A U-spin prediction for the CP-forbidden transition $e^{+}{e}^{-}\to D^0{\bar{D}}^0\to (K^{+}{K}^{-}{)}_D({\pi }^{+}{\pi }^{-}{)}_D$

Abstract

The LHCb Collaboration has recently reported the discovery of direct CP violation in combined $D^0\to K^{+}{K}^{-}$ and $D^0\to {\pi }^{+}{\pi }^{-}$ decay modes at the $5.3\sigma$ level. Assuming U-spin symmetry (i.e., $d\leftrightarrow s$ interchange symmetry) for the strong-interaction parts of these two channels, we find that their corresponding direct CP-violating asymmetries are ${\mathcal{A}}_{\mathrm{CP}}^{}(K^{+}{K}^{-})\simeq \left(-7.7\pm 1.5\right)\times 10^{-4}$ and ${\mathcal{A}}_{\mathrm{CP}}^{}({\pi }^{+}{\pi }^{-})\simeq \left(7.7\pm 1.5\right)\times 10^{-4}$. The CP-forbidden transition $e^{+}{e}^{-}\to D^0{\bar{D}}^0\to {\left(K^{+}{K}^{-}\right)}_D^{}{\left({\pi }^{+}{\pi }^{-}\right)}_D^{}$ on the $\psi (3770)$ resonance is therefore expected to have a rate of $\mathcal{O}(10^{-10})$ or smaller under U-spin symmetry, and it can be observed at a high-luminosity super-$\tau$-charm factory if at least $10^{10}$ pairs of coherent $D^0$ and ${\bar{D}}^0$ events are accumulated.

Comments: 7 pages, 2 figures. Modified version accepted for publication