$CP$-violation and $U$-spin symmetry in four-body bottom baryon decays

In view of the recent observation of $CP$-violation in bottom baryon decays, we explore $CP$-asymmetry relations in charmless four-body decays of bottom baryons featuring fully charged hadronic final states. Starting with a general effective Hamiltonian, we derive amplitude relations among various decay modes within the framework of $U$-spin symmetry. These relations lead to symmetry-based predictions for $CP$-violating rate asymmetries in $U$-spin conjugate decay channels. Furthermore, we demonstrate that all leading-order amplitude relations are violated once $U$-spin breaking effects are taken into account.