Magnetic-monopole resummation justifies perturbatively calculated collider production cross sections

Abstract

A one-loop resummation scheme, inspired by Dyson-Schwinger (DS) formalism of strongly coupled quantum field theories, is applied to spin-1/2 magnetic monopoles (MMs), in the context of an effective field theory (EFT), invariant under the gauge group U(1)_em x U(1)', where U(1)' is a dual strongly coupled Abelian interaction, associated with a "dark photon". The latter leads to a MM appearing as a limiting case of a "dyon", with a tiny "electric charge", compensated by a huge wave-function renormalization of the MM, thereby leading to a finite renormalized MM-photon coupling. An ultra-violet fixed point structure is found in the resummed theory, which is purely non-perturbative due to different boundary conditions of the resummation equations, compared to the weak coupling (perturbative) case. The renormalized coupling of the MM to the electromagnetic photon in the fixed-point theory is identified with the magnetic charge, compatible with the Dirac quantization condition. This provides for the first time a formal justification of the use of tree-level Drell-Yan and photon-fusion MM production processes in collider searches, and of the corresponding cross sections and MM mass bounds thereof. The latter provide a means to constrain the resummed-EFT parameters experimentally. The DS resummation applies here primarily to elementary MMs. However, this approach may also be applied to the last stage (collapse) of the formation of composite MM pairs at colliders, in case they behave as quantum excitations, with their core radius comparable to the Compton wavelength, thereby avoiding the extreme suppression of their production.