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

Abstract

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 ${\mathcal{P}}_{t,0}^{\pi }(0)=0.688_{-0.024}^{+0.020}$, ${\mathcal{P}}_{t,0}^K(0)=0.780_{-0.029}^{+0.024}$. 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 ${\mathcal{P}}_{t,0}^{\pi ,K}(0)$ 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 ${\mathcal{A}}_{\mathrm{FB}}^{\ell }(q^2)$ and lepton convexity parameter ${\mathcal{C}}_F^{\ell }(q^2)$, and further calculate the mean value of these two observations $⟨{\mathcal{A}}_{\mathrm{FB}}^{\ell }⟩$ and $⟨{\mathcal{C}}_F^{\ell }⟩$, which may provide a way to test those HFFs in future experiments.

Comments: 10 pages, 13 figures