  The new measurement of the muon's anomalous magnetic moment released by the
Muon g-2 experiment at Fermilab sets strong constraints on the properties of
many new particles. Using an effective field theory approach to the
interactions of higher-spin fields, we evaluate the contribution of an
electrically neutral and colour singlet spin-3/2 fermion to $(g-2)_\mu$ and
derive the corresponding constraints on its mass and couplings. These
constraints are then compared with the ones on spin-1/2 fermions, such as the
vector-like leptons that are predicted by various extensions of the Standard
Model, the excited leptons which appear in composite models, as well as the
charginos and neutralinos of supersymmetric theories. Unlike these new spin-1/2
fermions, the spin-3/2 particles generate only small contributions to the muon
anomalous magnetic moment.
