A Standard Model analysis of $D^0 \to π^- π^+, K^- K^+, K_{\rm S}^0 K_{\rm S}^0$

Abstract

We investigate the Standard Model (SM) description of the singly Cabibbo-suppressed charm decays $D^0\to π^-π^+$, $D^0\to K^-K^+$ and $D^0\to K_{\rm S}^0K_{\rm S}^0$. Using factorisation together with isospin symmetry, we constrain non-factorisable effects and the associated $U$-spin breaking required by the measured branching fractions. We find that corrections of order $50\%$ are sufficient to describe all modes, which although sizeable, are not unexpected for hadronic charm decays. Using the constraints from the branching fractions, we derive SM predictions for the direct CP asymmetry in $D^0\to K_{\rm S}^0K_{\rm S}^0$, finding it to be at most at the per-mille level in our benchmark scenario, providing motivation for future precision measurements.