Shallow trimers of two identical fermions and one particle in resonant regimes

We consider two identical fermions interacting in the p-wave channel. Each fermion also interacts with another particle in the vicinity of an s-wave resonance. We find that in addition to the Kartavtsev-Malykh universal trimer states resulting from the s-wave particle-fermion interaction, the fermion-fermion p-wave interaction induces one or two shallow trimers in a large domain of the control parameters, including a borromean regime where the ground-state trimer exists in the absence of dimer at any mass ratio between the fermions and the particle. A generic picture of the trimer spectrum emerges from this work in terms of the low-energy parameters of the interactions.