We discuss pairing of light-matter bosons under effective spin-orbit (SO) coupling in twodimensional semiconductors. The SO coupling is shown to induce dynamical broadening of a twobody bound state. Application of a transverse magnetic field yields the rich Feshbach resonance phenomenology. We predict quantum bosonic halos with a synthetic angular momentum Lz = ±2 . The d-wave-like dressing of the nominally s-wave bound state is induced by SO coupling to the continuum in the open channel. The fundamental properties of the emergent quantum number remain to be explored.