$CP$ violation in charmed hadron decays into neutral kaons

TL;DR

This paper identifies a new $CP$ violation effect in charmed hadron decays into neutral kaons caused by interference effects, which is larger than previously known direct $CP$ asymmetries and can be experimentally measured.

Contribution

It introduces a novel $CP$ violation effect in charmed hadron decays involving neutral kaons, overlooked in prior studies, and proposes an observable to detect it.

Findings

Estimated $CP$ violation effect of order $10^{-3}$

Proposed a new observable based on asymmetry differences

Facilitates extraction of direct $CP$ asymmetry for new physics searches

Abstract

We find a new $CP$ violating effect in charmed hadron decays into neutral kaons, which is induced by the interference between the Cabibbo-favored and doubly Cabibbo-suppressed amplitudes with the $K^{0}-\overline K^{0}$ mixing. It is estimated to be of order of $\mathcal{O}(10^{-3})$, much larger than the direct $CP$ asymmetry, but missed in the literature. To reveal this new $CP$ violation effect, we propose a new observable, the difference of the $CP$ asymmetries in the $D^{+}\to \pi^{+}K_S^0$ and $D_{s}^{+}\to K^{+} K_S^0$ modes. Once the new effect is determined by experiments, the direct $CP$ asymmetry then can be extracted and used to search for new physics.