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

TL;DR

This work revisits $D_{(s)} \to \eta^{(\prime)} \ell^+ \nu_\ell$ decays using QCD light-cone sum rules to obtain precise $D^{(s)}\to\eta^{(\prime)}$ transition form factors, incorporating high-twist LCDAs and NLO corrections. By employing the quark-flavor mixing scheme and the Bourrely–Caprini–Lellouch (BCL) extrapolation, the authors extract constraints on the $\eta$-$\eta'$ mixing parameters that best describe BESIII data, finding a set with small decay constants and a large mixing angle favorsably consistent with measurements. The analysis demonstrates rapid OPE convergence, with twist-3 two-particle contributions driving chiral enhancement, and shows overall good agreement with experimental differential rates for most channels, though a mild tension remains in $D\to\eta'\ell^+\nu_\ell$ in certain $q^2$ regions. The results provide robust form factors for CKM determinations and offer a stringent test of the $\eta$-$\eta'$ structure and potential gluonic components in charmed-meson semileptonic decays.

Abstract

In light of recent precision measurements from BESIII, we reanalyze the $D, D_s \to η^{(\prime)}$ 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 $η$-$η^\prime$ mixing parameters from the precise experimental data for the $D, D_s \to η^{(\prime)} \ell^+ ν_\ell$ (with $\ell = e, μ$) 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 $D \to η^{(\prime)} \ell^+ ν_\ell$, 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.

Figures (3)

• Figure 1: LCSR predictions of the $D,D_{s}\to \eta^{(\prime)}$ FFs, $f_+(q^2)$ and $f_0(q^2)$, in the whole kinematical region, derived under four $\eta-\eta^\prime$ mixing parameter sets (A, B, C and D). For comparison, the BESIII measurements BESIII:2025hjcBESIII:2023gbnBESIII:2024njj are shown, which are represented by the black dots and blue squares with error bars.
• Figure 2: LCSR predictions of the $D, D_{s} \to \eta^{(\prime)}$ FFs, derived with Set A mixing parameters. Alongside our results, we show for comparison the BESIII measurements BESIII:2025hjcBESIII:2023gbnBESIII:2024njj and other theoretical determinations from the CCQM Ivanov:2019nqd, LFQM Verma:2011yw, and LCSR2015 Duplancic:2015zna.
• Figure 3: LCSR predictions of differential decay rates (in units of $10^{-15}\,\mathrm{GeV}^{-1}$), derived using the Set A mixing parameters, for the decays $D_{(s)}\to \eta^{(\prime)}\ell^+\nu_\ell$. Left panels show the electronic modes with $\ell=e$, while right panels correspond to the muonic modes with $\ell=\mu$.