CP Violation in $D^0\rightarrow K_SK_S$

Abstract

The direct CP asymmetry $a_{CP}^{\mathrm{dir}}(D^0\rightarrow K_SK_S)$ involves exchange diagrams which are induced at tree level in the Standard Model. Since the corresponding topological amplitude $E_{KK}$ can be large, $D^0\rightarrow K_SK_S$ is a promising discovery channel for charm CP violation. We estimate the penguin annihilation amplitude with a perturbative calculation and extract the exchange amplitude $E_{KK}$ from a global fit to $D$ branching ratios. Our results are further used to predict the size of mixing-induced CP violation. We obtain $\vert a_{CP}^{\mathrm{dir}}(D^0\rightarrow K_SK_S)\vert \leq 1.1\%$ (95\% C.L.). The same bound applies to the nonuniversal part of the phase between the $D\!-\overline{\!D}\,$ mixing and decay amplitudes. If future data exceed our predictions, this will point to new physics or an enhancement of the penguin annihilation amplitude by QCD dynamics. We briefly discuss the implications of these possibilities for other CP asymmetries.