Searching for $C\!P$ violation through two-dimensional angular distributions in four-body decays of bottom and charmed baryons

It is proposed to search for $C\!P$ violation through the two-fold angular distributions in the four-body decays of bottom and charmed hadrons. The two polar angles in the two-fold angular distributions are correlated, to which the interferences of intermediate resonances are one important origin. These interferences will leave tracks in the two-fold angular distributions, with which the $C\!P$ violation can be studied. Special attention is paid to the case when all the intermediate resonances are different, which is unique to four-body decays. It is suggested to look for $C\!P$ violation in four-body decays such as $\Lambda_b^0\to p \pi^-\pi^+\pi^-$ through the analysis of the two-fold angular distributions. The method proposed in this paper is also widely applicable to other four-body decays processes.