An improved light-cone harmonic oscillator model for the $\varphi$-meson longitudinal leading-twist light-cone distribution amplitude

Abstract

In the present paper, we study the properties of $\varphi$-meson longitudinal leading-twist light-cone distribution amplitude ${\varphi }_{2;\varphi }^{\Vert }(x,\mu )$ by starting from a light-cone harmonic oscillator model for its wavefunction. To fix the input parameters, we derive the first ten $\xi$-moments of ${\varphi }_{2;\varphi }^{\Vert }(x,\mu )$ by using the QCD sum rules approach under the background field theory. The shape of ${\varphi }_{2;\varphi }^{\Vert }(x,\mu =2\mathrm{GeV})$ tends to be a single-peak behavior, which is consistent with the latest Lattice QCD result. As an application, we derive the $D_s^{+}\to \varphi$ transition form factors (TFFs) by using the light-cone sum rules approach. At the large recoil point, we obtain $A_1(0)=0.512_{-0.020}^{+0.030}$, $A_2(0)=0.402_{-0.067}^{+0.078}$, $A_0(0)=0.596_{-0.020}^{+0.025}$ and $V(0)=0.882_{-0.036}^{+0.040}$. As for the two typical ratios ${\gamma }_V$ and ${\gamma }_2$, we obtain ${\gamma }_V=1.723_{-0.021}^{+0.023}$ and ${\gamma }_2=0.785_{-0.104}^{+0.100}$. After extrapolating those TFFs to the physically allowable region, we then obtain the transverse, longitudinal and total decay widths for semi-leptonic decay $D_s^{+}\to \varphi {\ell }^{+}{\nu }_{\ell }$. Then the branching fractions are $\mathcal{B}(D_s^{+}\to \varphi e^{+}{\nu }_e)=(2.367_{-0.132}^{+0.256})\times 10^{-3}$ and $\mathcal{B}(D_s^{+}\to \varphi {\mu }^{+}{\nu }_{\mu })=(2.349_{-0.132}^{+0.255})\times 10^{-3}$, which show good agreement with the data issued by the BESIII, the CLEO, and the BABAR Collaborations. We finally calculate $D_s^{+}\to \varphi {\ell }^{+}{\nu }_{\ell }$ polarization and asymmetry parameters.

32 pages, 7 figures, comments welcome