Construction of a Model of Monopolium and its Search via Multi-Photon Channels at LHC

A model of monopolium is constructed based on an electromagnetic dual formulation of Zwanziger and lattice gauge theory. To cope with the strong coupling nature of the magnetic charge, for which the monopole is confined, $ U(1) $ lattice gauge theory is applied. The monopole is assumed to have a finite-sized inner structure based on a 't Hooft-Polyakov like solution in which the magnetic charge is uniformly distributed on the surface of a sphere. The monopole and antimonopole potential becomes linear plus Coulomb outside the sphere and is constant inside. Numerical estimation gives two kinds of solutions: One which has a small binding energy, and hence the para-($ J=0 $) and ortho-($ J=1 $) monopoliums have degenerate masses. For the parameter choices considered, they both have $ \mathcal{O}(1-10) $ TeV masses and are very short-lived. The other solution has a small monopole mass and large binding energy, with an illustrative example of parameter choices giving a 750 GeV para-monopolium and 1.4 TeV ortho-monopolium. The production rate of the former is one order of magnitude smaller than the announced enhancement, but they may be the target of future LHC searches and the 100 TeV colliders.