Direct CP Violation in D Decays in view of LHCb and CDF Results

Abstract

The LHCb and CDF Collaborations have recently reported evidence for a CP asymmetry around -0.7% in $\Delta A_{CP}$, the difference between $A_{CP}(D^0 \to K^+ K^-)$ and $A_{CP}(D^0 \to \pi^+\pi^-)$. In the Standard Model this effect may be accounted for by enhanced $1/m_c$ corrections in a CP-violating penguin amplitude governed by a Cabibbo-Kobayashi-Maskawa (CKM) factor $V^*_{cb}V_{ub}$. A consistent scheme based on broken flavor SU(3) is presented relating Cabibbo-favored (CF) and singly-Cabibbo-suppressed (SCS) $D$ meson decay rates into two pseudoscalars. Two important ingredients supporting the above interpretation for $\Delta A_{CP}$ are a large exchange amplitude in CF decays which is formally $1/m_c$-suppressed, and a pure $\Delta U=0$ U-spin breaking CP-conserving penguin amplitude involving $V^*_{cs}V_{us}$ and $V^*_{cd}V_{ud}$ which accounts for the difference between the $D^0\to K^+K^-$ and $D^0\to \pi^+\pi^-$ decay rates. The magnitudes of the CP conserving and CP violating penguin amplitudes, where the former involves U-spin breaking at a level of 10%, are shown to be related to each other by the magnitudes of corresponding CKM factors. This simple scheme leads to preferable sign predictions for CP asymmetries in charmed meson decays into two pseudoscalars and to correlations between asymmetries in two pairs of these processes.