CP Violation in $D^0\rightarrow K_SK_S$

TL;DR

This paper estimates the direct CP asymmetry in the decay $D^0 ightarrow K_SK_S$ within the Standard Model, predicting a maximum of 1.1%, and discusses potential signs of new physics if future measurements exceed this bound.

Contribution

It provides the first perturbative estimate of the penguin annihilation amplitude and constrains the CP asymmetry in $D^0 ightarrow K_SK_S$ decay.

Findings

Predicted CP asymmetry $oxed{ ext{≤} 1.1 ext{ extperthousand}}$ at 95% confidence level.

Established that exceeding this bound in future data could indicate new physics.

Linked the size of CP violation to penguin annihilation amplitude and QCD effects.

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.