The Standard Model confronts CP violation in $D^0 \to \pi^+\pi^-$ and $D^0 \to K^+K^-$

Abstract

The recently measured direct CP asymmetries in the processes $D^0\to \pi^+\pi^-$ and $D^0\to K^+K^-$ show a significant deviation from the naive Standard Model expectation. Using a general parameterization of the decay amplitudes, we show that the measured branching ratios imply large SU(3) breaking and large violations of the naive $1/N_c$ counting. Furthermore, rescattering constrains the I=0 amplitudes in the $\pi\pi$ and $KK$ channels. Combining all this information, we show that, with present errors, the observed asymmetries are marginally compatible with the Standard Model. Improving the experimental accuracy could lead to an indirect signal of new physics.