Universal trimers with p-wave interactions and the faux-Efimov effect

An unusual class of $p$-wave universal trimers with symmetry $L^{\Pi}=1^{\pm}$ is identified, for both a two-component fermionic trimer with $s$- and $p$-wave scattering length close to unitarity and for a one-component fermionic trimer at $p$-wave unitarity. Moreover, fermionic trimers made of atoms with two internal spin components are found for $L^{\Pi}=1^{\pm}$, when the $p$-wave interaction between spin-up and spin-down fermions is close to unitarity and/or when the interaction between two spin-up fermions is close to the $p$-wave unitary limit. The universality of these $p$-wave universal trimers is tested here by considering van der Waals interactions in a Lennard-Jones potential with different numbers of two-body bound states; our calculations also determine the value of the scattering volume or length where the trimer state hits zero energy and can be observed as a recombination resonance. The faux-Efimov effect appears with trimer symmetry $L^{\Pi}=1^{-}$ when the two fermion interactions are close to $p$-wave unitarity and the lowest $1/R^2$ coefficient gets modified, thereby altering the usual Wigner threshold law for inelastic processes involving 3-body continuum channels.