The consequences of on-shell supersymmetry are studied for scattering amplitudes with massive particles in four dimensions. Using the massive version of the spinor-helicity formalism, the supersymmetry transformations relating products of on-shell states are derived directly from the on-shell supersymmetry algebra for any massive representation. Solutions to the resulting Ward identities can be constructed as functions on the on-shell superspaces that are obtained from the coherent-state method. In simple cases, it is shown that these superspaces allow one to construct explicitly supersymmetric scattering amplitudes. Supersymmetric on-shell recursion relations for tree-level superamplitudes with massive particles are introduced. As examples, simple supersymmetric amplitudes are constructed in Supersymmetric Quantum Chromodynamics (SQCD), the Abelian Higgs model, the Coulomb branch of $\mathcal{N}=4$, QCD with an effective Higgs-gluon coupling and for massive vector-boson currents.

• Received 21 April 2011

DOI:https://doi.org/10.1103/PhysRevD.84.065006