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In this paper we study the scattering of massive fermions off of smooth,spherically symmetric monopoles in $4d$ $SU(2)$ gauge theory. We propose acomplete physical picture of the monopole-fermion interaction which encompassesall angular momentum modes. We show that as an in-going fermion scatters off amonopole, it excites trapped $W$-bosons in the monopole core by a version ofthe Witten effect so that the monopole can accrue charge and transform into adyon at parametrically low energies. The imparted electric charge is thenprotected from decay by an emergent $\mathbb{Z}_N$ generalized global symmetry,creating a stable dyon. At sufficiently low energies, the scattered fermion canbe trapped by the dyon's electrostatic potential, forming a bound state, whichcan decay into spherically symmetric fermion modes subject to the preserved$\mathbb{Z}_N$ global symmetry. We propose that monopole-fermion scattering canbe described in this way without needing to add ``new'' states to the Hilbertspace, thereby eliminating a long standing confusion in the Callan Rubakoveffect.

A New Solution to the Callan Rubakov Effect