Direct CP violation in two-body hadronic charmed meson decays

TL;DR

This paper investigates direct CP violation in two-body hadronic decays of charmed mesons within the Standard Model, using a topological-diagram approach to estimate asymmetries and compare with recent experimental observations.

Contribution

It provides a detailed analysis of direct CP asymmetries in charm decays, incorporating topological amplitudes and long-distance effects, and assesses the Standard Model's capacity to explain observed CP violation.

Findings

Predicted direct CP asymmetry range: 10^{-4} to 10^{-3}.

Long-distance effects dominate in certain decay modes, influencing CP violation.

SM predicts a maximum asymmetry difference of about -0.25%, below experimental values.

Abstract

Motivated by the recent observation of CP violation in the charm sector by LHCb, we study direct CP asymmetries in the standard model (SM) for the singly Cabibbo-suppressed two-body hadronic decays of charmed mesons using the topological-diagram approach. In this approach, the magnitude and the phase of topological weak annihilation amplitudes which arise mainly from final-state rescattering can be extracted from the data. Consequently, direct CP asymmetry $a_{dir}^{\rm (tree)}$ at tree level can be reliably estimated. In general, it lies in the range $10^{-4}<a_{dir}^{\rm (tree)}<10^{-3}$. Short-distance QCD penguins and penguin annihilation are calculated using QCD factorization. Their effects are generally small, especially for $D\to VP$ modes. Since weak penguin annihilation receives long-distance contributions from the color-allowed tree amplitude followed by final-state rescattering, it is expected to give the dominant contribution to the direct CP violation in the decays $D^0\to K^+K^-$ and $D^0\to \pi^+\pi^-$ in which $a_{dir}^{\rm (tree)}$ is absent. The maximal $\Delta a_{CP}^{\rm dir}$, the direct CP asymmetry difference between the above-mentioned two modes, allowed in the SM is around -0.25%, more than $2\sigma$ away from the current world average of $-(0.645\pm 0.180)%$.