The first experimental evidence for direct $CP$ violation in charm-quark decays has recently been presented by the LHCb collaboration in the difference between the $D\to K^{+}{K}^{-}$ and $D\to {\pi }^{+}{\pi }^{-}$ time-integrated $CP$ asymmetries. We estimate the size of the effects that can be expected within the Standard Model and find that at leading order in $1/m_c$ they are an order of magnitude smaller. However, tree-level annihilation type amplitudes are known to be large experimentally. This implies that certain formally $1/m_c$-suppressed penguin amplitudes could plausibly account for the LHCb measurement. Simultaneously, the flavor-breaking parts of these amplitudes could explain the large difference between the $D\to K^{+}{K}^{-}$ and $D\to {\pi }^{+}{\pi }^{-}$ decay rates.

• Received 23 November 2011

DOI:https://doi.org/10.1103/PhysRevD.86.014023