Weak-U(1) x Strong-U(1) Effective Gauge Field Theories and electron-monopole scattering

We present a gauge and Lorentz invariant model for the scattering of matter off magnetic poles, which justifies the presence of velocity-dependent magnetic charges as an effective description of either the behaviour of monopoles in scattering with matter or their production from matter particles at colliders. Hence, in such an approach, perturbativity of the magnetic charge is ensured for relative low velocities of monopoles with respect to matter particles. The model employs a ${\rm U(1)}_{\rm weak} \times {\rm U(1)}_{\rm strong}$ effective gauge field theory under which electrons and monopoles (assumed to be fermions) are appropriately charged. The non-perturbative quantum effects of the strongly coupled sector of the theory lead to dressed effective couplings of the monopole/dyon with the electromagnetic photon, due to non-trivial wave-function renormalization effects. For slowly-moving monopole/dyons, such effects lead to weak coupling, thus turning the bare non-perturbative magnetic charge, which is large due to the Dirac/Schwinger quantization rule, into a perturbative effective, velocity-("$\beta$")-dependent magnetic coupling. Our work thus offers formal support to previous conjectural studies, employing effective U(1)-electromagnetic gauge field theories for the description of monopole production from Standard Model matter, which are used in contemporary collider searches of such objects. This work necessarily pertains to composite monopoles, as seems to be the case of all known monopoles so far, that are solutions of specific particle physics models. This is a consequence of the fact that the wave-function renormalization of the (slowly-moving) monopole fermion turns out to violate unitarity bounds that would characterise asymptotic elementary particle states.