Muon mass correction in partial wave analyses of charmed meson semi-leptonic decays

We derive the parameterization formula for partial wave analyses of charmed meson semi-leptonic decays with consideration of the effects caused by the lepton mass. As the proposed super-tau-charm factory will reach much enhanced luminosity and BESIII is taking $\psi (3770)\to D\bar{D}$ data, our results are helpful to improve the measurement precision of future partial wave analyses of charmed meson semi-muonic decays.