Semileptonic decays $D_{(s)}\to {\eta }^{(\prime )}{\ell }^{+}{\nu }_{\ell }$ from QCD Light-Cone Sum Rules

Abstract

In light of recent precision measurements from BESIII, we reanalyze the $D,D_s\to {\eta }^{(\prime )}$ transition form factors using QCD light-cone sum rules, incorporating high-twist contributions and well-established next-to-leading-order QCD corrections. Our analysis confirms the chiral enhancement effect arising from twist-3 light-cone distribution amplitudes of the pseudoscalar mesons, and demonstrates a rapid convergence of the operator product expansion. The resulting high-accuracy form factors enable us to determine the optimal $\eta$-${\eta }^{\prime }$ mixing parameters from the precise experimental data for the $D,D_s\to {\eta }^{(\prime )}{\ell }^{+}{\nu }_{\ell }$ (with $\ell =e,\mu$) differential decay rates. We find that the BESIII data strongly favor a set of mixing parameters, characterized by small decay constants and a large mixing angle, in the quark flavor basis. Notably, the light-cone-sum-rule predictions for the decays $D\to {\eta }^{(\prime )}{\ell }^{+}{\nu }_{\ell }$, induced by weak $c\to d$ current, reach a precision comparable to the BESIII experimental results. Nevertheless, further refined measurements and more accurate form-factor determinations will be essential to scrutinize the potential role of gluonic components in charmed meson semileptonic decays.

Comments: 25 pages, 6 tables, 3 figures