Investigating the Ds+→π0ℓ+νℓ decay process within the QCD sum rule approach

In this paper, the semileptonic decays ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ with $\ensuremath{\ell}=(e,\ensuremath{\mu})$ are investigated using the light cone sum rule approach. Firstly, the neutral meson mixing scheme between ${\ensuremath{\pi}}^{0}$, $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}$ and pseudoscalar gluonium $G$ is discussed in a unified way, which leads to the direct connection between two different channels for ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ and ${D}_{s}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ by the ${\ensuremath{\pi}}^{0}\ensuremath{-}\ensuremath{\eta}$ mixing angle. Then we calculate the ${D}_{s}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}$ transition form factors (TFFs) within the QCD light cone sum rule approach up to next-to-leading order correction. At the large recoil point, we have ${f}_{+}^{{D}_{s}^{+}{\ensuremath{\pi}}^{0}}(0)=0.011{3}_{\ensuremath{-}0.0019}^{+0.0024}$ and ${f}_{\ensuremath{-}}^{{D}_{s}^{+}{\ensuremath{\pi}}^{0}}(0)=0.002{0}_{\ensuremath{-}0.0009}^{+0.0008}$. Furthermore, the TFFs are extrapolated to the whole physical ${q}^{2}$-region by using the simplified $z({q}^{2})$-series expansion. The behaviors of TFFs and related three angular coefficient functions ${a}_{{\ensuremath{\theta}}_{\ensuremath{\ell}}}({q}^{2})$, ${b}_{{\ensuremath{\theta}}_{\ensuremath{\ell}}}({q}^{2})$ and ${c}_{{\ensuremath{\theta}}_{\ensuremath{\ell}}}({q}^{2})$ are given. The differential decay widths for ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ with respect to ${q}^{2}$ and $\mathrm{cos}{\ensuremath{\theta}}_{\ensuremath{\ell}}$ are presented, and also lead to the branching fractions $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{e}^{+}{\ensuremath{\nu}}_{e})=2.6{0}_{\ensuremath{-}0.51}^{+0.57}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}})=2.5{8}_{\ensuremath{-}0.51}^{+0.56}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. These results show good agreement with the recent BESIII measurements and theoretical predictions. Then the differential distributions and integrated predictions for three angular observables, i.e. forward-backward asymmetries, ${q}^{2}$-differential flat terms and lepton polarization asymmetries are given separately. Lastly, we estimate the ratio for different decay channels, ${\mathcal{R}}_{{\ensuremath{\pi}}^{0}/\ensuremath{\eta}}^{\ensuremath{\ell}}=1.10{8}_{\ensuremath{-}0.071}^{+0.039}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.