Exploring New Physics in $D_{(s)}^+\rightarrow\eta^{(\prime)}\bar{\ell}\nu_{\ell}$ Decays

The observation of anomalies in the charged current $b\rightarrow c\bar{\ell}\nu_{\ell}$ transitions hints the possibility of the existence of new physics beyond the standard model. Inspired by the work done in the beauty quark sector, we explore new physics in the charm quark sector with $c \rightarrow (s,d)\bar{\ell}\nu_{\ell}$ charged current transitions. We analyze the decay modes $D_{(s)}^+ \to \eta^{(')} \bar{\ell} \nu_{\ell}$ within an effective Lagrangian framework which includes both standard model and new physics contributions. We use the available experimental measurements of the semileptonic $D$ meson decays to constrain the parameter space of new physics couplings. We then investigate the effects of new physics on four linearly independent observables, the branching fraction, forward-backward asymmetry, lepton polarization and convexity parameter.