  Spin-orbit coupled cold atom systems, governed by Hamiltonians that contain
quadratic kinetic energy terms typical for a particle's motion in the usual
Schr\"odinger equation and linear kinetic energy terms typical for a particle's
motion in the usual Dirac equation, have attracted a great deal of attention
recently since they provide an alternative route for realizing fractional
quantum Hall physics, topological insulators, and spintronics physics. The
present work focuses on the three-boson system in the presence of 1D spin-orbit
coupling, which is most relevant to ongoing cold atom experiments. In the
absence of spin-orbit coupling terms, the three-boson system exibits the Efimov
effect: the entire energy spectrum is uniquely determined by the $s$-wave
scattering length and a single three-body parameter, i.e., using one of the
energy levels as input, the other energy levels can be obtained via Efimov's
radial scaling law, which is intimately tied to a discrete scaling symmetry. It
is demonstrated that the discrete scaling symmetry persists in the presence of
1D spin-orbit coupling, implying the validity of a generalized radial scaling
law in five-dimensional space. The dependence of the energy levels on the
scattering length, spin-orbit coupling parameters, and center-of-mass momentum
is discussed. It is conjectured that three-body systems with other types of
spin-orbit coupling terms are also governed by generalized radial scaling laws,
provided the system exhibits the Efimov effect in the absence of spin-orbit
coupling.
