$\Delta A_{CP}$ within the Standard Model and beyond

In light of the recent LHCb observation of CP violation in the charm sector, we review standard model (SM) predictions in the charm sector and in particular for $\Delta A_{CP}$. We get as an upper bound in the SM $| \Delta A_{CP} ^{\rm SM}| \leq 3.6 \times 10^{-4}$, which can be compared to the measurement of $\Delta A_{CP} ^{\rm LHCb2019} = (-15.4 \pm 2.9) \times 10^{-4}$. We discuss resolving this tension within an extension of the SM that includes a flavour violating $Z'$ that couples only to $\bar{s}s$ and $\bar{c}u$. We show that for masses below 80 GeV and flavour violating coupling of the order of $10^{-4}$, this model can successfully resolve the tension and avoid constraints from dijet searches, $D^0-\overline{D}^0$ mixing and measurements of the $Z$ width.