$D\rightarrow π$ transitions from QCD Light-Cone Sum Rules with the chiral currents

Abstract

We present a systematic study of the transition form factors for the semileptonic decays $D\rightarrow Pe^{+}v_{e}$ and $D\rightarrow Pμ^{+}\bar{v}_μ$ using QCD light-cone sum rules with chiral currents, with emphasis on the nonperturbative structure of the pion. The distribution amplitudes of the meson $π$, including twist-2 and higher-twist components, are analyzed and incorporated in our computation, employing both Gegenbauer polynomial expansions and the Basis Light-Front Quantization (BLFQ) method, where the latter yields a distribution that rapidly converges to the asymptotic form. Two relations linking transition form factors are derived and found to be consistent with the chiral symmetry of QCD. Our numerical predictions for the $D$-to-pion form factors agee well with BES\uppercase\expandafter{\romannumeral3} measurements and lattice QCD calculations. Furthermore, the differential decay widths obtained thereby for the $D$-to-pion decay also show consistency with the BES\uppercase\expandafter{\romannumeral3} data in the high-momentum-transfer ($q$) region with the $q^{2}>1\ \rm{GeV^2}$, implying new opportunities for the precise extraction of the CKM matrix element and the exploration of physics beyond the Standard Model.