$D\to P(\pi ,K)$ helicity form factors within light-cone sum rule approach

In this paper, the $D\to P(\pi ,K)$ helicity form factors (HFFs) are studied by applying the QCD light-cone sum rule (LCSR) approach. The calculation accuracy is up to next-to-leading order (NLO) gluon radiation correction of twist-(2,3) distribution amplitude. The resultant HFFs at large recoil point are ${\mathcal{P}}_{t,0}^{\pi }(0)=0.688_{-0.024}^{+0.020}$, ${\cal P}{t,0}^K(0)=0.780^{+0.024}{-0.029}$. In which, the contributions from three particles of the leading order (LO) are so small that can be safely neglected, and the maximal contribution of the NLO gluon radiation correction for ${\cal P}{t,0}^{\pi,K}(0)$islessthan$3%$. After extrapolating the LCSR predictions for these HFFs to whole $q^2$-region, we obtain the decay widths for semileptonic decay processes $D\to P\mathrm{\ell }{\nu }_{\mathrm{\ell }}$, which are consistent with BES-III collaboration predictions within errors. After considering the $D^{+}\mathrm{/}{D}^0$-meson lifetime, we give the branching fractions of $D\to P\ell\nu\ell$with$\ell = e, \mu$, our predictions also agree with BES-III collaboration within errors, especially for $D\to \pi \mathrm{\ell }{\nu }_{\mathrm{\ell }}$ decay process. Finally, we present the forward-backward asymmetry ${\cal A}_{\rm FB}^\ell(q^2)$andleptonconvexityparameter${\cal C}F^\ell(q^2)$, and further calculate the mean value of these two observations $\langle{\cal A}{\rm FB}^\ell\rangle$and$\langle{\cal C}_F^\ell\rangle$, which may provide a way to test those HFFs in future experiments.