Investigating $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ decay process within QCD sum rule approach

Abstract

In this paper, the semileptonic decays $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ with $\ell =(e,\mu )$ are investigated by using the light-cone sum rule approach. Firstly, the neutral meson mixing scheme between ${\pi }^0$, $\eta$, ${\eta }^{\prime }$ and pseudoscalar gluonium $G$ is discussed in a unified way, which leads to the direct connection between two different channels for $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ and $D_s^{+}\to \eta {\ell }^{+}{\nu }_{\ell }$ by the ${\pi }^0-\eta$ mixing angle. Then we calculated the $D_s\to {\pi }^0$ transition form factors (TFFs) within QCD light-cone sum rule approach up to next-to-leading order correction. At the large recoil point, we have $f_{+}^{D_s^{+}{\pi }^0}(0)=0.0113_{-0.0019}^{+0.0024}$ and $f_{-}^{D_s^{+}{\pi }^0}(0)=0.0020_{-0.0009}^{+0.0008}$. 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 $a_{{\theta }_{\ell }}(q^2)$, $b_{{\theta }_{\ell }}(q^2)$ and $c_{{\theta }_{\ell }}(q^2)$ are given. The differential decay widths for $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ with respect to $q^2$ and $\cos {\theta }_{\ell }$ are presented, and also lead to the branching fractions $\mathcal{B}(D_s^{+}\to {\pi }^0{e}^{+}{\nu }_e)=2.60_{-0.51}^{+0.57}\times 10^{-5}$ and $\mathcal{B}(D_s^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu })=2.58_{-0.51}^{+0.56}\times 10^{-5}$. These results show well agreement with the recent BESIII measurements and theoretical predictions. Then the differential distributions and integrated predictions for three angular observables, {\it 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 ${\mathcal{R}}_{{\pi }^0/\eta }^{\ell }=1.108_{-0.071}^{+0.039}\times 10^{-3}$.

Comments: 10 pages, 5 figures. Matches version accepted for publication in PRD