CP violation observables in baryon decays

The era of baryon physics is on the horizon with the accumulation of increasing data by collaborations such as LHCb, Belle II, and BESIII. Despite the wealth of data, one of the critical issues in flavor physics, namely CP violation in baryon decays, still awaits experimental confirmation. It is evident that the development of formulas and phenomenological analyses will play a pivotal role in advancing theoretical investigations and experimental measurements in this domain. In this work, we discuss the fundamental definitions and properties of polarization, asymmetry parameters and their associated CP violating observables that may arise in baryon decays. Additionally, we provide a detailed analysis of b-baryon quasi-two and -three body decays based on angular distributions. We highlight the significance of CP asymmetries defined by spin and momentum correlations, as non-trivial spin distributions are expected in baryon decays due to their non-zero polarization in productions and decays. Of particular importance is a complementary relation can be establised for two different types of observables, that are $\mathcal{T}$-even and -odd CP asymmetries respectively. The complementarity indicates that one observable exhibits the sine dependence on strong phase $\Delta\delta$, while another exhibits as cosine. This gives us an distinctive opportunity to avoid the potential large suppression to CP asymmetries from small phase $\Delta\delta$. Two points (\textbf{i}) the exact proof of strong phase dependence behaviour, and (\textbf{ii}) the criterion for complementary observables are clarified. Based on these arguments from theoretical aside, some brief discussions and suggestions on experimental measurements are offered in the final discussions. Lastly, we present a pedagogical introduction to angular distribution techniques based on helicity descriptions for both two and three body decays.