{-}(1260){\mu }^{+}{\nu }_{\mu })=(4.732_{-0.590}^{+0.685})\times 10^{-5}$, $\mathcal{B}(D^{+}\to a_1^0(1260){\mu }^{+}{\nu }_{\mu })=(6.002_{-0.748}^{+0.796})\times 10^{-5}$.

13 pages, 4 figures, version published in EPJC

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