| Summary: | Abstract In addition to the strong and electromagnetic decay modes, the $$\psi (1S,2S)$$ ψ ( 1 S , 2 S ) and $$\eta _{c}(1S,2S)$$ η c ( 1 S , 2 S ) can also decay via the weak interaction. Such weak decays can be detected by the high-luminosity heavy-flavor experiments. At present, some of the semileptonic and nonleptonic $$J/\Psi $$ J / Ψ weak decays have been measured at BESIII. Researching for these charmonium weak decays to $$D_{(s)}$$ D ( s ) meson can provide a platform to check of the standard model (SM) and probe new physics (NP). So we investigate the semileptonic and nonleptonic weak decays of $$\psi (1S,2S)$$ ψ ( 1 S , 2 S ) and $$\eta _{c}(1S,2S)$$ η c ( 1 S , 2 S ) to $$D_{(s)}$$ D ( s ) within the covariant light-front quark model (CLFQM). With form factors of the transitions $$\psi (1S,2S)\rightarrow D_{(s)}$$ ψ ( 1 S , 2 S ) → D ( s ) and $$\eta _{c}(1S,2S)\rightarrow D_{(s)}$$ η c ( 1 S , 2 S ) → D ( s ) calculated under the CLFQM, we predict and discuss some physical observables, such as the branching ratios, the longitudinal polarizations $$f_{L}$$ f L and the forward–backward asymmetries $$A_{FB}$$ A FB . One can find that the Cabibbo-favored semi-leptonic decay channels $$\psi (1\,S,2\,S)\rightarrow D_{s}^{-}\ell ^{+}\nu _{\ell }$$ ψ ( 1 S , 2 S ) → D s - ℓ + ν ℓ with $$\ell =e,\mu $$ ℓ = e , μ and the nonleptonic decay modes $$\psi (1S,2S)\rightarrow D_{s}^{-}\rho ^{+}$$ ψ ( 1 S , 2 S ) → D s - ρ + have relatively large branching ratios of the order $$\mathcal {O}(10^{-9})$$ O ( 10 - 9 ) , which are most likely to be accessible at the future high-luminosity experiments.
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