We show that inclusive single-spin asymmetries (SSAs) with transversely polarized protons or electrons at a future electron ion collider (EIC) are sensitive to new physics contributions to electroweak dipole operators of electrons and quarks. We use the Standard Model Effective Field Theory (SMEFT) to parameterize possible heavy new physics contributions to these couplings. We show that new physics scales at or beyond the TeV-scale can be probed assuming realistic EIC run parameters, and that the transverse spin asymmetries are sensitive to different combinations of the dipole couplings than other measurements such as anomalous magnetic or electric dipole moments. We also study the physics potential of SSAs at a possible future upgrade of the EIC to collide muons and protons. Measurements at such an upgrade could probe the same SMEFT parameters that explain the current anomaly in the muon anomalous magnetic moment, and could also improve current bounds on the muon electric dipole moment.

12 pages, 8 figures