Decoding the Amplitude Pair with Distinct CPV Phases in Charmed Baryon Decays

TL;DR

This paper proposes a method to extract the suppressed $ ext{CP}$ violation amplitude in charmed baryon decays using SU(3) symmetry and current data, identifying key decay channels for experimental study.

Contribution

It introduces a strategy to determine the suppressed $ ext{CP}$ violation amplitude in charmed baryon decays via SU(3) symmetry and current experimental data, highlighting key decay channels.

Findings

$ ext{CP}$ violation amplitude can be up to 10% of tree amplitudes.

Current data suggests a 2.1$\sigma$ significance for the $ ext{CP}$ violation amplitude.

Two decay channels are identified as optimal for experimental $ ext{CP}$ violation studies.

Abstract

In this Letter, we propose a strategy to extract information on the hierarchical amplitude pair in singly Cabibbo-suppressed (SCS) charmed baryon two-body decays, with a dominant amplitude proportional to $\lambda_s = V_{cs}^* V_{us}$ from tree operators and sub-leading one proportional to $\lambda_b = V_{cb}^* V_{ub}$ from both penguin and tree contributions. The coexistence of these two amplitudes is essential for generating nonzero CP violation (CPV) effects. Since the $\lambda_b$ amplitude is strongly suppressed, its experimental determination is highly challenging. However, by exploiting SU(3) flavor symmetry, which relates the well-measured Cabibbo-favored (CF) amplitudes to the SCS tree amplitudes, information on the $\lambda_b$ amplitude can be extracted. Using current experimental data, a conservative analysis yields $\lambda_b$ amplitudes can be as large as about $10\%$ of the corresponding tree amplitudes with a significance of $2.1\sigma$. In addition, the Lee-Yang parameters of these decays provide an independent probe of this elusive term. We further identify two golden decay channels, $\Xi_c^0 \to p K^-$ and $\Xi_c^0 \to \Sigma^+ \pi^-$, which are particularly well suited for experimental studies of CPV.