On the EFT of Dyon-Monopole Catalysis

Monopole-fermion (and dyon-fermion) interactions provide a famous example where scattering from a compact object gives a cross section much larger than the object's geometrical size. This underlies the phenomenon of monopole catalysis of baryon-number violation because the reaction rate is much larger in the presence of a monopole than in its absence. It is sometimes claimed to violate the otherwise generic requirement that short distance physics decouples from long-distance observables -- a property that underpins the general utility of effective field theory (EFT) methods. Decoupling in this context is most simply expressed using point-particle effective field theories (PPEFTs) designed to capture systematically how small but massive objects influence their surroundings when probed only on length scales large compared to their size. These have been tested in precision calculations of how nuclear properties affect atomic energy levels for both ordinary and pionic atoms. We adapt the PPEFT formalism to describe low-energy $S$-wave dyon-fermion scattering with a view to understanding whether large catalysis cross sections violate decoupling (and show why they do not). We also explore the related but separate issue of the long-distance complications associated with polarizing the fermion vacuum exterior to a dyon and show in some circumstances how PPEFT methods can simplify calculations of low-energy fermion-dyon scattering in their presence. We propose an effective Hamiltonian governing how dyon excitations respond to fermion scattering in terms of a time-dependent vacuum angle and outline open questions remaining in its microscopic derivation.