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". 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.

Figures (13)

• Figure 1: Drell-Yan (left), photon fusion (center) and one-loop (right) processes for the production of structureless MMs, $\mathcal{M}$, of spin-1/2 at colliders. Wavy lines denote electrodynamical photons, $\gamma$. Straight black lines with arrows denote the scattered (anti)quarks, while red continuous arrow lines denote the (anti)monopoles. The shaded blob denotes the dressed coupling $Z^\star e_A$ due to quantum corrections induced by the strongly coupled dual photon, which, in the EFT of Alexandre:2019iub, couples only to monopoles. The fixed-point wavefunction renormalization $Z^\star$ is given in \ref{['fp']}.
• Figure 2: The MM mass \ref{['MMmasseps']} (in units of $\Lambda$, as a function of $\varepsilon^{1/2}\, e_B$, where $\varepsilon$ is given in \ref{['epsvseA']}, and is proportional to $e_A/n$. Qualitatively, the dependence on the strong coupling is similar to the case of fermion HECOs Alexandre:2023qjo, when their mass is plotted against the high electric charge in that case.
• Figure 3: Monopole mass $M^*$\ref{['MMmasseps']} versus parameters $e_A$ and $e_B$ for $\Lambda = 14~\hbox{TeV}\xspace$ and for different magnetic charges: $g_m = 2g_{\mathrm{D}}\xspace$ (left) and $g_m = 10g_{\mathrm{D}}\xspace$ (right).
• Figure 4: Monopole mass $M^*$\ref{['MMmasseps']} as a function of the mass scale $\Lambda$ and the product $e_Ae_B^2$ for different magnetic charges: $g_m = 2g_{\mathrm{D}}\xspace$ (left) and $g_m = 10g_{\mathrm{D}}\xspace$ (right).
• Figure 5: Tree-level Feynman Diagram relevant for the formation of a composite electroweak magnetic-monopole ($\mathbf M$)-antimonopole ($\mathbf{\overline{M}}$) pair from elementary SM particles, according to Drukier:1981fq. The diagram can represent the DY process or the appropriate part of the PF process. Continuous lines with arrows denote SM fermions (quarks or leptons, depending on the collider). Wavy lines denote $\gamma/Z^0$ combinations, short-dash lines $W^\pm$ SU(2) gauge bosons, while long-dash lines denote charged Higgs excitations $h^\pm$, which play a role in the presence of MMs, since the gauge symmetry is unbroken near the MM centre. The "Collapse stage" denotes the region at which $2/\alpha$ coherent-mode quanta of $W^\pm$ and $h^\pm$ collapse to form $\mathbf{M}$ or $\mathbf{\overline{M}}$.