Complementary $CP$ violation induced by $T$-odd and $T$-even correlations

In this letter, we propose a novel approach to concurrently measure the complementary $CP$ violation observables induced by $T$-odd correlations and their corresponding $T$-even counterparts, where $T$ represents time reversal. Our analysis demonstrates that $T$-odd and -even correlations, when satisfying specific conditions, result in cosine and sine strong phase dependencies of the corresponding $CP$ violation, respectively. Additionally, we identify pairs of these $CP$ violation observables in hadron decays depend on precisely the same strong phases within the helicity amplitude scheme. This complementarity effectively reduces the strong phase reliance in the study of $CP$ violation, while also mitigating the risk of suppressed $CP$ violation due to exceptionally small strong phases. Furthermore, our proposal holds potential for uncovering $CP$ violation in baryon decays that have not yet been observed in experiments.