Magnetic-monopole resummation justifies perturbatively calculated collider production cross sections

TL;DR

This paper develops a non-perturbative resummation scheme for magnetic monopoles, justifying collider production cross sections and providing a framework to constrain monopole parameters experimentally.

Contribution

It introduces a Dyson-Schwinger inspired resummation method for magnetic monopoles within an effective field theory, establishing a formal basis for collider production calculations.

Findings

Identifies a non-perturbative fixed point in monopole theory.

Justifies the use of tree-level collider cross sections for monopole searches.

Provides a way to experimentally constrain monopole parameters.

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". 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. A self-consistent identification of the renormalized coupling of the MM to the electromagnetic photon in the fixed-point theory with the magnetic charge, compatible with the Dirac quantization condition, is made. 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 the case of elementary (structureless) 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.