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 ${ \cal P}_{ t,0}^\pi(0) = 0.688^{ +0.020}_{ -0.024}$, ${ \cal P}_{ t,0}^K(0)=0.780^{ +0.024}_{ -0.029}$. 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 ${ \cal P}_{ t,0}^{ \pi,K}(0)$ is less than $3\%$. After extrapolating the LCSR predictions for these HFFs to whole $q^2$-region, we obtain the decay widths for semileptonic decay processes $D\to P\ell\nu_\ell$, which are consistent with BES-III collaboration predictions within errors. After considering the $D^{ +}/D^{ 0}$-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 $D\to \pi \ell\nu_\ell$ decay process. Finally, we present the forward-backward asymmetry ${ \cal A}_{ \rm FB}^\ell(q^2)$ and lepton convexity parameter ${ \cal C}_F^\ell(q^2)$, 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.
Categories: hep-ph