Supertwistors and massive particles

•Spin-shell constraints are related to Poincaré Casimirs.•Twistor form of 4D spinning particle for spin N/2N/2.•Twistor proof of scalar/antisymmetric tensor equivalence for 4D spin 0.•Twistor form of 3D particle with arbitrary spin.•Proof of equivalence of N=1N=1 and N=2N=2 BPS massive 4D superparticles.

In the (super)twistor formulation of massless (super)particle mechanics, the mass-shell constraint is replaced by a “spin-shell” constraint from which the spin content can be read off. We extend this formalism to massive (super)particles (with NN-extended space–time supersymmetry) in three and four space–time dimensions, explaining how the spin-shell constraints are related to spin, and we use it to prove equivalence of the massive N=1N=1 and BPS-saturated N=2N=2 superparticle actions. We also find the supertwistor form of the action for “spinning particles” with NN-extended worldline supersymmetry, massless in four dimensions and massive in three dimensions, and we show how this simplifies special features of the N=2N=2 case.