Semileptonic and nonleptonic weak decays of $$\psi (1S,2S)$$ and $$\eta _{c}(1S,2S)$$ to $$D_{(s)}$$ in the covariant light-front approach
Zhi-Jie Sun (School of Sciences, Institute of Theoretical Physics, Henan University of Technology, Zhengzhou, Henan, 450052, China); Zhi-Qing Zhang (School of Sciences, Institute of Theoretical Physics, Henan University of Technology, Zhengzhou, Henan, 450052, China); You-Ya Yang (School of Sciences, Institute of Theoretical Physics, Henan University of Technology, Zhengzhou, Henan, 450052, China); Hao Yang (School of Sciences, Institute of Theoretical Physics, Henan University of Technology, Zhengzhou, Henan, 450052, China)
In addition to the strong and electromagnetic decay modes, the $$\psi (1S,2S)$$ and $$\eta _{c}(1S,2S)$$ 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 $$J/\Psi $$ weak decays have been measured at BESIII. Researching for these charmonium weak decays to $$D_{(s)}$$ 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 $$\psi (1S,2S)$$ and $$\eta _{c}(1S,2S)$$ to $$D_{(s)}$$ within the covariant light-front quark model (CLFQM). With form factors of the transitions $$\psi (1S,2S)\rightarrow D_{(s)}$$ and $$\eta _{c}(1S,2S)\rightarrow D_{(s)}$$ calculated under the CLFQM, we predict and discuss some physical observables, such as the branching ratios, the longitudinal polarizations $$f_{L}$$ and the forward–backward asymmetries $$A_{FB}$$ . One can find that the Cabibbo-favored semi-leptonic decay channels $$\psi (1\,S,2\,S)\rightarrow D_{s}^{-}\ell ^{+}\nu _{\ell }$$ with $$\ell =e,\mu $$ and the nonleptonic decay modes $$\psi (1S,2S)\rightarrow D_{s}^{-}\rho ^{+}$$ have relatively large branching ratios of the order $$\mathcal {O}(10^{-9})$$ , which are most likely to be accessible at the future high-luminosity experiments.