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The mixing of $\eta-\eta'$ or $\eta-\eta'-G$ is of a great theoreticalinterest, because it concerns many aspects of the underlying dynamics andhadronic structure of pseudoscalar mesons and glueball. Determining the mixingparameters by fitting data is by no means trivial. In order to extract themixing parameters from the available processes where hadrons are involved,theoretical evaluation of hadronic matrix elements is necessary. Thereforemodel-dependence is somehow unavoidable. In fact, it is impossible to extractthe mixing angle from a unique experiment because the model parameters must beobtained by fitting other experiments. Recently $BR(D\to\eta+\bar l+\nu_l)$ and$BR(D_s\to\eta(\eta')+\bar l+\nu_l)$ have been measured, thus we are able todetermine the $\eta-\eta'$ mixing solely from the semileptonic decays ofD-mesons where contamination from the final state interactions is absent. Thuswe hope that the model-dependence of the extraction can be somehow alleviated.Once $BR(D\to\eta'+\bar l+\nu_l)$ is measured, we can further determine all themixing parameters for $\eta-\eta'-G$. As more data are accumulated, thedetermination will be more accurate. In this work, we obtain the transitionmatrix elements of $D_{(s)}\to \eta^{(\prime)}$ using the light-front quarkmodel whose feasibility and reasonability for such processes have been tested.

Determining the $\eta-\eta'$ mixing by the newly measured $BR(D(D_s)\to\eta(\eta')+\bar l+\nu_l$