CP Violation in Charmed Meson Decays into Final States with $\eta'$

We derive Standard Model predictions for the CP asymmetries of singly-Cabibbo suppressed $D\rightarrow P\eta'$ decays, where $P=K,\pi,\eta$. Our predictions are based on the approximate SU(3)$_F$ symmetry of QCD and include first-order symmetry-breaking effects in a systematic way. The underlying symmetry leads to correlations between different decay modes. To this end we predict the correlations between $a_{\rm CP}^{\rm dir}(D^+\to \pi^+ \eta')$ and $a_{\rm CP}^{\rm dir}(D_s^+ \to K^+ \eta')$ as well as $a_{\rm CP}^{\rm dir}(D^0\to \pi^0 \eta')$ and $a_{\rm CP}^{\rm dir}(D^0\to \eta \eta')$. Our results can be used to probe the Standard Model with future measurements by LHCb, Belle II and BESIII. At the same time, such future measurements permit the extraction of the key theory parameter related to the ratio of color-suppressed to color-favoured contributions to the decay amplitudes. Future data on both branching ratios and CP asymmetries will automatically improve our predictions and thereby also their sensitivity to physics beyond the Standard Model.